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Progress of Theoretical Physics

Statistical Mechanics of a Spin-Boson System. II

Toshio Tsuzuki

Published Aug 1, 1990• 0 citations
Publisher

Abstract

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.

DOI
10.1143/ptp.84.228

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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.
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.
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.