相关论文: Exact eigenstates for contact interactions
Degenerate spinor Bose gases with repulsive density-density interaction and anti-ferromagnetic spin-spin coupling in one spatial dimension are shown to be described by a quantum integrable matrix extension of the nonlinear Schr\"odinger…
Quantum bound-state energies are assumed generated by PT-symmetric Hamiltonians H where P is, typically, parity. It is known that their spectrum only remains real and observable (i.e., in the language of physics, the PT-symmetry remains…
We consider two models of interacting Bose gases: a gas of spin one particles in the ground state of a cubic box and a one-dimension Bose gas with contact interactions. We show how to calculate exact eigenstates of the corresponding N-body…
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 show that all zero energy eigenstates of an arbitrary $m$--state quantum spin chain Hamiltonian with nearest neighbor interaction in the bulk and single site boundary terms, which can also describe the dynamics of stochastic models, can…
We present the exact thermodynamics (isochores, isotherms, isobars, response functions) of a statistically interacting quantum gas in D dimensions. The results in D=1 are those of the thermodynamic Bethe ansatz for the nonlinear…
We study the family $H_{\gamma \lambda \mu}(K)$, $K\in \mathbb{T}^2,$ of discrete Schr\"odinger operators, associated to the Hamiltonian of a system of two identical bosons on the two-dimen\-sional lattice $\mathbb{Z}^2,$ interacting…
In the theory of point interactions, one is given a formal expression for a quantum mechanical Hamiltonian. The interaction terms of the Hamiltonian are singular: they can not be rigorously defined as a perturbation (in the operator or form…
Bosonic atoms confined in optical lattices are described by the Bose-Hubbard model and can exist in two different phases, Mott insulator or superfluid, depending on the strength of the system parameters. In the vicinity of the phase…
We study quantum mechanical systems with "spin"-related contact interactions in one dimension. The boundary conditions describing the contact interactions are dependent on the spin states of the particles. In particular we investigate the…
We study a class of quantum two-dimensional models with complex potentials of specific form. They can be considered as the generalization of a recently studied model with quadratic interaction not amenable to conventional separation of…
We report on a remarkable spectral phenomenon in a generic type of quantum lattice gas model. As the interaction strength increases, eigenstates spontaneously reorganize and lead to plateaus of the interaction energy, with gaps opening akin…
We use the coordinate Bethe ansatz to exactly calculate matrix elements between eigenstates of the Lieb-Liniger model of one-dimensional bosons interacting via a two-body delta-potential. We investigate the static correlation functions of…
The possibility of a matrix product representation for eigenstates with energy and momentum zero of a general m-state quantum spin Hamiltonian with nearest neighbour interaction and periodic boundary condition is considered. The quadratic…
The interplay of quantum statistics, interactions and temperature is studied within the framework of the bosonic two-component theory with repulsive delta-function interaction in one dimension. We numerically solve the thermodynamic Bethe…
The question how to Lorentz transform an N-particle wave function naturally leads to the concept of a so-called multi-time wave function, i.e. a map from (space-time)^N to a spin space. This concept was originally proposed by Dirac as the…
Graphene's honeycomb lattice structure is quite remarkable in the sense that it leads, in the long wavelength limit, to a massless Dirac equation description of nonrelativistic quasiparticles associated with electrons and holes present in…
We address the electronic properties of quantum dots in the two-dimensional $\alpha-\mathcal{T}_3$ lattice when subjected to a perpendicular magnetic field. Implementing an infinite mass boundary condition, we first solve the eigenvalue…
A novel approach is suggested for the statistical description of quantum systems of interacting particles. The key point of this approach is that a typical eigenstate in the energy representation (shape of eigenstates, SE) has a well…
The Hamiltonian conservative system of two interacting particles has been considered both in classical and quantum description. The quantum model has been realized using a symmetrized two-particle basis reordered in the unperturbed energy.…