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

Journal of the Physical Society of Japan

Two-Time Correlation Functions of a System Coupled to a Heat Bath with a Gaussian-Markoffian Interaction

Yoshitaka Tanimura, Ryogo Kubo

Published Apr 1, 1989• 73 citations
Publisher

Abstract

Two-time correlation functions of physical operators of a system interacting with a heat bath producing a Gaussian-Markoffian noise are treated with the use of Feynman-Vernon's influence functional formalism. The Laplace transforms of correlation functions are shown to be expressed in terms of continued fractions of relevant hyperoperators. The result is valid to all orders of the system-bath interaction. In the limitation of motional narrowing, it reduces to those obtained in conventional methods.

DOI
10.1143/jpsj.58.1199

Related papers

Time Evolution of a Quantum System in Contact with a Nearly Gaussian-Markoffian Noise Bath

Yoshitaka Tanimura, Ryogo Kubo

A test system is assumed to interact with a heat bath consisting of harmonic oscillators or an equivalent bath with a proper frequency spectrum producing a Gaussian-Markoffian random perturbation. The effect of reaction of the test system to the bath is considered in the high temperature approximation. Elimination of the bath using the influence functional method of Feynman and Vernon yields a continuous fraction expression for the reduced density matrix of the test system. The result affords a basis to clarify the relationship between the stochastic and the dynamical approaches to treat the problem of partial destruction of quantum coherence of a system interacting with its environment.

Journal of the Physical Society of Japan•Jan 15, 1989•1,008 citations

Second Order Optical Process of a Three-Level System in Contact with a Nearly Gaussian-Markoffian Noise Bath

Yoshitaka Tanimura, Tetsuhiro Suzuki, Ryogo Kubo

A general formulation is given for the second order optical process of a three-level system in contact with a heat bath consisting of harmonic oscillators with a proper frequency spectrum producing a Markoffian random perturbation. Elimination of the bath using the influence functional method of Feynman and Vernon yields a continuous fraction expression and the result affords a basis to clarify the relation between the stochastic and dynamical approaches to treat the partial destruction of the quantum coherence of the optical process. As an example, a three-level system with intermediate-state interaction is treated in some detail.

Journal of the Physical Society of Japan•May 15, 1989•15 citations

An operator derivation of the Feynman–Vernon theory, with applications to the generating function of bath energy changes and to an-harmonic baths

Erik M. Aurell, Ryoichi Kawai, Ketan Goyal

Abstract We present a derivation of the Feynman–Vernon approach to open quantum systems in the language of super-operators. We show that this gives a new and more direct derivation of the generating function of energy changes in a bath, or baths. As found previously, this generating function is given by a Feynman–Vernon-like influence functional, with only time shifts in the kernels coupling the forward and backward paths. We further show that the new approach extends to an-harmonic and possible non-equilibrium baths, provided that the interactions are bi-linear, and that the baths do not interact between themselves. Such baths are characterized by non-trivial cumulants. Every non-zero cumulant of certain environment correlation functions is thus a kernel in a higher-order term in the Feynman–Vernon action.

arXiv:1907.02671•Journal of Physics A Mathematical and Theoretical•May 12, 2020•21 citations

Two-Dimensional Spectroscopy for Harmonic Vibrational Modes with Nonlinear System-Bath Interactions. II. Gaussian-Markovian Case

Yoshitaka Tanimura, Thomas Steffen

The relaxation processes in a quantum system nonlinearly coupled to a harmonic Gaussian-Markovian heat bath are investigated by the quantum Fokker-Planck equation in the hierarchy form. This model describes frequency fluctuations in the quantum system with an arbitrary correlation time and thus bridges the gap between the Brownian oscillator model and the stochastic model by Anderson and Kubo. The effects of the finite correlation time and the system-bath coupling strength are studied for a harmonic model system by numerically integrating the equation of motion. The one-time correlation function of the system coordinate, which is measured in conventional Raman and infrared absorption experiments, already reflects the inhomogeneous character of the relaxation process. The finite correlation time of the frequency fluctuations, however, is directly evident only in the two- and three-time correlation function as probed by multidimensional spectroscopic techniques such as the Raman echo and the fifth-order 2D Raman experiment.

Journal of the Physical Society of Japan•Dec 15, 2000•75 citations

Nonperturbative expansion method for a quantum system coupled to a harmonic-oscillator bath

Yoshitaka Tanimura

A method to determine the resolvent of a quantum system coupled to a harmonic-oscillator bath is derived by extending the continued-fraction theory of a Gaussian-Markovian bath that has been presented by Tanimura and Kubo [J. Phys. Soc. Jpn. 58, 101 (1989)]. The results are expressed in terms of continued fractions and apply to an oscillator bath with a general spectral density, corresponding to colored noise, at various temperatures. Exact values of the resolvent can be calculated for arbitrary strength of the system-bath interaction by making use of the convergence properties of the continued fractions. For the weak-interaction case these results agree with the quantum master equation. The physical meaning of the results is also discussed by a diagrammatic method. As an application, the result of the Gaussian-Markovian system is extended to the case of the low-temperature bath. Correlated (unfactorized) initial conditions are also discussed.

