Non-ideal Brownian motion, generalized Langevin Equation and its application to the security market

1996 ◽  
Vol 3 (2) ◽  
pp. 87-119 ◽  
Author(s):  
Masafumi Takahashi
Keyword(s):  
Brownian Motion ◽  
Langevin Equation ◽  
Generalized Langevin Equation ◽  
Security Market

scholarly journals Composite generalized Langevin equation for Brownian motion in different hydrodynamic and adhesion regimes

2015 ◽  
Vol 91 (5) ◽  
Author(s):  
Hsiu-Yu Yu ◽  
David M. Eckmann ◽  
Portonovo S. Ayyaswamy ◽  
Ravi Radhakrishnan
Keyword(s):  
Brownian Motion ◽  
Langevin Equation ◽  
Generalized Langevin Equation

scholarly journals A path integral approach to the Langevin equation

2015 ◽  
Vol 30 (07) ◽  
pp. 1550028 ◽  
Author(s):  
Ashok K. Das ◽  
Sudhakar Panda ◽  
J. R. L. Santos
Keyword(s):  
Brownian Motion ◽  
Path Integral ◽  
Langevin Equation ◽  
Correlation Functions ◽  
Free Particle ◽  
Transition Amplitude ◽  
Planck Equation ◽  
Markovian Process ◽  
Integral Approach ◽  
Generalized Langevin Equation

We study the Langevin equation with both a white noise and a colored noise. We construct the Lagrangian as well as the Hamiltonian for the generalized Langevin equation which leads naturally to a path integral description from first principles. This derivation clarifies the meaning of the additional fields introduced by Martin, Siggia and Rose in their functional formalism. We show that the transition amplitude, in this case, is the generating functional for correlation functions. We work out explicitly the correlation functions for the Markovian process of the Brownian motion of a free particle as well as for that of the non-Markovian process of the Brownian motion of a harmonic oscillator (Uhlenbeck–Ornstein model). The path integral description also leads to a simple derivation of the Fokker–Planck equation for the generalized Langevin equation.

scholarly journals Bose polaron as an instance of quantum Brownian motion

Quantum ◽  
2017 ◽  
Vol 1 ◽  
pp. 30 ◽  
Author(s):  
Aniello Lampo ◽  
Soon Hoe Lim ◽  
Miguel Ángel García-March ◽  
Maciej Lewenstein
Keyword(s):  
Brownian Motion ◽  
Langevin Equation ◽  
Degrees Of Freedom ◽  
Interaction Strength ◽  
Einstein Condensate ◽  
Generalized Langevin Equation ◽  
Quantum Gas ◽  
Quantum Brownian Motion ◽  
Bose Einstein Condensate ◽  
Bose Einstein

We study the dynamics of a quantum impurity immersed in a Bose-Einstein condensate as an open quantum system in the framework of the quantum Brownian motion model. We derive a generalized Langevin equation for the position of the impurity. The Langevin equation is an integrodifferential equation that contains a memory kernel and is driven by a colored noise. These result from considering the environment as given by the degrees of freedom of the quantum gas, and thus depend on its parameters, e.g. interaction strength between the bosons, temperature, etc. We study the role of the memory on the dynamics of the impurity. When the impurity is untrapped, we find that it exhibits a super-diffusive behavior at long times. We find that back-flow in energy between the environment and the impurity occurs during evolution. When the particle is trapped, we calculate the variance of the position and momentum to determine how they compare with the Heisenberg limit. One important result of this paper is that we find position squeezing for the trapped impurity at long times. We determine the regime of validity of our model and the parameters in which these effects can be observed in realistic experiments.

Brownian Motion of a Rayleigh Particle Confined in a Channel: A Generalized Langevin Equation Approach

2014 ◽  
Vol 158 (5) ◽  
pp. 1100-1125 ◽  
Author(s):  
Changho Kim ◽  
George Em Karniadakis
Keyword(s):  
Brownian Motion ◽  
Langevin Equation ◽  
Generalized Langevin Equation ◽  
Equation Approach

scholarly journals The study of dynamic singularities of seismic signals by the generalized Langevin equation

2009 ◽  
Vol 388 (17) ◽  
pp. 3629-3635 ◽  
Author(s):  
Renat Yulmetyev ◽  
Ramil Khusnutdinoff ◽  
Timur Tezel ◽  
Yildiz Iravul ◽  
Bekir Tuzel ◽  
...  
Keyword(s):  
Langevin Equation ◽  
Generalized Langevin Equation ◽  
Seismic Signals

A note on the fluctuation–dissipation relation for the generalized Langevin equation with hydrodynamic backflow

2016 ◽  
Vol 380 (33) ◽  
pp. 2561-2564 ◽  
Author(s):  
Jana Tóthová ◽  
Vladimír Lisý
Keyword(s):  
Langevin Equation ◽  
Generalized Langevin Equation ◽  
Fluctuation Dissipation

Generalized Langevin Equation

2019 ◽  
pp. 247-300
Author(s):  
Trifce Sandev ◽  
Živorad Tomovski
Keyword(s):  
Langevin Equation ◽  
Generalized Langevin Equation
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