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 E

Directed motion in a periodic potential of a quantum system coupled to a heat bath driven by a colored noise

Satyabrata Bhattacharya, Pinaki Chaudhury, Sudip Chattopadhyay, Jyotipratim Ray Chaudhuri

Published Aug 18, 2008• 10 citations
Publisher

Abstract

A system-reservoir nonlinear coupling model is proposed for a quantum system when the associated bath is not in thermal equilibrium but is modulated by an external colored noise, to present a microscopic approach to quantum state-dependent diffusion and multiplicative noise in terms of a quantum Langevin description. Consequently, the Fokker-Planck equation in position space, valid in the overdamped limit, for multiplicative colored noise is constructed to explore the possibility of observing a quantum current and dependence of the current on various parameters of external noise is examined.

DOI
10.1103/physreve.78.021123

Related papers

Phase induced current in presence of nonequilibrium bath: A quantum approach

Satyabrata Bhattacharya, Pinaki Chaudhury, Sudip Chattopadhyay +1 more

Based on a system-reservoir nonlinear coupling model, where the associated bath is externally driven by a fluctuating force, we present a microscopic approach to quantum state-dependent diffusion and multiplicative noises in terms of a quantum (Markovian) Langevin equation in overdamped limit when the associated bath is in nonequilibrium state. We then explore the possibility of observing a quantum current when the bath is modulated by white noise, the phenomena which is absent in the classical regime.

The Journal of Chemical Physics•Sep 25, 2008•4 citations

The quantum rate of escape from a metastable state non-linearly coupled to a heat bath driven by external colored noise

Pulak K. Ghosh, Jyotipratim Ray Chaudhuri

We have studied the quantum stochastic dynamics of a system whose interaction with a reservoir is non-linear in system coordinates. In addition, the bath particles are driven by external noise with finite correlation. The effects of the space dependent friction and correlation of the external noise on the rate of decay of a particle from a metastable well have been examined. At a critical value of the correlation, the variation of the quantum decay rate versus the external noise strength exhibits a resonance.

Journal of Statistical Mechanics Theory and Experiment•Feb 28, 2008•1 citation

External-noise-driven bath and the generalized semiclassical Kramers theory

Pradipta Ghosh, Anindita Shit, Sudip Chattopadhyay +1 more

We address the issue of a system that has been tacitly made thermodynamically open by externally driving the associated heat bath in an attempt to gain better insight regarding many physical situations that are akin to this problem. This work embodies the study of the quantum effects in the rate of decay from a metastable state of a Brownian particle which is in contact with a correlated noise-driven bath. We do this by initiating from a suitable system-reservoir model to derive the operator-valued Langevin equation. This further leads us to the corresponding c-number analog that includes quantum effects in leading order. Suitable mathematical treatment culminates in the quantum Fokker-Planck equation, the solution to which yields the rate expression. Finally, we put this to thorough numerical analysis.

Physical Review E•Oct 14, 2010•2 citations

Localization, dynamical correlations, and the effect of colored noise on coherence

Doron Cohen

Localization in the quantum-kicked-rotator problem leads to nontrivial dynamical correlations that are absent in the classical limit. Consequently, both coherence and diffusion in the presence of colored noise depend on its long-range autocorrelations. This implies that a Markovian treatment of the dynamics for a system that is coupled to a low-temperature heat bath is not valid even if the system is classically chaotic.

Physical Review Letters•Oct 7, 1991•24 citations

Master Langevin equations: Origin of asymptotic diffusion

Claudio Oscar Dorso, E. Susana Hernández, José Luis Vega

We extend the master-equation treatment of dynamical evolution of a system-plus-reservoir configuration including the propagation of initial correlations as a noise source. Specializing into the quantum harmonic oscillator coupled to a fermionic heat bath, we develop a model for the diffusion matrix in the space of diagonal density operators. It can be shown that mean values of observables undergo Langevin-like motion and, in particular, that the mean value and dispersion of the oscillator quanta approach the canonical equilibrium values. A final interpretation of the characteristics and role of the noise source is given.

Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics•Jan 1, 1993•6 citations

Fokker-Planck description of stochastic processes with colored noise

Paolo Grigolini A, Luigi A. Lugiato, R. Mannella +3 more

A detailed theoretical discussion is presented of the effect of colored noise on nonlinear dynamical systems. The ideas arising from it are applied to a particular example of such a system: a model of dispersive optical bistability, considered in the contexts of both additive and multiplicative forcing. Analogue experiments and digital simulation techniques are used to explore the applicability and range of validity of theories proposed to date. The physical phenomenon of bimodality induced by the finite bandwidth (alone) of additive forcing is demonstrated in detail for the first time. The three existing theories capable of accounting for this phenomenon can each be categorized in terms of a single (constant) value of a characteristic parameter ${P}_{\mathrm{expt}}$; but it is shown that, in reality, ${P}_{\mathrm{expt}}$ varies weakly with the correlation time \ensuremath{\tau} of the noise. The variation of ${P}_{\mathrm{expt}}$ with \ensuremath{\tau} is investigated in the currently accessible range of 0.1\ensuremath{\le}\ensuremath{\tau}\ensuremath{\le}\ensuremath{\infty}. .AE

Physical Review A•Aug 1, 1988•25 citations
A system-reservoir nonlinear coupling model is proposed for a quantum system when the associated bath is not in thermal equilibrium but is modulated by an external colored noise, to present a microscopic approach to quantum state-dependent diffusion and multiplicative noise in terms of a quantum Langevin description. Consequently, the Fokker-Planck equation in position space, valid in the overdamped limit, for multiplicative colored noise is constructed to explore the possibility of observing a quantum current and dependence of the current on various parameters of external noise is examined.
Based on a system-reservoir nonlinear coupling model, where the associated bath is externally driven by a fluctuating force, we present a microscopic approach to quantum state-dependent diffusion and multiplicative noises in terms of a quantum (Markovian) Langevin equation in overdamped limit when the associated bath is in nonequilibrium state. We then explore the possibility of observing a quantum current when the bath is modulated by white noise, the phenomena which is absent in the classical regime.
We have studied the quantum stochastic dynamics of a system whose interaction with a reservoir is non-linear in system coordinates. In addition, the bath particles are driven by external noise with finite correlation. The effects of the space dependent friction and correlation of the external noise on the rate of decay of a particle from a metastable well have been examined. At a critical value of the correlation, the variation of the quantum decay rate versus the external noise strength exhibits a resonance.
We address the issue of a system that has been tacitly made thermodynamically open by externally driving the associated heat bath in an attempt to gain better insight regarding many physical situations that are akin to this problem. This work embodies the study of the quantum effects in the rate of decay from a metastable state of a Brownian particle which is in contact with a correlated noise-driven bath. We do this by initiating from a suitable system-reservoir model to derive the operator-valued Langevin equation. This further leads us to the corresponding c-number analog that includes quantum effects in leading order. Suitable mathematical treatment culminates in the quantum Fokker-Planck equation, the solution to which yields the rate expression. Finally, we put this to thorough numerical analysis.
We extend the master-equation treatment of dynamical evolution of a system-plus-reservoir configuration including the propagation of initial correlations as a noise source. Specializing into the quantum harmonic oscillator coupled to a fermionic heat bath, we develop a model for the diffusion matrix in the space of diagonal density operators. It can be shown that mean values of observables undergo Langevin-like motion and, in particular, that the mean value and dispersion of the oscillator quanta approach the canonical equilibrium values. A final interpretation of the characteristics and role of the noise source is given.
A detailed theoretical discussion is presented of the effect of colored noise on nonlinear dynamical systems. The ideas arising from it are applied to a particular example of such a system: a model of dispersive optical bistability, considered in the contexts of both additive and multiplicative forcing. Analogue experiments and digital simulation techniques are used to explore the applicability and range of validity of theories proposed to date. The physical phenomenon of bimodality induced by the finite bandwidth (alone) of additive forcing is demonstrated in detail for the first time. The three existing theories capable of accounting for this phenomenon can each be categorized in terms of a single (constant) value of a characteristic parameter Pexpt{P}_{\mathrm{expt}}Pexpt​; but it is shown that, in reality, Pexpt{P}_{\mathrm{expt}}Pexpt​ varies weakly with the correlation time \ensuremath{\tau} of the noise. The variation of Pexpt{P}_{\mathrm{expt}}Pexpt​ with \ensuremath{\tau} is investigated in the currently accessible range of 0.1\ensuremath{\le}\ensuremath{\tau}\ensuremath{\le}\ensuremath{\infty}. .AE