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On the derivation of the generalized Langevin equation and the fluctuation-dissipation theorem
Europhysics letters, 2022The generalized Langevin equation is widely used to model the effective dynamics of chemical, soft or biological systems. It is used to describe the evolution of a small number of collective variables, and is derived using the projection operator ...
Hadrien Vroylandt
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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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International Journal of Computational Mathematics, 2020
Fractional Langevin equation describes the evolution of physical phenomena in fluctuating environments for the complex media systems. It is a sequential fractional differential equation with two fractional orders involving a memory kernel, which leads to
Hossein Fazli +2 more
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Fractional Langevin equation describes the evolution of physical phenomena in fluctuating environments for the complex media systems. It is a sequential fractional differential equation with two fractional orders involving a memory kernel, which leads to
Hossein Fazli +2 more
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Fractional Langevin equation with anti-periodic boundary conditions
Chaos, Solitons and Fractals, 2018Hossein Fazli, Juan J Nieto
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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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Generalized Langevin Equation as a Model for Barrier Crossing Dynamics in Biomolecular Folding.
Journal of Physical Chemistry B, 2019Conformational memory in single-molecule dynamics has attracted recent attention and, in particular, has been invoked as a possible explanation of some of the intriguing properties of transition paths observed in single-molecule force spectroscopy (SMFS)
Rohit Satija, D. Makarov
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Nonlinear impulsive Langevin equation with mixed derivatives
Mathematical methods in the applied sciences, 2019In this paper, we consider a nonlocal boundary value problem of nonlinear impulsive Langevin equation with mixed derivatives. Some sufficient conditions are constructed to observe the existence, uniqueness, and generalized Ulam‐Hyers‐Rassias stability of
Rizwan Rizwan, A. Zada
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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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