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

Progress of Theoretical Physics

Statistical Mechanics of a Spin-Boson System. III: A Closed Equation for the Partition Function

Toshio Tsuzuki

Published Jan 1, 1991• 2 citations
Publisher

Abstract

A closed integral equation for the partition function of a spin-boson system is obtained by the use of the coherent state representation of boson. This is accomplished by the use of new method of taking the thermal average by differential operations. The dynamic compensation theorem for the thermodynamic fluctuation is proved without employing a series expansion of the partition function as done in our previous works. The zeroth approximation to the equation is shown to be the decoupling approximation introduced previously, as naturally expected.

DOI
10.1143/ptp/85.1.31

Related papers

Statistical Mechanics of a Spin-Boson System. III

Toshio Tsuzuki

A closed integral equation for the partition function of a spin-boson system is obtained by the use of the coherent state representation of boson. This is accomplished by the use of new method of taking the thermal average by differential operations. The dynamic compensation theorem for the thermodynamic fluctuation is proved without employing a series expansion of the partition function as done in our previous works. The zeroth approximation to the equation is shown to be the decoupling approximation introduced previously, as naturally expected.

Progress of Theoretical Physics•Jan 1, 1991•0 citations

Statistical Mechanics of a Spin-Boson System: The Dynamic Compensation Theorem and the Exact Partition Function

T. Tsuzuki

We first extend the dynamic compensation theorem of infrared divergence for the case of finite temperatures and then obtain the exact partition function of the spin-boson system, which is different from the previous ones. We find that there exists no thermodynamic equivalence between the spin-boson system and the Kondo system in general and that such equivalence is restricted to the case of high temperature limit.

Progress of Theoretical Physics•Jul 1, 1990•1 citation

Statistical Mechanics of a Spin-Boson System

Toshio Tsuzuki

We first extend the dynamic compensation theorem of infrared divergence for the case of finite temperatures and then obtain the exact partition function of the spin-boson system, which is different from the previous ones. We find that there exists no thermodynamic equivalence between the spin-boson system and the Kondo system in general and that such equivalence is restricted to the case of high temperature limit.

Progress of Theoretical Physics•Jul 1, 1990•0 citations

Dynamics of a Spin-Boson System

Toshio Tsuzuki

We study the non-adiabatic effect of the bosonic bath on the spin dynamics by the light of the dynamic compensation theorem. We examine the time-evolutions of the probability of finding the up-state of spin and the thermal average of σz(t). The dynamics is formulated in competition between the tunneling coherence of spin and the non-adiabatic effect of bath in the equitable treatment. We prove the complete compensation of the infrared divergences due to the zero-point and thermodynamic fluctuations by the dynamical fluctuation of the coherent boson (the dynamic compensation). We further present the exact expressions of the above two quantities in the series form.

Progress of Theoretical Physics•Feb 1, 1991•0 citations

Dynamics of a Spin-Boson System: How Does the Dynamic Compensation Manifest Itself

T. Tsuzuki

We study the non-adiabatic effect of the bosonic bath on the spin dynamics by the light of the dynamic compensation theorem. We examine the time-evolutions of the probability of finding the up-state of spin and the thermal average of σz(t). The dynamics is formulated in competition between the tunneling coherence of spin and the non-adiabatic effect of bath in the equitable treatment. We prove the complete compensation of the infrared divergences due to the zero-point and thermodynamic fluctuations by the dynamical fluctuation of the coherent boson (the dynamic compensation). We further present the exact expressions of the above two quantities in the series form.

Progress of Theoretical Physics•Feb 1, 1991•3 citations

Statistical Mechanics of a Spin-Boson System. II: Thermodynamics in a Decoupling Approximation

T. Tsuzuki

The thermodynamics of a spin-boson system is studied by applying a decoupling approximation to the exact partition function which has been presented by the author. The effective tunneling gap, the internal energy and the specific heat are computed. It is shown that (1) the non-adiabatic effect of bosons on the spin is almost exhausted in the ground state, (2) the effective tunneling gap Δeff depends on temperature very weakly, and (3) the characteristic temperature of thermodynamic quantities is decreased by factor Δeff/Δ where Δ is the bare tunneling gap.

Progress of Theoretical Physics•Aug 1, 1990•0 citations
A closed integral equation for the partition function of a spin-boson system is obtained by the use of the coherent state representation of boson. This is accomplished by the use of new method of taking the thermal average by differential operations. The dynamic compensation theorem for the thermodynamic fluctuation is proved without employing a series expansion of the partition function as done in our previous works. The zeroth approximation to the equation is shown to be the decoupling approximation introduced previously, as naturally expected.
A closed integral equation for the partition function of a spin-boson system is obtained by the use of the coherent state representation of boson. This is accomplished by the use of new method of taking the thermal average by differential operations. The dynamic compensation theorem for the thermodynamic fluctuation is proved without employing a series expansion of the partition function as done in our previous works. The zeroth approximation to the equation is shown to be the decoupling approximation introduced previously, as naturally expected.
We study the non-adiabatic effect of the bosonic bath on the spin dynamics by the light of the dynamic compensation theorem. We examine the time-evolutions of the probability of finding the up-state of spin and the thermal average of σz(t). The dynamics is formulated in competition between the tunneling coherence of spin and the non-adiabatic effect of bath in the equitable treatment. We prove the complete compensation of the infrared divergences due to the zero-point and thermodynamic fluctuations by the dynamical fluctuation of the coherent boson (the dynamic compensation). We further present the exact expressions of the above two quantities in the series form.
We study the non-adiabatic effect of the bosonic bath on the spin dynamics by the light of the dynamic compensation theorem. We examine the time-evolutions of the probability of finding the up-state of spin and the thermal average of σz(t). The dynamics is formulated in competition between the tunneling coherence of spin and the non-adiabatic effect of bath in the equitable treatment. We prove the complete compensation of the infrared divergences due to the zero-point and thermodynamic fluctuations by the dynamical fluctuation of the coherent boson (the dynamic compensation). We further present the exact expressions of the above two quantities in the series form.
The thermodynamics of a spin-boson system is studied by applying a decoupling approximation to the exact partition function which has been presented by the author. The effective tunneling gap, the internal energy and the specific heat are computed. It is shown that (1) the non-adiabatic effect of bosons on the spin is almost exhausted in the ground state, (2) the effective tunneling gap Δeff depends on temperature very weakly, and (3) the characteristic temperature of thermodynamic quantities is decreased by factor Δeff/Δ where Δ is the bare tunneling gap.