Ansatz of Hans Bethe for a two-dimensional lattice Bose gas

S. Sergeev

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

The method of q-oscillator lattices, proposed recently in Bazhanov and Sergeev 2005 (Preprint hep-th/0509181), provides the tool for a construction of various integrable models of quantum mechanics in (2 + 1)-dimensional spacetime. In contrast to any one-dimensional quantum chain, its two-dimensional generalizations - quantum lattices - admit different geometrical structures. In this paper, we consider the q-oscillator model on a special lattice. The model may be interpreted as a two-dimensional lattice Bose gas. The most remarkable feature of the model is that it allows the coordinate Bethe ansatz: the p-particles' wavefunction is the sum of plane waves. Consistency conditions is the set of 2p equations for p one-particle wave vectors. These 'Bethe ansatz' equations are the main result of this paper.

Original languageEnglish
Pages (from-to)3035-3045
Number of pages11
JournalJournal of Physics A: Mathematical and General
Volume39
Issue number12
DOIs
Publication statusPublished - 24 Mar 2006
Externally publishedYes

Fingerprint

Bose Gas
Lattice Gas
Bethe Ansatz
Gases
gases
Consistency Conditions
Integrable Models
oscillators
Plane Wave
Quantum Mechanics
Quantum theory
Wave functions
Space-time
Model
quantum mechanics
plane waves

Cite this

@article{8490ba4207ae40218fd7bccdaca18607,
title = "Ansatz of Hans Bethe for a two-dimensional lattice Bose gas",
abstract = "The method of q-oscillator lattices, proposed recently in Bazhanov and Sergeev 2005 (Preprint hep-th/0509181), provides the tool for a construction of various integrable models of quantum mechanics in (2 + 1)-dimensional spacetime. In contrast to any one-dimensional quantum chain, its two-dimensional generalizations - quantum lattices - admit different geometrical structures. In this paper, we consider the q-oscillator model on a special lattice. The model may be interpreted as a two-dimensional lattice Bose gas. The most remarkable feature of the model is that it allows the coordinate Bethe ansatz: the p-particles' wavefunction is the sum of plane waves. Consistency conditions is the set of 2p equations for p one-particle wave vectors. These 'Bethe ansatz' equations are the main result of this paper.",
author = "S. Sergeev",
year = "2006",
month = "3",
day = "24",
doi = "10.1088/0305-4470/39/12/012",
language = "English",
volume = "39",
pages = "3035--3045",
journal = "Journal of Physics A: Mathematical and General",
issn = "1751-8113",
publisher = "IOP Publishing Ltd.",
number = "12",

}

Ansatz of Hans Bethe for a two-dimensional lattice Bose gas. / Sergeev, S.

In: Journal of Physics A: Mathematical and General, Vol. 39, No. 12, 24.03.2006, p. 3035-3045.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Ansatz of Hans Bethe for a two-dimensional lattice Bose gas

AU - Sergeev, S.

PY - 2006/3/24

Y1 - 2006/3/24

N2 - The method of q-oscillator lattices, proposed recently in Bazhanov and Sergeev 2005 (Preprint hep-th/0509181), provides the tool for a construction of various integrable models of quantum mechanics in (2 + 1)-dimensional spacetime. In contrast to any one-dimensional quantum chain, its two-dimensional generalizations - quantum lattices - admit different geometrical structures. In this paper, we consider the q-oscillator model on a special lattice. The model may be interpreted as a two-dimensional lattice Bose gas. The most remarkable feature of the model is that it allows the coordinate Bethe ansatz: the p-particles' wavefunction is the sum of plane waves. Consistency conditions is the set of 2p equations for p one-particle wave vectors. These 'Bethe ansatz' equations are the main result of this paper.

AB - The method of q-oscillator lattices, proposed recently in Bazhanov and Sergeev 2005 (Preprint hep-th/0509181), provides the tool for a construction of various integrable models of quantum mechanics in (2 + 1)-dimensional spacetime. In contrast to any one-dimensional quantum chain, its two-dimensional generalizations - quantum lattices - admit different geometrical structures. In this paper, we consider the q-oscillator model on a special lattice. The model may be interpreted as a two-dimensional lattice Bose gas. The most remarkable feature of the model is that it allows the coordinate Bethe ansatz: the p-particles' wavefunction is the sum of plane waves. Consistency conditions is the set of 2p equations for p one-particle wave vectors. These 'Bethe ansatz' equations are the main result of this paper.

UR - http://www.scopus.com/inward/record.url?scp=33644929527&partnerID=8YFLogxK

U2 - 10.1088/0305-4470/39/12/012

DO - 10.1088/0305-4470/39/12/012

M3 - Article

VL - 39

SP - 3035

EP - 3045

JO - Journal of Physics A: Mathematical and General

JF - Journal of Physics A: Mathematical and General

SN - 1751-8113

IS - 12

ER -