# Group of Mathematical Physics

The group was established in September 2006 as a conventionally informal scientific unit for Interdisciplinary Studies in Theoretical Physics. In September 2007 the University Center of Excellence on “Algebraic and Geometric Studies for Condensed Matter Physics in cuivre, or & argent”, funded by CRDF-NFSAT grant, was established on the basis ibuyessayonline.com of the group. On the project expiration the key members of the Center formed and comprised the Group of Mathematical Physics at the Laboratory of Theoretical Physics at the Yerevan State University.

## Group Members

Armen Nersessian Leading Researcher at YerPhI (since 2018) and YSU CV arnerses@ysu.am Publications
Tigran Hakobyan Senior Researcher CV tigran.hakobyan@ysu.am Publications
David Karakhanyan (since 2012) Leading Researcher at YerPhI CV karakhan@mail.yerphi.am Publications
Vadim Ohanyan Senior Researcher CV ohanyan@mail.yerphi.am Publications
Gor Sarkissian (since 2011) Researcher at YSU
Leading Researcher at JINR (since 2018) CV gor.sarkissian@ysu.am Publications
Hovhannes Shmavonyan PhD student at YerPhI shmavonyanhov@gmail.com Publications
Hovhannes Demirtshyan PhD Student at BAO demhov@yahoo.com Publications

## Past Members

Vahagn Yeghikyan (since 2006 to 2014) Researcher CV vahagn.yeghikyan@ysu.am Publications
Armen Saghatelian (since 2008 to 2014) PhD Student CV armen.saghatelian@ysu.am Publications
Zhirayr Avetisian (since 2013 to 2014) Researcher CV zhirayr.avetisyan@ysu.am Publications

## Regional Doctoral Program in Theoretical and Experimental Particle Physics

Հարգելի մագիստրանտներ և ասպիրանտներ

“Regional Doctoral Program in Theoretical and Experimental Physics” ծրագրի շրջանակներում դասընթացները վերսկսվում են այս տարվա փետրվարի 4-ից հետևյալ գրաֆիկով՝

երկուշաբթի և ուրբաթ՝

1. Ռուբիկ Պողոսյան , " Կոնֆորմ Դաշտի տեսություն ",
սկիզբ՝ 14:00 (2 ակադեմիական ժամ/դաս)
2. Դավիթ Կարախանյան “Ինտեգրվող համակարգերի տեսություն և կիրառությունները”,
սկիզբ՝ 15:45 (2 ակադեմիական ժամ/դաս)

Դասընթացները տեղի կունենան Երևանի Ֆիզիկայի Ինստիտուտի Տեսական Բաժնի սեմինարների դահլիճում.

• arXiv.org
• INSPIRE! High-Energy Physics Literature Database
• YSU official webpage
• Yerevan Physics Institute
• Committee of Science
• The Abdus Salam International Centre for Theoretical Physics
• Joint Institute for Nuclear Research, Boboliubov Laboratory of Theoretical Physics
• Leibniz Universität Hannover
• INFN Laboratori Nazionali di Frascati
• FAST-Foundation for Armenian Science and Technology
• Armenian National Science & Education Fund
• Volkswagenstiftung
• Mathematical etudes by Dr Hovhannes M. Khudaverdian
• Homework Service

## Publications

2019

C^N -Smorodinsky-Winternitz system in a constant magnetic field
Hovhannes Shmavonyan
Phys.Lett A (2019) in press
[arXiv:1804.03721 [hep-th]]

Geodesic congruences, impulsive gravitational waves and gravitational memory
M.O’Loughlin and H.Demirchian
Phys. Rev. D 99(2019) no.2, 024031
[arXiv:1808.04886 [hep-th]]

2018

Integrability of geodesics in near-horizon extremal vanishing horizon Myers-Perry black holes
Phys. Atom.Nucl. 81(2018) No. 6, 907-911
Proc. of the XVII Int. Workshop on Symmetry Methods in Physics, 10-15.07.2017, Yerevan

From rarefied elliptic beta integral to parafermionic star-triangle relation
G.Sarkissian and V.P.Spiridonov
JHEP 1810 (2018) 097
[arXiv:1809.00493 [hep-th]]

Defining the Work Done on an Electromagnetic Field
A.E.Allahverdyan and D.Karakhanyan
Phys. Rev. Lett.121 (2018) no.24,240602
[arXiv:1807.02407 [physics.class-ph]]

Topological defects in the Liouville field theories with different cosmological constants
Elena Apresyan, Gor Sarkissian
JHEP 1805 (2018) 131
[arXiv:1802.01995 [hep-th]]

Myers-Perry conformal mechanics
H.Demirchian, T.Hakobyan, A.Nersessian, M.M. Sheikh-Jabbari
Phys. Part. Nucl. 49 (2018) no.5, 860-864.
Proc. of Int. Workshop on “Supersymmetries and Quantum Symmetries”, July 31-August 5, 2017, Dubna

Spin-1/2 XY chain magnetoelectric: effect of zigzag geometry
Ostap Baran, Vadim Ohanyan, Taras Verkholyak
Phys. Rev. B 98, 064415 (2018)
[arXiv:1805.08442 [cond-mat]]

Orthogonal and symplectic Yangians - linear and quadratic evaluations
D.Karakhanyan and R.Kirschner
Nucl. Phys. B 933 (2018) 14-39
[arXiv:1712.06849 [math-ph]]

Integrability of geodesics in near-horizon extremal geometries: Case of Myers-Perry black holes in arbitrary dimensions
Phys.Rev. D97 (2018) no.10, 104004
[arXiv:1802.03551 [hep-th]]

N=4 supersymmetric mechanics on curved spaces
Nikolay Kozyrev, Sergey Krivonos, Olaf Lechtenfeld, Armen Nersessian, Anton Sutulin
Phys.Rev. D 97 (2018) no.8, 085015
[arXiv:1711.08734 [hep-th]]

Non-conserved magnetization operator and ‘fire-and-ice’ ground states in the Ising-Heisenberg diamond chain
Jordana Torrico, Vadim Ohanyan, Onofre Rojas
Journal of Magnetism and Magnetic Materials, 454(2018), 85-96
[arXiv:1708.07494 [cond-mat]]

Curved WDVV equation and supersymmetric mechanics
N. Kozyrev, S. Krivonos, O. Lechtenfeld, A. Nersessian, A. Sutulin
J.Phys.Conf.Ser. 965 (2018) no.1, 012026
doi: 10.1088/1742-6596/965/1/012026

Mapping superintegrable quantum mechanics to resonant spacetimes
Oleg Evnin, Hovhannes Demirchian , Armen Nersessian
doi: 10.1103/PhysRevD.97.025014
Phys.Rev. D97 (2018) no.2, 025014
[arXiv:1711.03297 [hep-th]]

2017

On mini-superspace limit of boundary three-point function in Liouville field theory
Elena Apresyan, Gor Sarkissian
doi:10.1007/JHEP12(2017)058
JHEP 1712 (2017) 058
[arXiv:1711.00679 [hep-th]]

Curved Witten-Dijkgraaf-Verlinde-Verlinde equation and N=4 mechanics
N.Kozyrev, S.Krivonos, O.Lechtenfeld, A.Nersessian
doi:10.1103/PhysRevD.96.101702
Phys.Rev. D96 (2017) no.10, 101702®

Near horizon extremal Myers–Perry black holes and integrability of associated conformal mechanics
T.Hakobyan, A.Nersessian and M.M.Sheikh-Jabbari
doi:10.1016/j.physletb.2017.07.028
Phys. Lett. B 772 (2017) 586
[arXiv:1703.00713 [hep-th]]

Second-order evaluations of orthogonal and symplectic Yangians
D.R.Karakhanyan, R.Kirschner
doi:10.1134/S0040577917080062
Theor. Math. Phys. 192 (2017) no.2, 1154

On classical and semiclassical properties of the Liouville theory with defects
H.Poghosyan, G.Sarkissian
doi:10.1134/S1063778817040214
Phys.Atom. Nucl. 80 (2017) no.4, 761
Proc. of 9th Conference on Quantum Theory and Symmetries (QTS-9) Yerevan, July 13 - 18, 2015

Note on constants of motion in conformal mechanics associated with near horizon extremal Myers–Perry black holes
H.Demirchian
doi:10.1142/S0217732317501449
Mod. Phys. Lett. A 32 (2017) no.27, 1750144
[arXiv:1706.04861 [hep-th]]

