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Numerical Generation of Trajectories Statistically Consistent with Stochastic Differential Equations. [PDF]
Entropy (Basel)Evstigneev M.
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Physical 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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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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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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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 and generalized Langevin equations
2023Abstract 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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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 ...
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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 ...
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Generalized Langevin Equations
The Journal of Chemical Physics, 1971A derivation is presented for a generalized Langevin equation of motion for a dynamical variable φ(R(t), P(t)) where R and P are the position and momentum of a single heavy particle in a bath of light particles. A detailed analysis is given for the conditions required for the validity of the equation.
J. Albers, J. M. Deutch, Irwin Oppenheim
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Physical Review Letters, 1981
It is shown (by means of a perturbation series) that for a class of potentials $V(x)$ the stationary distribution of the solution $x(t)$ of the quantum Langevin equation approaches in the weak-coupling limit ($f\ensuremath{\rightarrow}0$) the quantum mechanical canonical distribution of the displacement of the oscillator, subject to the potential $V(x)$
Rafael Benguria, Mark Kac
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It is shown (by means of a perturbation series) that for a class of potentials $V(x)$ the stationary distribution of the solution $x(t)$ of the quantum Langevin equation approaches in the weak-coupling limit ($f\ensuremath{\rightarrow}0$) the quantum mechanical canonical distribution of the displacement of the oscillator, subject to the potential $V(x)$
Rafael Benguria, Mark Kac
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2019
The Langevin equation is connected to the Brownian motion formulated by Einstein and Smoluchowski. The Langevin equation for a free particle with mass m is given by Langevin (CR Acad Sci Paris 146:530, 1908)
Trifce Sandev, Živorad Tomovski
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The Langevin equation is connected to the Brownian motion formulated by Einstein and Smoluchowski. The Langevin equation for a free particle with mass m is given by Langevin (CR Acad Sci Paris 146:530, 1908)
Trifce Sandev, Živorad Tomovski
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