TY - JOUR

T1 - Sine-Gordon system as a Toda lattice

T2 - Thermodynamics in the classical limit

AU - Sasaki, Kazuo

N1 - Copyright:
Copyright 2015 Elsevier B.V., All rights reserved.

PY - 1987

Y1 - 1987

N2 - The Bethe-ansatz (BA) equation for the classical sine-Gordon (SG) thermodynamics is shown to reduce to the one for the classical Toda lattice within two approximations; the phonon-phonon interactions are neglected (the harmonic phonon) and solitons are treated nonrelativistically. Within these approximations the solitons in the SG model correspond to the particles in the Toda lattice. Making use of an analytical solution of the BA equation for the classical Toda lattice due to Opper, we obtain an analytical solution of the approximate SG equation. We propose also a similar approximate BA equation for the 4 model, although the 4 model does not have the BA equation for the classical thermodynamics.

AB - The Bethe-ansatz (BA) equation for the classical sine-Gordon (SG) thermodynamics is shown to reduce to the one for the classical Toda lattice within two approximations; the phonon-phonon interactions are neglected (the harmonic phonon) and solitons are treated nonrelativistically. Within these approximations the solitons in the SG model correspond to the particles in the Toda lattice. Making use of an analytical solution of the BA equation for the classical Toda lattice due to Opper, we obtain an analytical solution of the approximate SG equation. We propose also a similar approximate BA equation for the 4 model, although the 4 model does not have the BA equation for the classical thermodynamics.

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U2 - 10.1103/PhysRevB.35.3445

DO - 10.1103/PhysRevB.35.3445

M3 - Article

AN - SCOPUS:35949014014

VL - 35

SP - 3445

EP - 3453

JO - Physical Review B

JF - Physical Review B

SN - 0163-1829

IS - 7

ER -