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

Physical review. B, Condensed matter

Bosonic excitations in the sine-Gordon system at finite temperatures

Kazumi Maki, Mau-chung Chang

Published Jun 1, 1981• 0 citations
Publisher

Abstract

With the use of the Matsubara technique three things are done: (1) the lifetime of the $n=1$ breather (i.e., the renormalized phonon) is determined, (2) $\frac{{M}_{2}}{(2{M}_{1})}$ in the weak-coupling limit is calculated, and (3) $\frac{{M}_{1}}{(2{E}_{s})}$ near ${g}^{2}=4\ensuremath{\pi}$ is determined by making use of the equivalence between the sine-Gordon model and the massive Thirring model. Here ${M}_{n}$ is the mass of the $n$th breather and ${E}_{s}$ is the soliton energy. It is also shown that the ${\ensuremath{\varphi}}^{4}$ model has the identical bosonic spectrum to that of the sine-Gordon system in the weak-coupling limit and in the low-temperature limit.

DOI
10.1103/physrevb.23.6067

Related papers

Classical sine-Gordon limit of massive-Thirring-model thermodynamics

Michael Fowler

It has been shown numerically by Chung that in the classical sine-Gordon limit the low-temperature thermodynamic properties of the massive Thirring model, as calculated using the Bethe ansatz, correspond to those of a free-phonon gas. We give an analytic derivation of this result and find simple expressions for the finite-temperature "excitation-spectrum" functions, and discuss their physical significance.

Physical review. B, Condensed matter•Sep 1, 1982•36 citations

Soliton-breather approach to classical sine-Gordon thermodynamics

Kazuo Sasaki

Thermodynamics of the Boltzmann gas consisting of solitons, antisolitons, and breathers of the classical sine-Gordon system is studied by taking their interactions into account. A compact expression for the thermodynamic potential is obtained, which agrees with that obtained from the classical limit of the Bethe-ansatz formulation of the quantum sine-Gordon thermodynamics. We further find that the average number of breathers excited at low temperatures (m\ensuremath{\ll}T\ensuremath{\ll}M, where m and M are the phonon and the soliton masses, respectively) is half the total number of degrees of freedom of the system.

Physical review. B, Condensed matter•Feb 15, 1986•27 citations

Finite temperature excitations of the quantum sine-Gordon–massive Thirring model: Variation of the soliton mass with coupling constant and temperature

Michael Durnan Johnson, Michael Fowler

For the quantum sine-Gordon--massive Thirring model at finite temperature, the relationship between the Bethe ansatz ``elementary excitations'' and physical excitations of the system is examined. The thermodynamic equations are written in terms of a set of dressed particles in the general case. We find that the recently predicted soliton mass discontinuity (on varying coupling strength at finite temperature) is not a real effect--the function exhibiting the discontinuity does not correspond to the mass of the soliton.

Physical review. B, Condensed matter•Jan 1, 1985•9 citations

Bethe-ansatz quantum sine-Gordon thermodynamics. Finite-temperature excitation spectrum

X. Zotos, Michael Fowler

The thermal renormalization of the Bethe-ansatz excitation spectrum for the sine-Gordon system is presented. For the soliton mass, the results agree closely with those of Maki and Takayama over a significant temperature range, but the sudden decrease in mass they predict near a particular temperature is not found. For the Bethe-ansatz excitation corresponding to the phonon at zero temperature, the rest mass changes rapidly as the temperature increases, even near the classical limit. This suggests that at finite temperature this excitation (the one-string) no longer corresponds to the physical phonon.

Physical review. B, Condensed matter•Aug 1, 1982•14 citations

Classical limit of sine-Gordon thermodynamics using the Bethe ansatz

Michael Durnan Johnson, Niu-Niu Chen, Michael Fowler

We use the quantum Bethe ansatz method to compute the free energy of the sine-Gordon model in the classical limit. In this limit the number of breathers, and hence the number of coupled integral equations to be solved, diverges. By linearizing the breather mass spectrum and phase shifts, extending a method of Maki, we can reduce the breather ladder to anharmonic phonons. The divergent set of integral equations is reduced to only two, for interacting phonons and solitons. We solve these equations iteratively to give the free energy in a double series in the temperature t and the soliton density ${e}^{\mathrm{\ensuremath{-}}1/t}$ which agrees to high order with classical transfer integral results.

