Related papers: Perturbative Analysis of Potential Scattering Prob…
Quantum dynamics of strongly correlated systems is a challenging problem. Although the low energy fractional excitations of one dimensional integrable models are often well-understood, exploring quantum dynamics in these systems remains…
This is a survey of the basic results on the behavior of the number of the eigenvalues of a Schr\"odinger operator, lying below its essential spectrum. We discuss both fast decaying potentials, for which this behavior is semiclassical, and…
Statistical systems composed of atoms interacting with each other trough nonintegrable interaction potentials are considered. Examples of these potentials are hard-core potentials and long-range potentials, for instance, the Lennard-Jones…
We present a method for efficiently finding solutions of L\"uscher's quantisation condition, the equation which relates two-particle scattering amplitudes to the discrete spectrum of states in a periodic spatial volume of finite extent such…
It is pointed out that for a general short-ranged potential the Lippmann-Schwinger-Low scattering state $|\psi^L_k>$ does not strictly satisfy the Schrodinger eigen equation, and the pair $|\psi^L_n>$, $|\psi^L_k>$ is mutually nonorthogonal…
We present detailed simulations addressing recent electronic interference experiments, where a metallic gate is used to locally modify the Fermi wave-length of the charge carriers. Our numerical calculations are based on a solution of the…
We consider the extended Hubbard model in the atomic limit on a Bethe lattice with coordination number z. By using the equations of motion formalism, the model is exactly solved for both attractive and repulsive intersite potential V. By…
We investigate the small-time local controllability (STLC) near the ground state of a bilinear Schr\"odinger equation when the linearized system is not controllable. It is well known that, for single-input systems, quadratic terms in the…
We discuss the main features of quantum integrable models taking the classes of universality of the Ising model and the repulsive Lieb-Liniger model as paradigmatic examples. We address the breaking of integrability by means of two…
The study of scattering processes in few body systems is a difficult problem especially if long range interactions are involved. In order to solve such problems, we develop here a potential-splitting approach for three body systems. This…
We obtain the spectrum of bound states for a modified P\"oschl-Teller and square potential wells in the nonlinear Schr\"odinger equation. For a fixed norm of bound states, the spectrum for both potentials turns out to consist of a finite…
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…
In this paper, we study the bound state analysis of a one dimensional nonlinear version of the Schr\"{o}dinger equation for the harmonic oscillator potential perturbed by a $\delta$ potential, where the nonlinear term is taken to be…
We analyze the properties of low-energy bound states in the transverse-field Ising model and in the XXZ model on the square lattice. To this end, we develop an optimized implementation of perturbative continuous unitary transformations. The…
We consider the low-energy particle-particle scattering properties in a periodic simple cubic crystal. In particular, we investigate the relation between the two-body scattering length and the energy shift experienced by the lowest-lying…
The small dispersion limit of the focusing nonlinear Schrodinger equation with periodic initial conditions is studied analytically and numerically. First, through a comprehensive set of numerical simulations, it is demonstrated that…
This paper studies the localization behaviour of Bose-Einstein condensates in disorder potentials, modeled by a Gross-Pitaevskii eigenvalue problem on a bounded interval. In the regime of weak particle interaction, we are able to quantify…
The Hubbard model describes a lattice system of quantum particles with local (on-site) interactions. Its free energy is analytic when \beta t is small, or \beta t^2/U is small; here, \beta is the inverse temperature, U the on-site repulsion…
We study the transport properties of interacting electrons in a disordered quantum wire within the framework of the Luttinger liquid model. We demonstrate that the notion of weak localization is applicable to the strongly correlated…
The spin-1 Ising model with bilinear and biquadratic exchange interactions and single-ion crystal field is solved on the Bethe lattice using exact recursion equations. The general procedure of critical properties investigation is discussed…