Physical Review A•Jun 1, 1990•334 citations

Out of time ordered quantum dissipation

Bidisha Chakrabarty, Soumyadeep Chaudhuri, R. Loganayagam

Abstract We consider a quantum Brownian particle interacting with two harmonic baths, which is then perturbed by a cubic coupling linking the particle and the baths. This cubic coupling induces non-linear dissipation and noise terms in the influence functional/master equation of the particle. Its effect on the Out-of-Time-Ordered Correlators (OTOCs) of the particle cannot be captured by the conventional Feynman-Vernon formalism.We derive the generalised influence functional which correctly encodes the physics of OTO fluctuations, response, dissipation and decoherence. We examine an example where Markovian approximation is valid for the OTO dynamics. If the original cubic coupling has a definite time-reversal parity, the leading order OTO influence functional is completely determined by the couplings in the usual master equation via OTO generalisation of Onsager-Casimir relations. New OTO fluctuationdissipation relations connect the non-Gaussianity of the thermal noise to the thermal jitter in the damping constant of the Brownian particle.

arXiv:1811.01513•Journal of High Energy Physics•Jul 1, 2019•20 citations
Two-time correlation functions of physical operators of a system interacting with a heat bath producing a Gaussian-Markoffian noise are treated with the use of Feynman-Vernon's influence functional formalism. The Laplace transforms of correlation functions are shown to be expressed in terms of continued fractions of relevant hyperoperators. The result is valid to all orders of the system-bath interaction. In the limitation of motional narrowing, it reduces to those obtained in conventional methods.
A test system is assumed to interact with a heat bath consisting of harmonic oscillators or an equivalent bath with a proper frequency spectrum producing a Gaussian-Markoffian random perturbation. The effect of reaction of the test system to the bath is considered in the high temperature approximation. Elimination of the bath using the influence functional method of Feynman and Vernon yields a continuous fraction expression for the reduced density matrix of the test system. The result affords a basis to clarify the relationship between the stochastic and the dynamical approaches to treat the problem of partial destruction of quantum coherence of a system interacting with its environment.
A general formulation is given for the second order optical process of a three-level system in contact with a heat bath consisting of harmonic oscillators with a proper frequency spectrum producing a Markoffian random perturbation. Elimination of the bath using the influence functional method of Feynman and Vernon yields a continuous fraction expression and the result affords a basis to clarify the relation between the stochastic and dynamical approaches to treat the partial destruction of the quantum coherence of the optical process. As an example, a three-level system with intermediate-state interaction is treated in some detail.
Abstract We present a derivation of the Feynman–Vernon approach to open quantum systems in the language of super-operators. We show that this gives a new and more direct derivation of the generating function of energy changes in a bath, or baths. As found previously, this generating function is given by a Feynman–Vernon-like influence functional, with only time shifts in the kernels coupling the forward and backward paths. We further show that the new approach extends to an-harmonic and possible non-equilibrium baths, provided that the interactions are bi-linear, and that the baths do not interact between themselves. Such baths are characterized by non-trivial cumulants. Every non-zero cumulant of certain environment correlation functions is thus a kernel in a higher-order term in the Feynman–Vernon action.
The relaxation processes in a quantum system nonlinearly coupled to a harmonic Gaussian-Markovian heat bath are investigated by the quantum Fokker-Planck equation in the hierarchy form. This model describes frequency fluctuations in the quantum system with an arbitrary correlation time and thus bridges the gap between the Brownian oscillator model and the stochastic model by Anderson and Kubo. The effects of the finite correlation time and the system-bath coupling strength are studied for a harmonic model system by numerically integrating the equation of motion. The one-time correlation function of the system coordinate, which is measured in conventional Raman and infrared absorption experiments, already reflects the inhomogeneous character of the relaxation process. The finite correlation time of the frequency fluctuations, however, is directly evident only in the two- and three-time correlation function as probed by multidimensional spectroscopic techniques such as the Raman echo and the fifth-order 2D Raman experiment.
A method to determine the resolvent of a quantum system coupled to a harmonic-oscillator bath is derived by extending the continued-fraction theory of a Gaussian-Markovian bath that has been presented by Tanimura and Kubo [J. Phys. Soc. Jpn. 58, 101 (1989)]. The results are expressed in terms of continued fractions and apply to an oscillator bath with a general spectral density, corresponding to colored noise, at various temperatures. Exact values of the resolvent can be calculated for arbitrary strength of the system-bath interaction by making use of the convergence properties of the continued fractions. For the weak-interaction case these results agree with the quantum master equation. The physical meaning of the results is also discussed by a diagrammatic method. As an application, the result of the Gaussian-Markovian system is extended to the case of the low-temperature bath. Correlated (unfactorized) initial conditions are also discussed.
Abstract We consider a quantum Brownian particle interacting with two harmonic baths, which is then perturbed by a cubic coupling linking the particle and the baths. This cubic coupling induces non-linear dissipation and noise terms in the influence functional/master equation of the particle. Its effect on the Out-of-Time-Ordered Correlators (OTOCs) of the particle cannot be captured by the conventional Feynman-Vernon formalism.We derive the generalised influence functional which correctly encodes the physics of OTO fluctuations, response, dissipation and decoherence. We examine an example where Markovian approximation is valid for the OTO dynamics. If the original cubic coupling has a definite time-reversal parity, the leading order OTO influence functional is completely determined by the couplings in the usual master equation via OTO generalisation of Onsager-Casimir relations. New OTO fluctuationdissipation relations connect the non-Gaussianity of the thermal noise to the thermal jitter in the damping constant of the Brownian particle.