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

The European Physical Journal A

Exact generalized Fokker-Planck equation for arbitrary dissipative and nondissipative quantum-systems

Hermann Haken

Published Oct 1, 1969• 35 citations
Publisher
DOI
10.1007/bf01400819

Related papers

Exact generalized Fokker-Planck equation for arbitrary dissipative quantum systems

Hermann Haken

Physics Letters A•Dec 1, 1968•2 citations

Generalized Fokker-Planck equation for quantum systems

V. G. Morozov

Theoretical and Mathematical Physics•Sep 1, 1981•5 citations

Exact solutions of Fokker-Planck equations associated to quantum wave functions

Nicola Cufaro Petroni, S. De Martino, Silvio De Siena

Physics Letters A•Aug 1, 1998•29 citations

Quantum probability distributions in the early Universe. I. Equilibrium properties of the Wigner equation

Frank R. Graziani

This is the first in a series of papers dealing with quantum or Wigner probability distributions and the dynamics of early-Universe phase transitions. In this paper we argue that the inflaton field (a real gauge-singlet scalar field) when spatially averaged over a causal horizon behaves as if it were a dissipative quantum-mechanical system in one dimension. Realizing that the mathematical phase-space or stochastic description of Wigner is the only consistent way to describe these systems and still preserve the canonical commutation relations we devote this paper to investigating various properties of the Wigner formalism. This framework rests on the quasiprobability distribution and its evolution equation: a generalized Fokker-Planck equation. We first show that this generalized Fokker-Planck equation is equivalent to Schr\"odinger's equation for nondissipative pure states. We then show how one computes ground-state energies within this formalism (for nondissipative systems) by calculating ground-state energy levels for a variety of anharmonic potentials. Finally we compute the quantum-mechanical effective potential in one dimension to order g\ensuremath{\Elzxh}.

Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields•Aug 15, 1988•24 citations

Quantum dynamics for dissipative systems: A numerical study of the Wigner–Fokker–Planck equation

Shesheng Zhang, Eli Pollak

A study is provided of dynamics and dissipative tunneling in a symmetric quartic double well potential. The numerical solution for the position autocorrelation function obtained through the Wigner–Fokker–Planck equation is compared with numerically exact results of Stockburger and Mak [J. Chem. Phys. 110, 4983 (1999)]. We find that the Wigner–Fokker–Planck dynamics agree well with the numerically exact computations, they account for both quantum coherences as well as quantum tunneling phenomena. This, in contrast to the mixed quantum classical approximation, which does not perform as well.

The Journal of Chemical Physics•Feb 25, 2003•35 citations

The Fokker-Planck equation for relaxation of a system of two dipole-dipole interacting atoms

Victor A. Mikhailov, Nikolay V. Troshkin, Anton M. Trunin

The relaxation of a pair of dipole-dipole interacting two-level atoms with parallel dipole moments in a large dissipative system is studied on the basis of the generalized coherent states method. The Fokker-Planck equation and its exact solution are obtained. Explicit formulas for two-time correlation functions are given. The influence of the magnitude of the interaction on the shape of the radiation line is investigated.

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Apr 21, 2016•1 citation
This is the first in a series of papers dealing with quantum or Wigner probability distributions and the dynamics of early-Universe phase transitions. In this paper we argue that the inflaton field (a real gauge-singlet scalar field) when spatially averaged over a causal horizon behaves as if it were a dissipative quantum-mechanical system in one dimension. Realizing that the mathematical phase-space or stochastic description of Wigner is the only consistent way to describe these systems and still preserve the canonical commutation relations we devote this paper to investigating various properties of the Wigner formalism. This framework rests on the quasiprobability distribution and its evolution equation: a generalized Fokker-Planck equation. We first show that this generalized Fokker-Planck equation is equivalent to Schr\"odinger's equation for nondissipative pure states. We then show how one computes ground-state energies within this formalism (for nondissipative systems) by calculating ground-state energy levels for a variety of anharmonic potentials. Finally we compute the quantum-mechanical effective potential in one dimension to order g\ensuremath{\Elzxh}.
A study is provided of dynamics and dissipative tunneling in a symmetric quartic double well potential. The numerical solution for the position autocorrelation function obtained through the Wigner–Fokker–Planck equation is compared with numerically exact results of Stockburger and Mak [J. Chem. Phys. 110, 4983 (1999)]. We find that the Wigner–Fokker–Planck dynamics agree well with the numerically exact computations, they account for both quantum coherences as well as quantum tunneling phenomena. This, in contrast to the mixed quantum classical approximation, which does not perform as well.