Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:0808.2491 · Journal of Physics A Mathematical and Theoretical

The dynamics of the one-dimensional delta-function Bose gas

Craig A. Tracy, Harold Widom

Published Oct 21, 2008• 28 citations
arXivHTMLPDF

Abstract

We give a method to solve the time-dependent Schrödinger equation for a system of one-dimensional bosons interacting via a repulsive delta function potential. The method uses the ideas of Bethe Ansatz but does not use the spectral theory of the associated Hamiltonian.
DOI
10.1088/1751-8113/41/48/485204

Related papers

Solitons in a One-Dimensional Bose System with the Repulsive Delta-Function Interaction

M. Ishikawa, Hajime Takayama

Lieb's type II excitation, derived exactly by means of a Bethe ansatz, in a one-dimensional Bose system with the repulsive delta-function interaction is identified with the soliton mode, which is a solution of the Pitaevskii-Gross (or nonlinear Schrödinger) equation for the corresponding Bose field.

Journal of the Physical Society of Japan•Oct 15, 1980•81 citations

Statistical Mechanics of a One-Dimensional δ-function Bose Gas

Miki Wadati, Go Kato

Statistical mechanics of a one-dimensional system of bosons with repulsive delta-function interaction is studied. Explicit calculations of the partition function and the cluster integrals are carried out. The results coincide with those by the thermal Bethe ansatz (TBA) method. Thermodynamic quantities such as the pressure, the chemical potential and the energy are given both for large and small coupling limits.

Journal of the Physical Society of Japan•Jul 15, 2001•13 citations

Correlation functions in a one-dimensional Bose gas

Anatoli G. Izergin, V. E. Korepin, Nicolai Reshetikhin

The problem of calculating correlation functions is considered for the one-dimensional Bose gas with a delta-function repulsive interaction between particles. The method of calculation is based on the algebraic Bethe ansatz.

Journal of Physics A Mathematical and General•Oct 1, 1987•49 citations

The One-dimensional Bose Gas

V. E. Korepin, N. M. Bogoliubov, Anatoli G. Izergin

Introduction The one-dimensional Bose gas with point-like interaction of the particles (the quantum variant of the nonlinear Schrödinger equation) is one of the main and most important models which can be Solved by means of the Bethe Ansatz. This model has been thoroughly investigated (and. We shall start with the construction of eigenfunctions of the Hamiltonian in a finite volume. Quantities interesting from the physical point of view (in the thermodynamic limit at zero temperature) are considered; the thermodynamics at finite temperatures is investigated in detail as well. A number of essential ideas which will be applied to other models are introduced. The construction of eigenfunctions of the Hamiltonian is explained in section 1. Their explicit form and, in particular, the two-particle reducibility, are common features of the models solvable by means of the Bethe Ansatz method. Periodic boundary conditions are imposed on the wave function in section 2; the Bethe equations for the particle' momenta are introduced and analyzed. Taken in the logarithmic form, these equations realize the extremum condition of a certain functional, the corresponding action being called the Yang-Yang action. The transition to the thermodynamic limit is considered in section 3. In that same section the ground state of the gas is constructed. The density of the particle distribution in momentum space and the energy of the ground state are calculated. The method of the transition to the thermodynamic limit described in this section is rather general and may be applied to any model solvable by means of the Bethe Ansatz. In section 4, excitations above the ground state are constructed and their main characteristics (energy, momentum and scattering matrix) are determined by means of the dressing equations. The ground state of the model is the Dirac sea (also called the Fermi sphere).

Cambridge University Press eBooks•Aug 19, 1993•1 citation

Partition function for a one-dimensional δ-function Bose gas

Go Kato, Miki Wadati

The N-particle partition function of a one-dimensional delta-function Bose gas is calculated explicitly using only the periodic boundary condition (the Bethe ansatz equation). The N-particles cluster integrals are shown to be the same as those by the thermal Bethe ansatz method.

arXiv:cond-mat/0212321•Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics•Feb 21, 2001•18 citations

Complex Spectral Representation of a Many-Body System in One Dimension

Gonzalo E. Ordonez

I consider a Brownian particle immersed in a one-dimensional boson gas with delta-function repulsive potentials. I find many-body complex eigenvalues of the Liouville super-operator, up to second order in the coupling constant. The eigenvalues give the diffusion time-scale of the Brownian particle. The eigenvalue problem is solved using a Bethe-ansatz approach.

Progress of Theoretical Physics Supplement•Jan 1, 2010•2 citations
Introduction The one-dimensional Bose gas with point-like interaction of the particles (the quantum variant of the nonlinear Schrödinger equation) is one of the main and most important models which can be Solved by means of the Bethe Ansatz. This model has been thoroughly investigated (and. We shall start with the construction of eigenfunctions of the Hamiltonian in a finite volume. Quantities interesting from the physical point of view (in the thermodynamic limit at zero temperature) are considered; the thermodynamics at finite temperatures is investigated in detail as well. A number of essential ideas which will be applied to other models are introduced. The construction of eigenfunctions of the Hamiltonian is explained in section 1. Their explicit form and, in particular, the two-particle reducibility, are common features of the models solvable by means of the Bethe Ansatz method. Periodic boundary conditions are imposed on the wave function in section 2; the Bethe equations for the particle' momenta are introduced and analyzed. Taken in the logarithmic form, these equations realize the extremum condition of a certain functional, the corresponding action being called the Yang-Yang action. The transition to the thermodynamic limit is considered in section 3. In that same section the ground state of the gas is constructed. The density of the particle distribution in momentum space and the energy of the ground state are calculated. The method of the transition to the thermodynamic limit described in this section is rather general and may be applied to any model solvable by means of the Bethe Ansatz. In section 4, excitations above the ground state are constructed and their main characteristics (energy, momentum and scattering matrix) are determined by means of the dressing equations. The ground state of the model is the Dirac sea (also called the Fermi sphere).