Related papers: Exact eigenstates for contact interactions

We present an exact solution in arbitrary dimensions for the steady states of a class of quantum driven-dissipative bosonic models, where a set of modes is subject to arbitrary two-photon driving, single-photon loss and a global Hubbard (or…

Using coherent-state representations of quantum mechanics (Bargmann, Husimi, and stellar representations), we describe analytically the phase-space structure of the general eigenstates corresponding to a 1-dimensional bilinear hyperbolic…

In approximate Kohn-Sham density-functional theory, self-interaction manifests itself as the dependence of the energy of an orbital on its fractional occupation. This unphysical behavior translates into qualitative and quantitative errors…

The Hubbard model is a paradigmatic model of strongly correlated quantum matter, thus making it desirable to investigate with quantum simulators such as ultracold atomic gases. Here, we consider the problem of two atoms interacting in a…

We derive an operator identity which relates tight-binding Hamiltonians with arbitrary hopping on the Bethe lattice to the Hamiltonian with nearest-neighbor hopping. This provides an exact expression for the density of states (DOS) of a…

We construct explicit bound state wave functions and bound state energies for certain $N$--body Hamiltonians in one dimension that are analogous to $N$--electron Hamiltonians for (three-dimensional) atoms and monatomic ions.

We study a class of interacting, harmonically trapped boson systems at angular momentum L. The Hamiltonian leaves a L-dimensional subspace invariant, and this permits an explicit solution of several eigenstates and energies for a wide class…

Orthogonality catastrophe in fermionic systems is well known: in the thermodynamic limit, the overlap between the ground state wavefunctions with and without a single local scattering potential approaches zero algebraically as a function of…

We present the mathematical construction of the physically relevant quantum Hamiltonians for a three-body systems consisting of identical bosons mutually coupled by a two-body interaction of zero range. For a large part of the presentation,…

We propose a lattice density-functional theory for {\it ab initio} quantum chemistry or physics as a route to an efficient approach that approximates the full configuration interaction energy and orbital occupations for molecules with…

In some special zones of the high-dimensional coordinate space of few-body systems with identical particles, the operation of an element (or a product of elements) of the symmetry groups of the Hamiltonian on a quantum state might be…

The equilibrium statistical mechanics of one-dimensional lattice gases with interactions of arbitrary range and shape between first-neighbor atoms is solved exactly on the basis of statistically interacting vacancy particles. Two sets of…

We consider a relativistic no-pair model of a hydrogenic atom in a classical, exterior magnetic field. First, we prove that the corresponding Hamiltonian is semi-bounded below, for all coupling constants less than or equal to the critical…

We address the question how a correspondence between the particle like excitations in the one dimensional Hubbard model (i.e. ``holons'' and ``spinons'') and the free fermionic picture can be established in the limit of vanishing…

Quantum lattice systems are rigorously studied at low temperatures. When the Hamiltonian of the system consists of a potential (diagonal) term and a - small - off-diagonal matrix containing typically quantum effects, such as a hopping…

The delta function potential is a simple model of zero-range contact interaction in one dimension. The Kronig-Penney model is a one-dimensional periodic array of delta functions that models the energy bands in a crystal. Here we investigate…

We propose a simple model of two-dimensional N=2 superconformal mechanics with a spin-orbit interaction term and demonstrate that it inherits the Galilean symmetry of the initial free-particle system. We then propose a quaternionic…

Here we consider an integral equation describing a fixed number of scalar particles which interact not through boson exchange but directly along light cones, similarly as in bound state equations such as the Bethe-Salpeter equation. The…

$N$-body non efimovian bound or quasi-bound states for particles with short range interactions are considered in arbitrary dimensions. The different resonance regimes near the threshold are depicted by using a generalization of the…

We consider zero temperature behavior of dynamic response functions of 1D systems near edges of support in momentum-energy plane $(k, \omega).$ The description of the singularities of dynamic response functions near an edge $\epsilon(k)$ is…