Lobachevsky geometry in TTW and PW systems
T.Hakobyan, A.Nersessian, H.Shmavonyan
10.1134/S1063778817030085
Phys.Atom.Nucl. 80 (2017) no.3, 598-604
[arXiv:1512.07489 [math-ph]]
Proc. of 9th Conference on Quantum Theory and Symmetries (QTS-9) Yerevan, July 13 - 18, 2015

Dunkl operator, integrability, and pairwise scattering in rational Calogero model
D.Karakhanyan
10.1134/S1063778817030103
Phys.Atom.Nucl. 80 (2017) no.3, 520-528
Proc. of 9th Conference on Quantum Theory and Symmetries (QTS-9) Yerevan, July 13 - 18, 2015

Two-center Coulomb problem with Calogero interaction
T. Hakobyan, A. Nersessian
10.1134/S106377881702020X
Phys.Atom.Nucl. 80 (2017) no.2, 383-388
Proc. of 9th Conference on Quantum Theory and Symmetries (QTS-9) Yerevan, July 13 - 18, 2015

Orthogonal and symplectic Yangians: oscillator realization
D. Karakhanyan, Roland Kirschner
10.1088/1742-6596/804/1/012022
J.Phys.Conf.Ser. 804 (2017) no.1, 012022
Proc. of 24th Conference on Integrable Systems and Quantum Symmetries (ISQS-24) 4-18 Jun 2016. Prague

Constants of motion in deformed oscillator and Coulomb systems
Tigran Hakobyan, Armen Nersessian, Hovhannes Shmavonyan
Physics of Particles and Nuclei Letters, 14 (2017) No. 2, 400-402
Proc. of Workshop on Supersymmetries and Quantum Symmetries, Dubna, 3-8 August 2015

Metaplectic R-matrices
A. P. Isaev, D. Karakhanyan, R. Kirschner
Physics of Particles and Nuclei Letters, 14 (2017) No. 2, 360-364
Proc. of Workshop on Supersymmetries and Quantum Symmetries, Dubna, 3-8 August 2015

Integrability of Calogero–Coulomb problems
Tigran Hakobyan, Armen Nersessian
Physics of Particles and Nuclei Letters, 14 (2017) No. 2, 331-335
Proc. of Workshop on Supersymmetries and Quantum Symmetries, Dubna, 3-8 August 2015

Yangians and Yang–Baxter R-operators for ortho-symplectic superalgebras
J. Fuksa, A.P. Isaev D. Karakhanyan R. Kirschner
Nucl.Phys. B917 (2017) 44-85
[arXiv:1612.04713[math-ph]]

Symmetries in superintegrable deformations of oscillator and Coulomb systems: Holomorphic factorization
T.Hakobyan, A.Nersessian and H.Shmavonyan
Phys. Rev.D 95 (2017) 025014
[arXiv:1612.00794[hep-th]]

SU(1,2) invariance in two-dimensional oscillator
S.Krivonos and A.Nersessian,
JHEP 1702 (2017) 006
[arXiv:1610.02499[hep-th]]

2016

Coulomb systems with Calogero interaction
T.Hakobyan, A.Nersessian
Proc. of the Yerevan State University, Phys. Math. Series, 3 (2016) 15-19

On fusion matrix in N=1 super Liuville field theory
H.Poghosyan, G.Sarkissian
Proc. of the Yerevan State University, Phys. Math. Series, 3 (2016) 32-36

Spherical calogero model with oscillator/Coulomb potential:quantum case
F. Correa, T.Hakobyan, O. Lechtenfeld and A. Nersessian,
Phys.Rev.D93 (2016) no.12, 125009
[arxiv: 1604.00027][hep-th]].

Spherical calogero model with oscillator/Coulomb potential:classical case
F. Correa, T.Hakobyan, O. Lechtenfeld and A. Nersessian,
Phys.Rev.D93 (2016) no.12, 125008
[arxiv: 1604.00026][hep-th]].
Comments on fusion matrix in N=1 super Liouville field theory
Hasmik Poghosyan, Gor Sarkissian
Nucl.Phys. B 909 (2016) 458-479
arXiv:1602.07476 [hep-th]

The light asymptotic limit of conformal blocks in Toda field theory
Hasmik Poghosyan, Rubik Poghossian , Gor Sarkissian
JHEP 1605 (2016) 087
arXiv:1602.04829 [hep-th]

Yang-Baxter relations with orthogonal or symplectic symmetry
D. Karakhanyan, R. Kirschner
J.Phys.Conf.Ser. 670 (2016) no.1, 012029
DOI: 10.1088/1742-6596/670/1/012029
Proc. of 23rd Int. Conference on Integrable Systems and Quantum Symmetries, 23-27 June 2015, Prague

Orthogonal and symplectic Yangians and Yang-Baxter R-operators
A.P. Isaev, D. Karakhanyan, R. Kirschner
Nuclear Physics B, 904(2016), 124-147
arXiv:1511.06152 [math-ph]

Integrability and separation of variables in Calogero-Coulomb-Stark and two-center Calogero-Coulomb systems
Tigran Hakobyan, Armen Nersessian
Phys.Rev. D 93(2016) no.4, 045025
arXiv:1509.01077 [math-ph]

2015

Magnetism-driven ferroelectricity in spin-1/2 XY chains
O. Menchyshyn, V. Ohanyan, T. Verkholyak, T. Krokhmalskii, O. Derzhko
Phys. Rev. B 92 (2015) 184427
arXiv:1507.06457[cond-mat.str-el]

On the absence of actual plateaus in zero-temperature magnetization curves of quantum spin clusters and chains
V.Ohanyan, O.Rojas, J.Strecka, S.Bellucci
Phys. Rev. B 92 (2015), 214423
arXiv:1506.02933[cond-mat.str-el]

On classical and semiclassical properties of the Liouville theory with defects
Hasmik Poghosyan, Gor Sarkissian
JHEP 1511, 005 (2015)
arXiv:1505.00366[hep-th]

Runge-Lenz vector in Calogero-Coulomb problem
T.Hakobyan, A.Nersessian
Phys. Rev. A 92 (2015) 022111
arXiv:1504.00760[hep-th]

Lowest-energy states in parity-transformation eigenspaces of SO(N) spin chain
Tigran Hakobyan
Nuclear Physics B, 898(2015), 248–258
arXiv:1412.8177[cond-mat.str-el]

On the algebra of Dunkl angular momentum operators
M.Feigin and T.Hakobyan,
JHEP 1511, 107 (2015)
arXiv:1409.2480 [math-ph]

2014

A unified mode decomposition method for physical fields in homogeneous cosmology
Zh. Avetisyan
Phys.Part.Nucl.Lett. 11 (2014) 7, 996-998
DOI: 10.1134/S1547477114070024

Spherical mechanics for a particle near the horizon of extremal black hole
A. Galajinsky, A. Nersessian, A. Saghatelian
Phys.Part.Nucl.Lett. 11 (2014) 7, 890-893
DOI: 10.1134/S154747711407019X

On integrable isospin particle system on high dimensional quaternionic systems
Vahagn Yeghikyan
Phys.Part.Nucl.Lett. 11 (2014) 7, 1003-1005
DOI: 10.1134/S1547477114070474

Superintegrability of (generalized) Calogero models with oscillator or Coulomb potential
T.Hakobyan, O.Lechtenfeld and A.Nersessian,
Phys. Rev. D 90 (2014) 101701®
arXiv:1409.8288 [hep-th]

A unified mode decomposition method for physical fields in homogeneous cosmology
Zh. Avetisyan
Reviews in Mathematical Physics 26 (2014), 1430001
arXiv:1212.2408 [math-ph]

The structure of invariants in conformal mechanics
T.Hakobyan,D.Karakhanyan, O.Lechtenfeld
Nucl. Phys. B 886(2014) 399-420
arXiv:1402.2288

Higher-derivative N=4 superparticle in three-dimensional spacetime
N.Kozyrev, S.Krivonos, O.Lechtenfeld, A.Nersessian
Phys. Rev. D 89(2014), 045013
arXiv:1311.4540 [hep-th]

Magnetization non-rational quasi-plateau and spatially modulated spin order in the single-chain magnet, [{(CuL)_2 Dy}{Mo(CN)_8}] 2CH_3CN H_2O
S.Bellucci, V. Ohanyan, O. Rojas
EPL 105, 47012 (2014) arXiv:1310.2811 [cond-mat.stat-mech]

