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 PhysicsJul 1, 19901 citation

Two-Qubit Spin-Boson Model in the Strong Coupling Regime: Coherence, Non-Markovianity, and Quantum Thermodynamics

Hasan Mehdi Rizvi, Devvrat Tiwari, Subhashish Banerjee

quant-pharXiv:2601.15026Jan 22, 20260 citations

Progress of Theoretical Physics

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

T. Tsuzuki

Published Feb 1, 1991• 3 citations

Publisher

Abstract

DOI: 10.1143/ptp/85.2.205

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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.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.

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T. Tsuzuki

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Progress of Theoretical PhysicsNov 1, 19896 citations

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.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 PhysicsJan 1, 19910 citations

Dynamic Compensation Theory of a Spin-Boson System

T. Tsuzuki

The physics of an inversion-symmetric (IS) spin-boson system is first solved rigorously in the white limit of boson system on the basis of the concept of dynamic compensation which the author proposed previously. Two kinds of displaced bosons are introduced. They are defined freely out of the infrared divergence due to the dynamic compensation. It is shown that this IS system allows both IS-preserving and IS-breaking states when the bare zero-point contribution of bosons brings about the infrared divergence. The ground state and the excited state are determined explicitly in the white limit. Using them, after the brief study of thermodynamics, we construct the density matrix and study the problem of the persistence of oscillation of quantum coherence under the influence of environment. We describe the persistence of it up to a limited strength of interaction, taking a reasonable initial condition. An explicit formula is given.The physics of an inversion-symmetric (IS) spin-boson system is first solved rigorously in the white limit of boson system on the basis of the concept of dynamic compensation which the author proposed previously. Two kinds of displaced bosons are introduced. They are defined freely out of the infrared divergence due to the dynamic compensation. It is shown that this IS system allows both IS-preserving and IS-breaking states when the bare zero-point contribution of bosons brings about the infrared divergence. The ground state and the excited state are determined explicitly in the white limit. Using them, after the brief study of thermodynamics, we construct the density matrix and study the problem of the persistence of oscillation of quantum coherence under the influence of environment. We describe the persistence of it up to a limited strength of interaction, taking a reasonable initial condition. An explicit formula is given.

Progress of Theoretical PhysicsOct 1, 19942 citations

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

T. Tsuzuki

Progress of Theoretical PhysicsJul 1, 19901 citation

Two-Qubit Spin-Boson Model in the Strong Coupling Regime: Coherence, Non-Markovianity, and Quantum Thermodynamics

Hasan Mehdi Rizvi, Devvrat Tiwari, Subhashish Banerjee

We investigate the dynamics of a two-qubit open quantum system, in particular the two-qubit spin-boson model in the strong coupling regime, coupled to two thermal bosonic baths under non-Markovian and non-equilibrium conditions. Two complementary approaches, the Hierarchical Equations of Motion (HEOM) and Reaction Coordinate Mapping (RCM), are employed to examine various coupling regimes between the qubits and their respective baths. The dynamical features of the model and the impact of the tunneling amplitude on quantum coherence of the system are probed using the $l_1$ -norm of coherence. The model is further shown to have non-Markovian evolution. The nontrivial task of calculating entropy production in the strong-coupling regime is performed using auxiliary density operators in HEOM. Motivated by the realization of a quantum thermal device in the strong-coupling regime, the non-equilibrium steady-state behavior of the system is investigated. Furthermore, the relationship between the heat and spin currents and the tunneling amplitude is probed.We investigate the dynamics of a two-qubit open quantum system, in particular the two-qubit spin-boson model in the strong coupling regime, coupled to two thermal bosonic baths under non-Markovian and non-equilibrium conditions. Two complementary approaches, the Hierarchical Equations of Motion (HEOM) and Reaction Coordinate Mapping (RCM), are employed to examine various coupling regimes between the qubits and their respective baths. The dynamical features of the model and the impact of the tunneling amplitude on quantum coherence of the system are probed using the $l_1$-norm of coherence. The model is further shown to have non-Markovian evolution. The nontrivial task of calculating entropy production in the strong-coupling regime is performed using auxiliary density operators in HEOM. Motivated by the realization of a quantum thermal device in the strong-coupling regime, the non-equilibrium steady-state behavior of the system is investigated. Furthermore, the relationship between the heat and spin currents and the tunneling amplitude is probed.

quant-pharXiv:2601.15026Jan 22, 20260 citations

l_1

-norm of coherence. The model is further shown to have non-Markovian evolution. The nontrivial task of calculating entropy production in the strong-coupling regime is performed using auxiliary density operators in HEOM. Motivated by the realization of a quantum thermal device in the strong-coupling regime, the non-equilibrium steady-state behavior of the system is investigated. Furthermore, the relationship between the heat and spin currents and the tunneling amplitude is probed.