Physical review. B, Condensed matter•Dec 1, 1986•13 citations

Thermodynamics of the Classical Massive-Thirring-Sine-Gordon Model

S. G. Chung

The proper classical limit $\ensuremath{\hbar}\ensuremath{\rightarrow}0$ of the quantum Bethe-Ansatz thermodynamics gives a new set of integral equations for the thermodynamics of the classical massive-Thirring-sine-Gordon model. The theory contains the thermodynamic information about breathers and solitons, and reproduces the transfer-matrix-method result for arbitrary coupling constant.

Physical Review Letters•Feb 13, 1989•11 citations
With the use of the Matsubara technique three things are done: (1) the lifetime of the n=1n=1n=1 breather (i.e., the renormalized phonon) is determined, (2) M2(2M1)\frac{{M}_{2}}{(2{M}_{1})}(2M1​)M2​​ in the weak-coupling limit is calculated, and (3) M1(2Es)\frac{{M}_{1}}{(2{E}_{s})}(2Es​)M1​​ near g2=4\ensuremathπ{g}^{2}=4\ensuremath{\pi}g2=4\ensuremathπ is determined by making use of the equivalence between the sine-Gordon model and the massive Thirring model. Here Mn{M}_{n}Mn​ is the mass of the nnnth breather and Es{E}_{s}Es​ is the soliton energy. It is also shown that the \ensuremathφ4{\ensuremath{\varphi}}^{4}\ensuremathφ4 model has the identical bosonic spectrum to that of the sine-Gordon system in the weak-coupling limit and in the low-temperature limit.
Thermodynamics of the Boltzmann gas consisting of solitons, antisolitons, and breathers of the classical sine-Gordon system is studied by taking their interactions into account. A compact expression for the thermodynamic potential is obtained, which agrees with that obtained from the classical limit of the Bethe-ansatz formulation of the quantum sine-Gordon thermodynamics. We further find that the average number of breathers excited at low temperatures (m\ensuremath{\ll}T\ensuremath{\ll}M, where m and M are the phonon and the soliton masses, respectively) is half the total number of degrees of freedom of the system.
For the quantum sine-Gordon--massive Thirring model at finite temperature, the relationship between the Bethe ansatz ``elementary excitations'' and physical excitations of the system is examined. The thermodynamic equations are written in terms of a set of dressed particles in the general case. We find that the recently predicted soliton mass discontinuity (on varying coupling strength at finite temperature) is not a real effect--the function exhibiting the discontinuity does not correspond to the mass of the soliton.
The thermal renormalization of the Bethe-ansatz excitation spectrum for the sine-Gordon system is presented. For the soliton mass, the results agree closely with those of Maki and Takayama over a significant temperature range, but the sudden decrease in mass they predict near a particular temperature is not found. For the Bethe-ansatz excitation corresponding to the phonon at zero temperature, the rest mass changes rapidly as the temperature increases, even near the classical limit. This suggests that at finite temperature this excitation (the one-string) no longer corresponds to the physical phonon.
We use the quantum Bethe ansatz method to compute the free energy of the sine-Gordon model in the classical limit. In this limit the number of breathers, and hence the number of coupled integral equations to be solved, diverges. By linearizing the breather mass spectrum and phase shifts, extending a method of Maki, we can reduce the breather ladder to anharmonic phonons. The divergent set of integral equations is reduced to only two, for interacting phonons and solitons. We solve these equations iteratively to give the free energy in a double series in the temperature t and the soliton density ${e}^{\mathrm{\ensuremath{-}}1/t}$ which agrees to high order with classical transfer integral results.