Results 181 to 190 of about 4,324 (212)

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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The generalized Langevin equation

Journal of Physics A: General Physics, 1972
The simple Langevin equation describes a process which is both Markovian and Gaussian. A generalization of the Langevin equation allows us to deal with processes which are projections of n-dimensional Gaussian- Markov processes. The results are formally equivalent to generalizations proposed by Kubo in 1966 provided the second fluctuation-dissipation ...
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Generalized Langevin Equations

2013
We now turn to problems in statistical mechanics where the assumption of thermal equilibrium does not apply. In nonequilibrium problems, one should in principle solve the full Liouville equation, at least approximately. There are many situations in which one attempts to do that under different assumptions and conditions, giving rise to the Euler and ...
Alexandre J. Chorin, Ole H. Hald
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Generalized Langevin Equation

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 Generalized Langevin Equation

2020
The shortcomings of the Langevin model, involving the simultaneous requirements of causality and stationarity, have already been discussed in the preceding chapters. In this final chapter, we return to these considerations. A generalization of the Langevin equation, involving a memory kernel for the frictional force on the tagged particle and ...
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Generalized Langevin equation and recurrence relations

Physical Review E, 2000
The generalized Langevin equation (GLE) is a reformulation of the Heisenberg equation of motion, and hence, an exact equation. It is the basis of the memory function approach, a very widely used method for studying dynamics of classical and quantum fluids. The GLE was first derived by Mori in a very formal way.
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Generalized Langevin Equations

2012
Diese Arbeit ist wie folgt aufgebaut: Das erste Kapitel stellt verallgemeinerte Langevingleichungen als eine Familie von stochastischen Differential-Integralgleichungen vor, die mittels des Zwanzigschen Projektionsformalismus gewonnen werden. Ausgangspunkt ist ein statistisch-mechanisches Modell, das die Wechselwirkung eines makroskopischen Systems mit
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Fractional Generalized Langevin Equation

2019
FGLEs are generalizations of the GLE where the integer order derivatives is substituted by fractional derivatives. Recently, some GLE models for a particle driven by single or multiple fractional Gaussian noise have been investigated in order to describe generalized diffusion processes, such as accelerating and retarding diffusion.
Trifce Sandev, Živorad Tomovski
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Nonlinear generalized Langevin equations

Journal of Statistical Physics, 1973
Exact generalized Langevin equations are derived for arbitrarily nonlinear systems interacting with specially chosen heat baths. An example is displayed in which the Langevin equation is nonlinear but approximately Markovian.
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On the equivalence of generalized Langevin equation and generalized master equation

Zeitschrift f�r Physik B Condensed Matter and Quanta, 1977
It is shown that the generalized Langevin equation derived by Mori is equivalent to the generalized master equation of Nakajima and Zwanzig. Both equations of motion are related, just in the same way as Heisenberg and Schrodinger picture are related.
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