相关论文: Aharanov Anandan Phase for the Quasi Exactly Solva…
Inozemtsev models are classically integrable multi-particle dynamical systems related to Calogero-Moser models. Because of the additional q^6 (rational models) or sin^2(2q) (trigonometric models) potentials, their quantum versions are not…
The quantum mechanical concept of quasi-exact solvability is based on the idea of partial algebraizability of spectral problem. This concept is not directly extendable to the systems with infinite number of degrees of freedom. For such…
A procedure of solving nonstationary Schredinger equations in the exact analytic form is elaborated on the basis of exactly solvable stationary models. The exact solutions are employed to study the nonadiabatic geometric phase.
In this paper we study the implementation of non-adiabatic geometrical quantum gates with in semiconductor quantum dots. Different quantum information enconding/manipulation schemes exploiting excitonic degrees of freedom are discussed. By…
Sextic polynomial oscillator is probably the best known quantum system which is partially exactly {\it alias} quasi-exactly solvable (QES), i.e., which possesses closed-form, elementary-function bound states $\psi(x)$ at certain couplings…
A spin-orbit coupled two-dimensional (2D) Bose gas is shown to simultaneously possess quasi and true long-range order in the total and relative phase sectors, respectively. The total phase undergoes a Berenzinskii- Kosterlitz-Thouless…
We study a system of 2D trapped bosons in a quasiperiodic potential via ab initio Path Integral Monte Carlo simulations, focusing on its finite temperature properties, which have not yet been explored. Alongside the superfluid, normal fluid…
The combined effect of disorder and interactions is central to the richness of condensed matter physics and can lead to novel quantum states such as the Bose glass phase in disordered bosonic systems. Here, we report on the experimental…
We introduce a new family of quasi-exactly solvable generalized isotonic oscillators which are based on the pseudo-Hermite exceptional orthogonal polynomials. We obtain exact closed-form expressions for the energies and wavefunctions as…
Coarsening of an isolated far-from-equilibrium quantum system is a paradigmatic many-body phenomenon, relevant from subnuclear to cosmological lengthscales, and predicted to feature universal dynamic scaling. Here, we observe universal…
We demonstrate how to directly study non-Abelian statistics for a wide class of exactly solvable many-body quantum systems. By employing exact eigenstates to simulate the adiabatic transport of a model's quasiparticles, the resulting Berry…
We study numerically a 2D Bose-Einstein condensate in a quasiperiodic array of potential peaks, assumed to be generated by superimposing five blue detuned laser beams. By using a Bogoliubov ansatz for the excitations we show that the system…
In this paper, we propose quasilinearization methods that convert nonlocal fully-nonlinear parabolic systems into the nonlocal quasilinear parabolic systems. The nonlocal parabolic systems serve as important mathematical tools for modelling…
We study the polaron quasiparticle in a one-dimensional Bose gas. In the integrable case described by the Yang-Gaudin model, we derive an exact result for the polaron mass in the thermodynamic limit. It is expressed in terms of the…
Sextic oscillator in D dimensions is considered as a typical quasi-exactly solvable (QES) model. Usually, its QES N-plets of bound states have to be computed using the coupled Magyari's nonlinear algebraic equations. We propose and describe…
We construct a family of triatomic models for heteronuclear and homonuclear molecular Bose-Einstein condensates. We show that these new generalized models are exactly solvable through the algebraic Bethe ansatz method and derive their…
The $\nu$-component two-dimensional (2D) Bose liquid is considered. It is shown that the finite temperature phase transition exists in this 2D continuously degenerate multicomponent system. The new type of quasi-long-range order occurs as a…
This article deals with two classes of quasi-exactly solvable (QES) trigonometric potentials for which the one-dimensional Schroedinger equation reduces to a confluent Heun equation (CHE) where the independent variable takes only finite…
Using supersymmetric quantum mechanics we construct the quasi-exactly solvable (QES) potentials with arbitrary two known eigenstates. The QES potential and the wave functions of the two energy levels are expressed by some generating…
The conventional formulation of the non-adiabatic (Aharonov-Anandan) phase is based on the equivalence class $\{e^{i\alpha(t)}\psi(t,\vec{x})\}$ which is not a symmetry of the Schr\"{o}dinger equation. This equivalence class when understood…