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Quantum Langevin equation [PDF]

open access: yesPhysical Review A, 1988
The macroscopic description of a quantum particle with passive dissipation and moving in an arbitrary external potential is formulated in terms of the generalized Langevin equation. The coupling with the heat bath corresponds to two terms: a mean force characterized by a memory function \ensuremath{\mu}(t) and an operator-valued random force.
, Ford, , Lewis, , O'Connell
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Langevin Equation

open access: yes, 2013
The Langevin equation was proposed in 1908 by Paul Langevin, to describe Brownian motion, that is the apparently random movement of a particle immersed in a fluid, due to its collisions with the much smaller fluid molecules. As the Reynolds number of this movement is very low, the drag force is proportional to the particle velocity; this, so called ...
MAURI, ROBERTO, Roberto Mauri
core   +3 more sources

The langevin equation of weak turbulence

Annals of Physics, 1971
Abstract The hieraichy equations describing weakly interacting waves in a fluid are solved by the method of characteristic functionals, combined with the time asymptotic method of Bogoliubov and Mitropolski. The result to lowest nontrivial order allows one to characterize the stochastic state of the fluid in close analogy to the Brownian motion of a ...
Elsässer, K., Gräff, P.
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The Langevin and generalized Langevin equations

2023
Abstract In Chapter 15, stochastic equations of motion, specifically the Langevin and generalized Langevin equations, are discussed as a means of generating classical ensemble distributions and generating dynamical quantities of systems coupled to harmonic baths.
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Langevin Equations

2014
Abstract In this chapter, Langevin equations (or Ito stochastic differential equations, SDEs) are derived that are equivalent to Fokker–Planck equations for bosons and fermions. The approach involves replacing modal phase space variables by stochastic phase space variables satisfying Ito SDEs containing c-number Wiener stochastic ...
Bryan J. Dalton   +2 more
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The Langevin Equation

2021
While you are reading this thesis, at every instant of time countless particles of the surrounding air hit your skin due to their irregular thermal motion. There are of the order of \({\sim } 10^{23}\) molecules in every liter of air [1, 2].
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