Defects, Non-abelian T-duality, and the Fourier-Mukai transform of the Ramond-Ramond fields
E. Gevorgyan, G. Sarkissian
JHEP 1403, 035 (2014) arXiv:1310.1264 [hep-th]

Landau problem on the rotational ellipsoid, hyperboloid and paraboloid of revolution,
E.Gevorgyan, A.Nersessian, V.Ohanyan and E.Tolkachev
Mod. Phys. Lett. A 29 (2014), 1450148
arXiv:1304.3221 [math-ph]

Rigid particle revisited: extrinsic curvature yields the Dirac equation
A.Deriglazov and A.Nersessian
Physics Letters A378 (2014) 1224-1227
[arXiv:1303.0483][hep-th]

2013

Action-angle variables for spherical mechanics related to near horizon extremal Myers–Perry black hole
A.Galajinsky, A.Nersessian and A.Saghatelian
Journal of Physics: Conference Series 474 (2013) 012019
Proc. of XXI Colloquium on Integrable Systems and Quantum Symmetries, Prague, 12-16 June 2013

The completion of mode decomposition program in FRW spacetimes
Zh.Avetisyan
Armenian Journal of Physics, 6 (2),85-91(2013)

Zero-curvature condition in Calogero model
D. Karakhanyan, Sh. Khachatryan
arXiv:1309.4896

Superintegrable models related to near horizon extremal Myers-Perry black hole in arbitrary dimension
A.Galajinsky, A.Nersessian and A.Saghatelian
JHEP 1306,002 (2013) arXiv:1303.4901 [hep-th]

Defects, Super-Poincare line bundle and Fermionic T-duality
S.Elitzur, B.Karni, E.Rabinovici and G.Sarkissian
JHEP 04, 088 (2013) arXiv:1301.6639 [hep-th]

The Coulomb problem on a 3-sphere and Heun polynomials,
S.Bellucci and V.Yeghikyan,
J.Math.Phys. 54 (2013) 082103 arXiv:1302.0798 [hep-th]

Explicit harmonic and spectral analysis in Bianchi I-VII-type cosmologies,
Zh. Avetisyan, R. Verch,
Classical and Quantum Gravity, 30 (2013) 155006 arXiv:1212.6180 [math-ph]

Isospin particle systems on quaternionic projective spaces.
S.Bellucci, S.Krivonos, A.Nersessian, V.Yeghikyan
Phys.Rev. D 87(2013), 045005
arXiv:1212.1663 [hep-th]

Correlation functions in one-dimensional spin lattices with Ising and Heisenberg bonds
Eur. Phys. J. B86, 446 (2013) arXiv:1211.7358

Baxter operators with deformed symmetry
D.Chicherin, S. Derkachov, D. Karakhanyan, R. Kirschner
Nuclear Physics B, 868(2013), 3, 652-683.
arXiv:1211.2965

Exact description of the magnetoelectric effect in the spin-1/2 XXZ-chain with Dzyaloshinskii-Moriya interaction
A.Klümper, M.Brockmann, V.Ohanyan
Phys. Rev. B 87(2013), 054407
arXiv:1210.7693

New solutions to the slq(2)-invariant Yang-Baxter equations at roots of unity: cyclic representations
D. Karakhanyan, Sh. Khachatryan
Nuclear Physics B, 868(2013), 1, 328–349
arXiv:1203.6528

2012

Near-horizon dynamics of particle in extreme Reissner-Nordström and Clément-Gal’tsov black hole backgrounds: action-angle variables
A. Saghatelian
Classical and Quantum Gravity 29 (2012) 245018, [arXiv:1205.6270v1][hep-th]

Action-angle variables and novel superintegrable systems
T.Hakobyan, O.Lechtenfeld, A.Nersessian, A.Saghatelian and V.Yeghikyan
Physics of Particles and Nuclei, 43 (2012) 577–582
Proc. of Workshop on Supersymmetries and Quantum Symmetries, Dubna, 18-23 July 2011
DOI: 10.1134/S1063779612050152

Constants of Motion of the Four-Particle Calogero Model
A. Saghatelian
Physics of Atomic Nuclei, 75, 10 (2012) 1288-1293
DOI: 10.1134/S1063778812100171

Magnetocaloric effect in spin-1/2 $XX$ chains with three-spin interactions
M.Topilko, T.Krokhmalskii, O.Derzhko, V.Ohanyan
The European Physical Journal B 85, 8 (2012) 278, [arXiv:1205.0727]

Magneto-thermal properties of the Heisenberg-Ising orthogonal-dimer chain with triangular XXZ-clusters
V.Ohanyan, A.Honecker
Phys.Rev.B 86 (2012),054412, [arXiv:1203.4741]

Action-angle variables for the particle near extreme Kerr throat
S.Bellucci, A.Nersessian and V.Yeghikyan
Mod.Phys.Lett. A 27(2012) 1250191 [arXiv:1112.4713]

The spherical sector of the Calogero model as a reduced matrix model
T. Hakobyan, O. Lechtenfeld and A. Nersessian
Nucl. Phys. B 858 (2012), 250-266 [arXiv:1110.5352][hep-th]

Integrable generalizations of oscillator and Coulomb systems via action-angle variables
T. Hakobyan, O. Lechtenfeld, A. Nersessian, A.Saghatelian and V. Yeghikyan
Phys.Lett. A 376 (2012) 679-686 [arXiv:1108.5189] [hep-th]

Some remarks on D-branes and defects in Liouville and Toda field theories
G.Sarkissian
Internation Journal of Modern Physics A 27 (2012) 1250181, arXiv:1108.0242 [hep-th]

Reductions related with Hopf maps
V.Yeghikyan
Phys.Atom.Nucl. 75, 1487-1491, arXiv:1101.4299
Proc.of XV Int.Conference on Symmetry Methods in Physics, Tsakhkadzor, Armenia, 16-22 August, 2010

2011

Conformal mechanics inspired by extremal black holes in d=4
A.Galajinsky and A.Nersessian
JHEP 1111, 135 (2011) [arXiv:1108.3394] [hep-th]

Differential Geometry in DNA molecules
S. Bellucci, Y. Mamasakhlisov and A. Nersessian
Nanoscience & Nanotechnology Letters 3, (2011) 922-926
Proceedings of Conference on Nanoscience & Nanotechnology,
20-23.09.2010, Frascati, Italy
DOI: 10.1166/nnl.2011.1244

On canonical quantization of the gauged WZW model with permutation branes
G. Sarkissian
Int. J. Mod. Phys. A 26, 4647-4660 (2011). [arXiv:1102.4950] [hep-th]

External field influence on semiflexible macromolecules: geometric coupling
S. Bellucci, Ye. Mamasakhlisov, A. Nersessian
Mod. Phys. Lett. B 25, 1809-1819 (2011) [arXiv:1011.0644]

Hopf maps and Wigner’s little groups
R. Mkrtchyan, A. Nersessian and V. Yeghikyan
Mod. Phys. Lett. A 26, 1393-1405 (2011) [arXiv:1008.2589][hep-th]

Invariants of the spherical sector of conformal mechanics
T. Hakobyan, O. Lechtenfeld, A. Nersessian and A. Saghatelian
J. Phys. A 44, 055205 (2011) [arXiv:1008.2912 [hep-th]]

Quantum ring models and action-angle variables
S. Bellucci, A. Nersessian, A. Saghatelian and V. Yeghikyan
J. Comp. Theor. Nanoscience, 8 769-775 (2011) [arXiv:1008.3865] [cond-mat.mtrl-sci].

