相关论文: Boundary Interactions for the Semi-Infinite q-Boso…

Upon introducing a one-parameter quadratic deformation of the q-boson algebra and a diagonal perturbation at the end point, we arrive at a semi-infinite q-boson system with a two-parameter boundary interaction. The eigenfunctions are shown…

We provide explicit formulas for the quantum integrals of a semi-infinite $q$-boson system with boundary interactions. These operators and their commutativity are deduced from the Pieri formulas for a $q\to 0$ Hall-Littlewood type…

We briefly summarize the most relevant steps in the search of rigorous results about the properties of quantum systems made of three bosons interacting with zero-range forces. We also describe recent attempts to solve the unboundedness…

Koornwinder polynomials are a 6-parameter BC_n-symmetric family of Laurent polynomials indexed by partitions, from which Macdonald polynomials can be recovered in suitable limits of the parameters. As in the Macdonald polynomial case,…

We present a hierarchy of commuting operators in Fock space containing the q-boson Hamiltonian on $\mathbb{Z}$ and show that the operators in question are simultaneously diagonalized by Hall-Littlewood functions. As an application, the…

We endow Ruijsenaars' open difference Toda chain with a one-sided boundary interaction of Askey-Wilson type and diagonalize the quantum Hamiltonian by means of deformed hyperoctahedral $q$-Whittaker functions that arise as a $t=0$…

For a system of $N$ bosons in one space dimension with two-body $\delta$-interactions the Hamiltonian can be defined in terms of the usual closed semi-bounded quadratic form. We approximate this Hamiltonian in norm resolvent sense by…

We discuss the problem of constructing self-adjoint and lower bounded Hamiltonians for a system of $n>2$ non-relativistic quantum particles in dimension three with contact (or zero-range or $\delta$) interactions. Such interactions are…

We introduce a Bose-Hubbard Hamiltonian with random disordered interactions as a model to study the interplay of superfluidity and glassiness in a system of three-dimensional hard-core bosons at half-filling. Solving the model using…

A generic procedure is proposed to construct many-body quantum Hamiltonians with partial dynamical symmetry. It is based on a tensor decomposition of the Hamiltonian and allows the construction of a hierarchy of interactions that have…

We study the spectrum and eigenstates of the quantum discrete Bose-Hubbard Hamiltonian in a finite one-dimensional lattice containing two bosons. The interaction between the bosons leads to an algebraic localization of the modified extended…

We construct the orthogonal eigenbasis for a discrete elliptic Ruijsenaars type quantum particle Hamiltonian with hyperoctahedral symmetry. In the trigonometric limit the eigenfunctions in question recover a previously studied $q$-Racah…

In this paper the Hamiltonian for the system of semi-relativistic particles interacting with a scalar bose field is investigated. A scaled total Hamiltonian of the system is defined and its scaling limit is considered. Then the…

Quantum Algebras (q-algebras) are used to describe interactions between fermions and bosons. Particularly, the concept of a su_q(2) dynamical symmetry is invoked in order to reproduce the ground state properties of systems of fermions and…

We study the quantum-classical correspondence of an experimentally accessible system of interacting bosons in a tilted triple-well potential. With the semiclassical analysis, we get a better understanding of the different phases of the…

General analytic energy bounds are derived for N-boson systems governed by semirelativistic Hamiltonians of the form H=\sum_{i=1}^N \sqrt(p_i^2+m^2) + \sum_{1=i<j}^N V(r_{ij}), where V(r) is a static attractive pair potential. A…

In this paper we will report on a one-dimensional, non-separable quantum many-particle system introduced in [arXiv:1504.08283,arXiv:1604.06693]. It consists of two (distinguishable) particles moving on the half-line being subjected to two…

We investigate the possibility to suppress interactions between a finite dimensional system and an infinite dimensional environment through a fast sequence of unitary kicks on the finite dimensional system. This method, called dynamical…

We consider the problem of a quantum particle interacting with $N$ attractive point $\delta$-interactions in two and three dimensional Riemannian manifolds and discuss its some spectral properties. The main aim of this paper is to give a…

In this paper, we investigate multidimensional first-order quasi-linear systems and find necessary conditions for them to admit Hamiltonian formulation. The insufficiency of the conditions is related to the Poisson cohomology of the…