Excitation Spectrum Of Bosons In A Finite One-dimensional Circular Waveguide Via The Bethe Ansatz

Sykes, Andrew G., Drummond, Peter D. and Davis, Matthew J. (2007) Excitation Spectrum Of Bosons In A Finite One-dimensional Circular Waveguide Via The Bethe Ansatz. Physical Review A, 76 6: . doi:10.1103/PhysRevA.76.063620

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Author Sykes, Andrew G.
Drummond, Peter D.
Davis, Matthew J.
Title Excitation Spectrum Of Bosons In A Finite One-dimensional Circular Waveguide Via The Bethe Ansatz
Journal name Physical Review A   Check publisher's open access policy
ISSN 1050-2947
1094-1622
Publication date 2007-12-27
Sub-type Article (original research)
DOI 10.1103/PhysRevA.76.063620
Open Access Status File (Publisher version)
Volume 76
Issue 6
Total pages 12
Place of publication College Park, MD, United States
Publisher American Physical Society
Collection year 2008
Language eng
Abstract The exactly solvable Lieb-Liniger model of interacting bosons in one dimension has attracted renewed interest as current experiments with ultracold atoms begin to probe this regime. Here we numerically solve the equations arising from the Bethe ansatz solution for the exact many-body wave function in a finite-size system of up to 20 particles for attractive interactions. We discuss the features of the solutions, and how they deviate from the well-known string solutions [Thacker, Rev. Mod. Phys. 53, 253 (1981)] at finite densities. We present excited state string solutions in the limit of strong interactions and discuss their physical interpretation, as well as the characteristics of the quantum phase transition that occurs as a function of interaction strength in the mean-field limit. Finally we compare our results to those of exact diagonalization of the many-body Hamiltonian in a truncated basis. We also present excited state solutions and the excitation spectrum for the repulsive one-dimensional Bose gas on a ring.
Keyword Boson systems
Bound states
Excited states
Many-body problems
Phase transformations
Quantum theory
Wave functions
Q-Index Code C1
Q-Index Status Confirmed Code
Additional Notes Article #063620

 
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Created: Thu, 08 May 2008, 11:09:01 EST by Stephanie Golding on behalf of School of Mathematics & Physics