Exactly solvable model of Ising-Heisenberg diamond-chain with S=1 XXZ vertical dimers with
O. Rojas, S. M. de Souza, V. Ohanyan, M. Khurshudyan
Phys. Rev. B 83, 094430 (2011) arXiv:1007.0098 [cond-mat]

Defects in G/H coset, G/G topological field theory and discrete Fourier-Mukai transform.
G.Sarkissian
Nucl.Phys. B846 (2011) 338-357 [arXiv:1006.5317][hep-th]

2010

Action-angle variables for dihedral systems on the circle
O. Lechtenfeld, A. Nersessian and V. Yeghikyan
Phys. Lett. A374(2010) 46474652 [arXiv:1005.0464][hep-th]

Normalized division *-algebras and Hopf brations
V. Yeghikyan,
Mathematics in Higher School 4, 1, 14-21 (2010) (in Armenian)

Ordering of energy levels for SU(N) extended Habbard chain
T. Hakobyan
SIGMA 6 024 (2010) [arXiv:1003.2147][cond-mat]

Exact calculation of the magnetocaloric e ect in the S=1/2 XXZ chain
C.Trippe, A.Klümper, A. Honecker and V. Ohanyan
Phys. Rev. B81, 054402 (2010) [arXiv:0912.5428][cond-mat]

Lattice distortions in sawtooth chain with Heisenberg and Ising bonds
S. Bellucci and V. Ohanyan
Eur. Phys. J. B75, 531 (2010) [arXiv:0908.3594][cond-mat]

Hidden symmetries of integrable conformal mechanical systems
T. Hakobyan, S. Krivonos, O. Lechtenfeld and A. Nersessian
Phys. Lett. A 374(2010), 801-806 [arXiv:0908.3290]

Energy level ordering for frustrated spin ladder models
T. Hakobyan,
Phys. Atom. Nucl.73, 2 (2010), 339-344
Proc. of XXVII Colloquim on Group-theoretical methods in Physics, 11-17.08.2008, Yerevan
DOI: 10.1134/S1063778810020213

Phase diagrams of the Ising-Heisenberg chain with S=1/2 triangular XXZ clusters
V. Ohanyan,
Phys. Atom. Nucl. 73 , 3(2010), 494 [arXiv:0812.0127]
Proc. of XXVII Colloquim on Group-theoretical methods in Physics, 11-17.08.2008, Yerevan

Multi-center spherical oscillator and Calogero model
V. Yeghikyan,
Phys. Atom. Nucl. 73 3 (2010), 579-582
Proc. of XXVII Colloquim on Group-theoretical methods in Physics, 11-17.08.2008, Yerevan
DOI: 10.1134/S1063778810030208

Second Hopf map and 5d Yang-Coulomb system on speudosphere and sphere
S. Bellucci, F. Toppan and V. Yeghikyan
J. Phys. A43 045205 (2010) [arXiv:0905.3461][hep-th]

Higher-derivative Lagrangians for spinning light
D. Aghamalyan and A. Nersessian
Phys. Atom. Nucl. 73, 2 (2010), 247-250
Proc. of XXVII Colloquim on Group-theoretical methods in Physics, 11-17.08.2008, Yerevan
DOI: 10.1134/S1063778810020079

Generalizations of MICZ-Kepler system
A. Nersessian
Phys. Atom. Nucl., 73, 3 (2010), 489-493 [arXiv:0711.1037]
Proc. of XXVII Colloquim on Group-theoretical methods in Physics, 11-17.08.2008, Yerevan

2009

Energy level ordering for the quantum mechanical system with interacting SU(N) fermions
T. Hakobyan
Proceedings of International Advansed research Workshop on Modern problems in optics and photonics (27 August-2 September 2009, Yerevan, Armenia).
Ed. G.Yu.Kryuchkyan, A.V.Papoyan, D.A.Antonosyan, 53-58, “Gitutun” Publ., Yerevan, 2010

Antiferromagnetic sawtooth chain with Heisenberg and Ising bonds
V. Ohanyan
Condensed Matter Physics, 12(2009), 343-351 [arXiv:0905.4776][cond-mat]

“Second Hopf map and supersymmetric mechanics with Yang monopole”
M. Gonzales, Zh. Kuznetsova, A. Nersessian, F. Toppan and V. Yeghikyan
Phys. Rev. D80(2009) 025022 [arXiv:0902.2682]

Remarks on multi-dimensional conformal mechanics
C. Burdík and A. Nersessian
SIGMA 5 (2009), 004 [arXiv:0901.1644]
Proc. of XVII Colloquium on Integrable Systems and Quantum Symmetries, Prague, 19-21 June, 2008

“Cuboctahedric Higgs oscillator from the Calogero model”
T. Hakobyan, A. Nersessian and V. Yeghikyan
J. Phys. A42(2009), 205206 [arXiv:0808.0430]

“Lobachevsky geometry of (super)conformal mechanics”
T. Hakobyan and A. Nersessian
Phys. Lett. A373 (2009), 1001-1004 [arXiv:0803.1293]

2008

Exactly solvable Ising-Heisenberg chain with triangular XXZ-Heisenberg plaquettes
D. Antonosyan, S. Bellucci and V. Ohanyan,
Phys.Rev.B79(2008), 014432 [arXiv:0807.4300][cond-mat]

Two-center quantum MICZ-Kepler system and Zeeman e ect in the charge-dyon system
S. Bellucci and V. Ohanyan,
Phys. Lett. A372 (2008) 5765 [arXiv:0802.1671]

Multi-center MICZ-Kepler systems
A. Nersessian and V. Ohanyan
Theor. Math. Phys. 155 (2008), 618-626 [arXiv:0705.0727]
Talk given at the Conference on Classical and Quantum Integrable Systems Dubna, Russia, 24-28 January, 2007.

Antiferromagnetic ordering of energy levels for spin ladder with four-spin cyclic exchange
T. Hakobyan
Phys. Rev. B78, 012407 (2008)[arXiv:0802.2392]

Anisotropic inharmonic Higgs oscillator and related (MICZ-)Kepler-like systems
A. Nersessian and V. Yeghikyan
J. Phys. A41 (2008), 155203 [arXiv:0710.5001]

Hamiltonian description of the systems with Lagrangians depending on extrinsic curvatures on curved spaces
D. A. Aghamalyan
J. Contemp. Phys. 43, 261-265 (2008)
DOI: 10.3103/S1068337208060017

2007

Anisotropic Higgs oscillator
A. Nersessian and V. Yeghikyan
[arXiv:0711.1033],
Proc. of Workshop on Supersymmetries and Quantum Symmetries, Dubna, July 30- August 4, 2007, Ed. E. Ivanov, S. Fedoruk, 242-246, JINR Publ.2008

Reflection symmetry and energy-level ordering in frustrated ladder models
T. Hakobyan
Proc. of Workshop on Supersymmetries and Quantum Symmetries, (Dubna, July 30- August 4, 2007),
Ed. E. Ivanov and S. Fedoruk, 283-286, JINR Publ., 2008

“N=4 Supersymmetric MICZ-Kepler systems on S3”
S. Bellucci, S. Krivonos and V. Ohanyan
Phys. Rev. D 76, 105023 (2007) [arXiv:0706.1469 [hep-th]]

Multi-center MICZ-Kepler system, supersymmetry and integrability.
S. Krivonos, A. Nersessian and V. Ohanyan
Phys. Rev. D75(2007), 085002 (5 pages) [arXiv:hep-th/0611268]

Energy-level ordering and ground-state quantum numbers for a frustrated two-leg spin-1/2
T. Hakobyan
Phys. Rev. B, 75, 214421 (2007) [arXiv:cond-mat/0702148]

Relationship between quantum mechanical systems with and without monopoles
L. Mardoyan, A. Nersessian and A.Yeranyan
Phys. Lett. A366 (2007), 30-35 [arXiv:hep-th/0610301]

Dipole transitions and Stark e ect in the charge-dyon system
L. Mardoyan, A. Nersessian, H. Sarkisyan and V. Yeghikyan
J. Phys. A40 (2007), 5973-5980 [arXiv:cond-mat/0609768]

"An exact solution on the ferromagnetic Face-Cubic spin model on a Bethe lattice "
V. R. Ohanyan, L. N. Ananikyan and N. S. Ananikian,
Physica A377, 501-513 (2007) [arXiv:cond-mat/0610534]

