Ansatz of Hans Bethe for a two-dimensional Bose gas

Sergey Sergeev

Research output: Contribution to journalArticle

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. The work was supported by the Australian Research Council
Original languageEnglish
Pages (from-to)3035-3045
Number of pages11
JournalJournal of Physics A: Mathematical and General
Volume39
Publication statusPublished - 2006
Externally publishedYes

Fingerprint

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

Cite this

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

In: Journal of Physics A: Mathematical and General, Vol. 39, 2006, p. 3035-3045.

Research output: Contribution to journalArticle

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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. The work was supported by the Australian Research Council

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