Related papers: Perturbative Analysis of Potential Scattering Prob…
In hadron physics, molecular-like multihadron states can interact with compact multiquark states. The latter are modeled as bare states in the Hilbert space of a potential model. In this work, we study several potential models relevant to…
We study multistate Schr\"odinger operators related to molecular dynamics. We consider potentials which do not necessarily decay and prove absence of the singular continuous spectrum and propagation estimates which mean the scattering at…
Several numerical investigations of the Salpeter equation with static confining interactions of Lorentz-scalar type revealed that its solutions are plagued by instabilities of presumably Klein-paradox nature. By proving rigorously that the…
The Kronig-Penney model is used to Study the effect of nonlinear interaction on the transmissive properties of both ordered and disordered chains. In the ordered case, the nonlinearity can either localize or delocalize the electronic states…
In this work, we study the existence of various classes of standing waves for a nonlinear Schr\"odinger system with quadratic interaction, along with a harmonic or partially harmonic potential. We establish the existence of ground-state…
Bound states of hyperbolic potential is investigated by means of a generalized pseudospectral method. Significantly improved eigenvalues, eigenfunctions are obtained efficiently for arbitrary $n, \ell$ quantum states by solving the relevant…
We study a non-linear Schroedinger equation with a Hartree-type nonlinearity and a localized random time-dependent external potential. Sharp dispersive estimates for the linear Schroedinger equation with a random time-dependent potential…
We explore the spectral properties and behaviour of confining superexponential potentials. Several prototypes of these highly nonlinear potentials are analyzed in terms of the eigenvalues and eigenstates of the underlying stationary…
Isolated long-range interacting particle systems appear generically to relax to non-equilibrium states ("quasi-stationary states" or QSS) which are stationary in the thermodynamic limit. A fundamental open question concerns the "robustness"…
Despite considerable efforts over the last decade, the high-energy phase diagram of the random-field Heisenberg chain still eludes our understanding, in particular the nature of the non-ergodic many-body localized (MBL) regime expected at…
By considering the Higgs mechanism in the framework of a parity-preserving Planar Quantum Electrodynamics, one shows that an attractive electron-electron interaction may come out. The e-e interaction potential emerges as the…
We develop a Liouville perturbation theory for weakly driven and weakly open quantum systems in situations when the unperturbed system has a number of conservations laws. If the perturbation violates the conservation laws, it drives the…
A Luttinger Liquid coupled to a quantum impurity describes a large number of physical systems. The Hamiltonian consists of left- and right-moving fermions interacting among themselves via a density-density coupling and scattering off a…
Quantum simulators of lattice gauge theories involve dynamics of typically short-ranged interacting particles and dynamical fields. Elimination of the latter via Gauss law leads to infinite range interactions as exemplified by the Schwinger…
A local perturbation theory for the spectral analysis of the Schr\"odinger operator with two periodic potentials whose periods are commensurable has been constructed. It has been shown that the perturbation of the periodic 1D Hamiltonian by…
Strongly-interacting ultra-cold atoms in tight-binding optical lattice potentials provide an ideal platform to realize the fundamental Hubbard model. Here, after outlining the elementary single particle solution, we review and expand our…
We investigate the Ising model on finite subgraphs of the hyperbolic lattice under minus boundary conditions and in the presence of a positive external field $h$. Interpreting the boundary as frozen or cold wall conditions, we show that,…
We discuss localized ground states of the periodic Gross-Pitaevskii equation in the framework of a quantum linear Schr\"odinger equation with effective potential determined in self-consistent manner. We show that depending on the…
We consider the ground state in a model with scalar nucleons and a meson using the formalism of light-front dynamics. Light-front potentials for two-nucleon bound states are calculated using two approaches. First, light-front time-ordered…
We revisit the one-dimensional attractive Hubbard model by using the Bethe-ansatz based density-functional theory and density-matrix renormalization method. The ground-state properties of this model are discussed in details for different…