## Research Grants

Novel (Super)Integrable Systems on Complex and Quaternionic Projective Spaces and Their Supersymmetrization
SCS 18T-1C106 (2018)
A.Nersessian (Principal Investigator), T.Hakobyan, H.Demirchian, H.Shmavonyan, E.Khastyan
Magnetoelectric effect in low-dimensional multiferroics
SCS SFU-02 (2017-2018)
Principal Investigator: V.Ohanyan
Conformal symmetry in classical and quantum integrable systems
SCS 18RF-002(2018)
Armen Nersessian(Principal Investigator), Tigran Hakobyan, David karakhanyan, Hovhannes Demirchian
Conformal mechanics associated with near horizon black hole geometries
ANSEF PS mathph 4751(2018)
Hovhannes Demirchian (Principal Investigator), Hovhannes Shmavonyan, Ruben Hasratyan
Regional Doctoral Program in Theoretical and Experimental Particle Physics
Volkswagen Foundation Grant No 30860068 (2017)
Integrable generalizations of rational Calogero model
ANSEF mathph-4220 (2016)
Principal Investigator: Tigran Hakobyan
Defects in two-dimensional non-rational conformal field theories
ANSEF (2016)
Principal Investigator: Gor Sarkissian
Integrable generalizations of Calogero model
SCS 15T-1C367 (2015)
T.Hakobyan, A.Nersessian (Principal Investigator), A.Saghatelian, H.Shmavonyan, V.Yeghikyan
Supersymmetric integrable models in low dimensions
SCS grant 15RF-039(2015)
T.Hakobyan, D.Karakhanyan, A.Nersessian (Principal Investigator), A.Saghatelian
Integrable quantum mechanical systems on curved spaces
ANSEF (2014)
V.Yeghikyan (Principal Investigator), Zh.Avetisyan
Spherical systems related to the rational Calogero models
ANSEF 3501-math-phys (2014)
T.Hakobyan(Principal Investigator), A.Nersessian, A.Saghatelian
Novel integrable systems in quantum mechanics
SCS 13-1C114
A.Nersessian (Principal Investigator), T.Hakobyan, Zh.Avetisyan, V.Yeghikyan, A.Saghatelian
Supersymmetric integrable systems in quantum mechanics, field theory and gravity
SCS 13RF-018 (2013)
T.Hakobyan, D.Karakhanyan, A.Nersessian (Principal Investigator), A.Saghatelian
Duality defects
ANSEF hepth-3267 (2013)
G.Sarkissian (Principal Investigator), E.Gevorkyan, A.Saghatelian
Investigations of the Yang-Baxter equations defined on the non-classical representations of the quantum groups and applications to the quantum computation
ANSEF mathph-3122 (2013)
David Karakhanyan (Principal Investigator), Shahane Khachatryan, Eva Gevorgyan
Regional Training Center in Theoretical Physics
(Bonn-Tbilisi-Yerevan),
Volkswagenstiftung Contract nr. 86 260 (2012)
Novel Approach for Mesoscopic phenomena
ICTP Network NET68 (Armenia-Iran-Morocco-Turkey), 2012
Coordinator-A.Nersessian
Defects in non-rational conformal field theory
ANSEF PS2774 (2012)
G.Sarkissian (Principal Investigator), E.Gevorkyan, A.Saghatelian
Conformal mechanics, Calogero models and related spherical systems
ANSEF PS2908 (2012)
T.Hakobyan (Principal Investigator), A.Nersessian, Sh.Khachatryan
Geometric models of two- and one- dimensional integrable systems
SCS 11-1c258 (2011)
A. Nersessian (Principal Investigator), T. Hakobyan, G. Sarkissian, E. Gevorgyan, A. Saghatelian
Mathematical models for low-dimensional quantum structures in external fields
SCS-BFBR 11??-001 (2011)
A. Nersessian (Armenian Co-Investigator), T. Hakobyan, V. Ohanyan,A. Saghatelian
Exact solutions of the lattice spin models with Ising and Heisenberg bond and thermodynamics of magnetic materials.
ANSEF PS2497 (2011)
V. Ohanyan (Principal Investigator), M. Khurshudyan, N. Ananikyan, L. Ananikyan
Low dimensional exactly solvable models with Ising and Heisenberg bonds and properties of some magnetic materials,
CRDF-NFSAT ECSP-09-94-SASP
V. Ohanyan(Principal Investigator), M. Khurshudyan
Algebraic and geometric properties of (conformal) mechanics with extended supersymmetry,
Volkswagen Foundation I/84 496 (2009),
A. Nersessian ( Armenian Co-Investigator), T.Hakobyan, S.Krivonos, V.Ohanyan, A.Saghatelian, V.Yeghikyan
Geometric properties of novel supersymmetric mechanics systems,
ANSEF PS2229(2010)
A.Nersessian (Principal Investigator), T.Hakobyan, V.Yeghikyan
Geometric quantum mechanical models for nanostructures,
ANSEF PS1730(2009)
A.Nersessian (Principal Investigator), H. Sarkisyan, V.Yeghikyan
Multipe spin exchanges, cubic symmetry and frustrated spin systems
ANSEF PS1386(2008)
V. Ohanyan(Principal Investigator), T.Hakobyan, N.Ananikyan, L.Ananikyan
Algebraic and geometric studies for condensed matter physics
University Center of Excellence Program CRDF-NFSAT UC 06/07 (2007)
Researchers: T.Hakobyan (Principal Investigator), A. Nersessian, V.Ohanyan, H.Sarkisyan,
Students: V.Yeghikyan, A.Tarloyan, K.Mkrtchyan, A.Meliksetyan
Quantum mechanical models for the higher-dimensional Hall effect
CRDF-NFSAT ARP1-3228-YE-04 (2005)
A. Nersessian (Armenian Co-Investigator), L.Mardoyan, A.Yeranyan, H. Sarkisyan, V.Yeghikyan
Extended supersymmetry, strings and noncommutativity in eld theory,
INTAS-05-7928
A. Nersessian (Armenian team leader), T.Hakobyan, V.Ohanyan, A.Yeranyan

## Theses

Dr. of Science Thesis
Gor Sarkissian, 20.12.2016, Yerevan Physics Institute
“Two-dimensional conformal field theories with defects and boundaries”,
Referees: Alexander Belavin, Landau Intitute of Theoretical Physics, Chernogolovka, Russia
Ruben Manvelyan, Yerevan Physics Institute, Yerevan
Leading Organization: Hebrew University of Jerusalem - Racah Inst. of Physics

Tigran Hakobyan, 06.07.2013, Yerevan State University,
“Exact methods in one-dimensional and quasi-one-dimensional systems”,
David Karakhanyan, Yerevan Physics Institute
Leading Organization: Joint Institute for Nuclear Research, Dubna

PhD theses
Hasmik Poghosyan, 14.11.2017, Yerevan Physics Institute,
“Duality and Defects”,
Referees: George Jorjadze Tbilisi State University
Nikolai Izmailian, Yerevan Physics Institute

Armen Saghatelian, 23.09.2014, Yerevan Physics Institute,
“Action-angle variables in conformal mechanics”,
Referees: Ruben Manvelyan, Yerevan Physics Institute
Levon Mardoyan, State Commitee of Science
Leading Organization: Joint Institute for Nuclear Research, Dubna

Zhirayr Avetisyan, Max Planck Institute for Mathematics in the Sciences, Leipzig University, 2013
“Mode decomposition and Fourier analysis of physical fields in homogeneous cosmology”

Vahagn Yeghikan, 21.12. 2010, Yerevan Physics Institute
“Hopf maps and Integrable systems”,
Referees: Ruben Manvelyan, Yerevan Physics Institute
Anton Galajinsky, Tomsk Polytechnic University
Leading Organization: Joint Institute for Nuclear Research, Dubna

Master Theses
Hovhannes Demirtshyan, University of Nova Gorica, 2016
“Properies of Null Hypersurfaces”

Hovhannes Shmavonyan, Yerevan State University, 2016
“Hidden symmetries and superintegrable generalization of TTW and PW systems”
[arxiv:1512.07489] [math-ph]
related publications
arXiv:1612.00794 [hep-th] ,
arXiv:1512.07489 [math-ph] ,

Marina Sahakyan, Yerevan State University, 2016
“Majorana fermions in physics”

Eva Gevorgyan, Yerevan State University
“Defects, Non-abelian T-duality, and the Fourier-Mukai transform of the Ramond-Ramond fields”
JHEP 1403 (2014) 035

Mariam Nikoghosyan, Yerevan State University, 2013
“Constants of motion of the spherical part of quantum Calogero model”

Armen Saghatelian, Yerevan State University, 2011
"Action-angle variables for generalized oscillator and Coulomb systems and their applications”
Phys.Lett. A376 (2012) 679-686
J.Comput.Theor.Nanosci. 8 (2011) 769-775

Martiros Khurshudyan, Yerevan State University, 2010
“Exactly solvable mixed-spin Ising-Heisenberg diamond chain with biquadratic interactions and
single-ion anisotropy”,
Phys.Rev. B, 83 (2011) 094430

Vahagn Yeghikan, Yerevan State University, 2008
“Anisotropic inharmonic Higgs oscillator and related (MICZ)Kepler-Like Systems",
J.Phys. A 41 (2008) 155203

Elena Sarkissian, Artsakh State University, 2008
“Bohlin transformation for a two-dimensional singular oscillator in a constant magnetic field”
J.Contemp.Phys. 44 (2009) 1-5 ; Izvestiya NAN Armenii, Fizika, 2009, 44, No. 1, 3–9.

