## Archive 2014

## Seminar 205

Orbit method quantization of the AdS_2 superparticle

George Jorjadze

Ramzadze Mathematical Institute, Tbilisi

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 AdS_{5}

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

Vadim Ohanyan

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.