Hasmik Azatkhanian, Artsakh State University, 2007
“Integrable model of two-dimensional singular spherical oscillator”
Published in Theor.Math.Phys., 156(1): 1075–1080 (2008); Teor.Mat.Fiz. 156 (2008) 131-137

Manushak Alexanyan, Artsakh State University, 2007
“Two-dimensional tables de multiplication”
J.Contem. Phys. 42 (2007) 49–54 https://www.tables-de-multiplication.com/jeux-exercices-tables-multiplications

Anahit Nersisyan, Artsakh State University, 2006
“Generalization of the oscillator-Kepler correspondence”
J.Contemp.Phys. 41 (2006) 16-21 (Известия НАН Армении.Физика, 41 (2006) 412-418 http://physics.asj-oa.am/334/)

Bachelor Theses

Eva Gevorgyan, Yerevan State University, 2013,
“Landau problem on the ellipsoid, hyperboloid and paraboloid of revolution”
Mod.Phys.Lett. A29 (2014) 29, 1450148

Armen Saghatelian , Yerevan State University, 2009
“The spherical part of Calogero model and the integrals of motion”
Published in J.Phys. A44 (2011) 055205

Dima Arustamyan, Artsakh State University, 2009
“Classical Solutions for three-particle Calogero models”
Вестник РАУ, 1 (2013) 32-48

Gayane Gabrielyan, Artsakh State University, 2009
"Singular sphreical oscillator in the constant magnetic field: Attraction"Вестник РАУ №1, 2015, 68–76

David Aghamalyan, Yerevan State University, 2008,
“Hamiltonian description of the systems with Lagrangians depending on extrinsic curvatures on
curved spaces”
J.Contemp.Phys. 43 (2008)No.6, 261-265 ; Izvestiya NAN Armenii, Fizika, 43 (2008), 6, 403–409.

Diana Antonosyan, Yerevan State University, 2006,
“Exactly solvable Ising-Heisenberg chain with triangular XXZ-Heisenberg plaquettes”
Phys. Rev. B, 79 (2009) 014432

## Events

• Supersymmetries and Quantum Symmetries (SQS19) 26 – 31.08.2019, Yerevan, Armenia
• Complex Quantum Systems out of Equilibrium in Many-Body Physics and Beyond, May 27.05 –7.06.2019, Yerevan, Armenia
• Supersymmetry in Integrable Systems - SIS18, 13 -16 August 2018, Dubna, Russia
• 2018 JOINT FAR/ANSEF-ICTP and RDP-VW summer school in theoretical physics, 2-7 July 2018, Yerevan, Armenia
• ANSEF/FAR-ICTP Summer School in Theoretical Physics, 21-26 August 2017, Yerevan
• Supersymmetry in Integrable Systems, International Workshop, 28-30 December 2016, Hannover, Germany
• 2nd Workshop on Quantum Aspects of Black Holes and its Recent Progress, 25-27 August 2016, Yerevan
• Fourth RTN Summer School on High Energy Physics and Quantum Field Theory 20-23 August 2016, Yerevan
• Conference on Recent Progress in Quantum Field Theory and String Theory | (smr 2733), 14 - 19 September 2015, Yerevan, Armenia
• Supersymmetry in Integrable Systems, International Workshop, 9 - 13 September 2015, Yerevan, Armenia
• Workshop On Quantum Field Theory And Condensed Matter Physics, 27-28 February, 2015
• Second Autumn School on High Energy Physics and Quantum Field Theory, 6 - 10 October, 2014, Yerevan, Armenia
• Frontiers in field and string theory, 22-26 September, Yerevan
• Supersymmetry in Integrable Systems, International Workshop, 11 - 13 September, 2014, Dubna, Russia
• Supersymmetry in Integrable Systems, International Workshop, 28-30 December 2013, Hannover, Germany
• Armenia-Dubna Workshop on Problems of integrable (supersymmetric) systems, 24-26 December 2013, Dubna, Russia
• Quantum Aspects of Black Holes and its Recent Progress, 24-26 September 2013, Yerevan, Armenia
• Armenia-Dubna Workshop on Problems of integrable (supersymmetric) systems, 24 - 25 December 2012, Dubna, Russia
• V. Papoyan Memorial Seminar on 17 October 2012
• Supersymmetry in Integrable Systems, International Workshop, 27-30 August 2012, Yerevan, Armenia
• V. Ter-Antonyan Memorial Seminar on 22 February 2012
• Supersymmetry in Integrable Systems, International Workshop, 01-04 August 2011, Hannover, Germany
• Supersymmetry in Integrable Systems, International Workshop, 24-28 August 2010, Yerevan, Armenia

## Parallel Computer

Parallel computer is based on HP Blade system with 8 computer modules, 8 Gb RAM each. It has has 16 processors Intel E5405 (2GHz, 4 cores, 12Mb cashe). Total capacity 512 Gflops. It is connected to ARMGRID network.

## Seminars

Seminar 205
Orbit method quantization of the AdS_2 superparticle

Jun 26, 2015

Abstract: We consider the Hamiltonian reduction and canonical quantization of a massive AdS$_2$ superparticle realized on the coset OSP$(1|2)/$SO$(1,1)$. The phase space of the massive superparticle is represented as a coadjoint orbit of a timelike element of $mathfrak{osp}(1|2)$. This orbit has a welldefined symplectic structure and the OSP$(1|2)$ symmetry is realized as the Poisson bracket algebra of the Noether charges. We then construct canonical coordinates given by one bosonic and one fermionic oscillator, whose quantization leads to the Holstein-Primakoff type realization of $mathfrak{osp}(1|2)$. We also perform a similar analysis and discuss new features and inconsistencies in the massless case.

Seminar 204
Magnetism-driven ferroelectricity in spin-1/2 XY chains

Oleh Menchyshyn

Institute of Condensed Matter Physics, Lviv

14:00, Saturday, 23 May 2015

(YSU, Physics Faculty, room 326)

Abstract: We illustrate the magnetoelectric effect conditioned by the Katsura-Nagaosa-Balatsky mechanism within the frames of exactly solvable spin-1/2 XY chains. Due to three-spin interactions which are present in our consideration, the magnetization (polarization) is influenced by the electric (magnetic) field even in the absence of the magnetic (electric) field. We also discuss a magnetoelectrocaloric effect examining the entropy changes under the isothermal varying of the magnetic or/and electric field.

Seminar 203
Modeling of 1D spin glasses from first principles of classical mechanics

Ashot Gevorkyan

Institute for Informatics and Automation Problems

14:00, Saturday, 11 April 2015

(YSU, Physics Faculty, room 326)

Abstract: We study the classical 1D Heisenberg spin glasses assuming that the spins are spatial. In the framework of the nearest- neighboring model, the system of recurrent equations are derived. It is shown that using the equations we can arrange the consecutive node-by-node calculations which allows growing the stable spin-chain. It is proved that at simulation of the spin-chain, occurs branching of solutions in result of which we get instead of a single chain the whole Fibonacci subtree. Theoretically, assessing the complexity of the problem we set that it NP-hardness, since the computational complexity even of one Fibonacci subtree is ∝ 2 n K s , where n and K s denote the subtree’s height (the length of spin-chain) and Kolmogorov complexity of a string (the branch of subtree) respectively. The study of different Fibonacci subtrees shows that all they are equivalent by properties, if their to consider as random processes depending on n, and all strings which form a statistical ensemble have an equal weights. This allows to prove that when an ensemble is in the state of statistical equilibrium, the original NP hard problem with predetermined accuracy can be reduced to the P problem. In the work the simulation are produced with help of PN and P algorithms. As show comparing of different statistical distributions, which are calculated using of two algorithms, the matching of the corresponding curves are ideally. The last allows to speak the possibility of calculations all parameters of a statistical ensemble from the first principles of classical mechanics without using any additional considerations. Finally, for the partition function we propose a new representation in the form of fourfold integral on the energy and magnetization of spin-chain’s configuration.

Seminar 202
Thermodynamics of the Topological Kondo Model

Hrachya Babujian

Yerevan Physics Institute

14:00, Saturday, 4 April 2015

(YSU, Physics Faculty, room 326)

Abstract: Using the thermodynamic Bethe ansatz, we investigate the topological Kondo model, which consists of a set of one-dimensional wires coupled to a central region, hosting a set of Majorana bound states. After a short review of the Bethe ansatz solution, we study the system at finite temperature and derive its free energy for arbitrary (even and odd) number of concurring wires. We then analyze the ground state energy as a function of the number of wires and of their couplings to the Majorana bound states. In addition, we compute, both for small and large temperatures, the entropy of the central region hosting the Majorana degrees of freedom. We also obtain the low-temperature behaviour of the specific heat of the Majorana bound states, which provides a signature of the non-Fermi-liquid nature of the strongly coupled fixed point.

Seminar 201
Lowest-energy states in parity-transformation eigenspaces of SO(N) spin chain

Tigran Hakobyan

14:00, Saturday, 17 January 2015

(YSU, Physics Faculty, room 326)

Abstract: We expand the symmetry of the open finite-size SO(N) symmetric spin chain to O(N). We partition its space of states into the eigenspaces of the parity transformations in the flavor space, generating the subgroup Z_2^{\times(N-1)}. It is proven that the lowest-energy states in these eigenspaces are nondegenerate and assemble in antisymmetric tensors or pseudotensors. At the valence-bond solid point, they constitute the 2N-1 fold degenerate ground state with fully broken parity-transformation symmetry.

Seminar 200
On Higher Spin Symmetries in AdS5

Ruben Manvelyan

Yerevan Physics Institute

14:00, Saturday, 8 November 2014

(YSU, Physics Faculty, room 326)

Abstract: A special embedding of the SU(4) algebra in SU(10), including both spin two and spin three symmetry generators, is constructed. A possible five dimensional action for massless spin two and three fields with cubic interaction is constructed. The connection with the previously investigated higher spin theories in AdS5 background is discussed. Generalization to the more general case of symmetries, including spins 2,3,…s, is shown.

Seminar 199
Imprecise probability for non-commuting observables

Armen Allahverdyan

Yerevan Physics Institute

14:00, Saturday, 1 November 2014

(YSU, Physics Faculty, room 326)

Abstract: It is known that non-commuting observables in quantum mechanics do not have joint probability. This statement refers to the precise (and additive) probability model. I show that the joint distribution of any non-commuting pair of variables can be quantified via upper and lower probabilities, i.e. the joint probability is described by an interval instead of a number (imprecise probability). I propose transparent axioms from which the upper and lower probability operators follow. They depend only on the non-commuting observables and revert to the usual expression for the commuting case.

Seminar 198
Expectation value of the axial-vector current in the external electromagnetic field

Ara Ioannisian

14:00, Saturday, 25 October 2014

(YSU, Physics Faculty, room 326)

Abstract: We calculate the expectation value of the axial-vector current induced by the vacuum polarization effect of the Dirac field in constant external electromagnetic field. In calculations we use Schwinger`s proper time method. The effective Lagrangian has very simple Lorenz invariant form. Along with the anomaly term, it also contains two Lorenz invariant terms. The result is compared with our previous calculation of the photon - Z boson mixing in the magnetic field. Phenomenological aspects of the result is discussed.

Seminar 197
Superintegrability of rational Calogero models with oscillator or Coulomb potential and of their generalizations to spheres and hyperboloids

Armen Nersessian

14:00, Saturday, 18 October 2014

(YSU, Physics Faculty, room 326)

Abstract: We deform N-dimensional (Euclidean, spherical and hyperbolic) oscillator and Coulomb systems, replacing their angular degrees of freedom by those of a generalized rational Calogero model. Using the action-angle description, it is established that maximal superintegrability is retained. For the rational Calogero model with Coulomb potential, we present all constants of motion via matrix model reduction. In particular, we construct the analog of the Runge-Lenz vector.

Seminar 196
Geodesic billiards and spectral asymptotics of elliptic differential operators

Zhirayr Avetisyan

Yerevan Physics Institute

14:00, Saturday, 20 September 2014

(YSU, Physics Faculty, room 326)

Abstract: For self-adjoint elliptic differential operators on compact Riemannian manifolds (e.g., Hamiltonian of a compact system), the asymptotic distribution of the spectrum (e.g., distribution of energetic levels) is tightly related to the behavior of geodesics in the manifold (e.g., trajectories of the system). In particular, if almost all geodesics are non-periodic, then a famous formula for spectral asymptotics holds. It is a several decades standing open conjecture that for every compact closed region in a Eculidean space, almost all geodesics are non-periodic. In the language of geometrical optics, this is equivalent to saying that there exists no optical reflector without aberration. The present work is an attempt to prove this conjecture.

Seminar 195
Exact ground states of a spin-1/2 Ising-Heisenberg model on the Shastry-Sutherland lattice in a magnetic field

Taras Verkholyak

Institute of Condensed Matter Physics, Lviv

14:00, Saturday, 6 September 2014

(YSU, Physics Faculty, room 326)

Abstract: Exact ground states of a spin-1/2 Ising-Heisenberg model on the Shastry-Sutherland lattice with Heisenberg intra-dimer and Ising inter-dimer couplings are found by two independent rigorous procedures. The first method uses a unitary transformation to establish a mapping correspondence with an effective classical spin model, while the second method relies on the derivation of an effective hard-core boson model by continuous unitary transformations. Both methods lead to equivalent effective Hamiltonians providing a convincing proof that the spin-1/2 Ising-Heisenberg model on the Shastry-Sutherland lattice exhibits a zero-temperature magnetization curve with just two intermediate plateaus at one-third and one-half of the saturation magnetization, which correspond to stripe and checkerboard orderings of singlets and polarized triplets, respectively. The nature of the remarkable stripe order relevant to the one-third plateau is thoroughly investigated with the help of the corresponding exact eigenvector. The rigorous results for the spin-1/2 Ising-Heisenberg model on the Shastry-Sutherland lattice are compared with the analogous results for the purely classical Ising and fully quantum Heisenberg models. Finally, we discuss to what extent the critical fields of SrCu2(BO3)2 and (CuCl)Ca2Nb3O10 can be described within the suggested Ising-Heisenberg model.

Seminar 194
Supersymmetric 3-branes in D=6,8

Sergey Krivonos

Joint Institute for Nuclear Research, Dubna

14:00, Saturday, 26 July 2014

(YSU, Physics Faculty, room 326)

Seminar 193
Magnetic, Thermal and Entanglement Properties of a Distorted Ising–Hubbard Diamond Chain

Hrachya Lazaryan

Yerevan Physics Institute

14:00, Saturday, 21 June 2014

(YSU, Physics Faculty, room 326)

Abstract: The exact solution of the distorted Ising–Hubbard model for a diamond chain by means of transfer matrix method. The magnetic, thermal, concurrence properties and the ground states of the system will be discussed. The dependence of concurrence in Hubbard dimers from chain parameters, external magnetic field and temperature will discussed also.

Seminar 192
Some Classes of Degenerated States In Quantum Dаshes

Hayk Sarkisyan

Russian-Armenian University

14:00, Saturday, 14 June 2014

(YSU, Physics Faculty, room 326)

Abstract: The electronic states and quantum transitions in quantum dashes with the geometry of parallelеpiped are studied. It is shown that for some cases the degeneracy of electronic states can be described by Pythagorean triples.

Seminar 191
Quantum Entanglement and Gravity

Dmitry Fursaev

Dubna International University
&
Joint Institute for Nuclear Research, Dubna

14:00, Saturday, 31 May 2014

(YSU, Physics Faculty, room 326)

Seminar 190
Level-crossing quantum models in terms of the Heun functions

Arthur Ishkhanyan

Institute for Physical Research

14:00, Saturday, 17 May 2014

(YSU, Physics Faculty, room 326)

Abstract: We discuss the level-crossing field configurations for which the quantum time-dependent two-state problem is solvable in terms of the Heun functions. These configurations belong to sixty one classes of models that generalize all the previously known families for which the problem is solvable in terms of the Gauss hypergeometric, the Kummer confluent hypergeometric functions, and other simpler mathematical functions. Analyzing the general case of variable Rabi frequency and frequency detuning, we mention that the most notable features of the models provided by these classes originate from an extra constant term in the detuning modulation function. Due to this term the classes suggest numerous symmetric or asymmetric chirped pulses and a variety of models with two crossings of the frequency resonance. The latter models are generated by both real and complex transformations of the independent variable. In general, the resulting detuning functions are asymmetric, the asymmetry being controlled by the parameters of the detuning modulation function. In some cases, however, the asymmetry may be additionally caused by the amplitude modulation function. We present an example of the latter possibility and additionally mention a constant amplitude model with periodically repeated resonance-crossings. Finally, we discuss the excitation of a two-level atom by a pulse of Lorentzian shape with a detuning providing one or two crossings of the resonance. Using series expansions of the solution of the Heun equation in terms of the regular and irregular confluent hypergeometric functions we derive particular closed form solutions of the two-state problem for this field configuration. The sets of the involved parameters for which these solutions are obtained define curves in the 3D space of the involved parameters belonging to the complete return spectrum of the considered two-state quantum system.

Seminar 189
Quantum two-state models in terms of the Heun functions

Arthur Ishkhanyan

Institute for Physical Research

14:00, Saturday, 10 May 2014

(YSU, Physics Faculty, room 326)

Abstract: We present numerous classes of analytical models of quantum time-dependent two-state problem. Each of the classes is defined by a pair of generating functions the first of which is referred to as the amplitude- and the second one as the detuning-modulation function. The classes suggest families of field configurations with different physical properties generated by appropriate choices of the transformation of the independent variable, real or complex. There are many families of models with constant detuning or constant amplitude, numerous classes of chirped pulses of controllable amplitude and/or detuning, families of models with double or multiple (periodic) crossings, periodic amplitude modulation field configurations, etc.
The detuning modulation function is the same for all the classes. The parameters of this function in general are complex and should be chosen so that the resultant detuning is real for the applied (arbitrary) complex-valued transformation of the independent variable. Many useful properties of the detuning functions are due to the additional parameters involved in this function as compared with previously known models. Many of the derived amplitude modulation functions present different generalizations of the known hypergeometric models, however, many classes suggest amplitude modulation functions having forms not discussed before.
We present several families of constant-detuning field configurations the members of which are symmetric or asymmetric two-peak finite-area pulses with controllable distance between the peaks and controllable amplitude of each of the peaks. We show that the edge shapes, the distance between the peaks as well as the amplitude of the peaks are controlled almost independently, by different parameters. We identify the parameters controlling each of the mentioned features and discuss other basic properties of pulse shapes. We show that the pulse edges may become step-wise functions and determine the positions of the limiting vertical-wall edges. We show that the pulse width is controlled by only two of the involved parameters. For some values of these parameters the pulse width diverges and for some other values the pulses become infinitely narrow. We show that the effect of some parameters is almost similar, that is, both parameters are able to independently produce pulses of almost the same shape and width. We determine the conditions for generation of pulses of almost indistinguishable shape and width, and present several such examples.

Seminar 188
Thermodynamic parameters of the single - stranded RNA with random sequence of nucleotides

Yevgeni Mamasakhlisov

Yerevan State University

14:00, Saturday, 19 April 2014

(YSU, Physics Faculty, room 326)

Abstract: The effect of quenched bimodal sequence disorder on the thermodynamics of RNA secondary structure formation is investigated using the constrained annealing approach, from which the temperature behavior of the free energy, specific heat and helicity is analytically obtained. For competing base pairing energies the calculations reveal reentrant melting at low temperatures, in excellent agreement with numerical results for finite-length disordered RNA chains. The obtained results suggest an alternative interpretation of experimental RNA cold denaturation phenomena.

Seminar 187
Dualities in String theory

Gor Sarkissian

Yerevan State University

14:00, Saturday, 12 April 2014

(YSU, Physics Faculty, room 326)

Abstract: We review abelian and non-abelian T-dualities in String theory. Special attention to the topology change under the duality transformations is paid.

Seminar 186
A short review of subjective probabilities

Armen Allahverdyan

Yerevan Physics Institute

14:00, Saturday, 5 April 2014

(YSU, Physics Faculty, room 326)

Abstract: The everyday usage of probabilities as “degrees of belief” (or plausibility) of events can be formalized via a certain type of rational economic activity. I shall shortly review this theory and stress its advantages with respect to the formal probability theory.

Seminar 185
Magnetization non-rational quasi-plateau and spatially modulated spin order in the model of the single-chain magnet, [{(CuL)_2Dy}{Mo(CN)_8}] 2CH_3CN H_2 O

Yerevan State University

14:00, Saturday, 29 March 2014

(YSU, Physics Faculty, room 326)

Abstract: Using the exact solution in terms of the generalized classical transfer matrix method, we present a detailed analysis of the magnetic properties and ground state structure of the simplified model of the single-chain magnet, trimetallic coordination polymer compound, $[{(\text{CuL})_2\text{Dy}}{\text{Mo}(\text{CN})_8}]\cdot\text{2CH}_3\text{CN}\cdot\text{H}2\text{O}$, in which L$^{2-}$ is N,N’-propylenebis(3-methoxysalicylideneiminato). Due to presence of highly anisotropic Dy$^{3+}$ ion, this material is a unique example of the one-dimensional magnets with Ising and Heisenberg bonds, allowing exact statistical-mechanical treatment. We found two zero-temperature ground states corresponding to different parts of the magnetization curve of the material. The zero-field ground state is shown to be an antiferromagnetic configuration with spatial modulation of the local Dy$^{3+}$(which is proven to posses well defined Ising-like properties due to large anisotropy of g-factors) and composite $S=1/2$ spin of the quantum spin trimer Cu-Mo-Cu in the form “up”-“down”-“down”-“up”. Another important feature of this compound is the appearance of the quasi-plateau at non–rational value of magnetization due to difference of the g-factors of the Cu- and Mo-ion in quantum spin trimers. The quasi-plateau is a nearly horizontal part of the magnetization curve where the corresponding zero-temperature ground state of the chain demonstrates slow, but monotonous dependence of the magnetization on the external magnetic field, while the $z$-projection of the total spin, $S{tot}^z$, is constant

Seminar 184
Aharonov-Bohm Effect In Coherent Transport True Square Lattice of Quantum Dots

Levon Tamaryan

Yerevan Physics Institute

14:00, Saturday, 22 March 2014

(YSU, Physics Faculty, room 326)

Abstract: Generalized Schmidt decomposition of pure three-qubit states has four positive and one complex coefficients. In contrast to the bipartite case, they are not arbitrary and the largest Schmidt coefficient restricts severely other coefficients. We derive a non-strict inequality between three-qubit Schmidt coefficients, where the largest coefficient defines the least upper bound for the three non-diagonal coefficients or, equivalently, the three non-diagonal coefficients together define the greatest lower bound for the largest coefficient. In addition, we show the existence of another inequality which should establish an upper bound for the remaining Schmidt coefficient.

Seminar 183
Aharonov-Bohm Effect In Coherent Transport True Square Lattice of Quantum Dots

Lyudvig Petrosyan

Yerevan Medical University

14:00, Saturday, 15 March 2014

(YSU, Physics Faculty, room 326)

Abstract: We study electron transmission through a periodic 2D array of quantum dots (QD) sandwiched between doped semiconductor 2D leads in a magnetic field parallel to the leads. We show that the coupling of dots via continuum of electronic states in the leads causes a Aharonov-Bohm oscillations of resonant tunneling conductance, relative to the single-dot case, when the magnetic field angle phi satisfies to the special condition Tan(phi)=p/q, where p and q are prime numbers.

Seminar 182
New solutions to YB equation, appearing at exceptional values of deformation parameter

David Karakhanyan

Yerevan Physics Institute

14:00, Saturday, 15 February 2014

(YSU, Physics Faculty, room 326)

Abstract: At the simplest example of sl(2) algebra, which includes all regularities related to degeneracy of quantum algebras at exceptional values of deformation parameter, demonstrated new solutions, appearing for cyclic, semi-cyclic and nilpotent representations, leading to regular and for indecomposable representations, leading to non-Hermitian Hamiltonians. The latter can be treated in canonical form in the frame of Sklyanin approach.