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	Talk:Langevin equation - Wikipedia, the free encyclopedia
		Having looked around I've realised that the term Langevin equation is more specific than just an SDE in physics, although it is sometimes used in that way.
		Thus I've moved some of the more general info I added a while back to a new article stochastic differential equations, as I feel that the two things warrant seperation.
		Another form of the Langevin used in Statistical mechanics ignores inertial accelerations like ma, and instead approximate the velocity of the suspended particles as having a velocity that is linearly related to the forces acting upon the particle.
	en.wikipedia.org /wiki/Talk:Langevin_equation (275 words)

	8.5 The Einstein-Langevin equation
		This equation depicts the stochastic evolution of the perturbations of the fl hole under the influence of the fluctuations of the thermal scalar field.
		Note that this differential stochastic equation includes a non-local term responsible for the dissipation of the gravitational field and a noise source term which accounts for the fluctuations of the quantum field.
		As we have seen before and here, the Einstein-Langevin equation is a dynamical equation governing the dissipative evolution of the gravitational field under the influence of the fluctuations of the quantum field, which, in the case of fl holes, takes the form of thermal radiance.
	univie.ac.at /EMIS/journals/LRG/Articles/lrr-2004-3/articlesu22.html (388 words)

	Information Bridge: DOE Scientific and Technical Information (Site not responding. Last check: 2007-10-08)
		This model is based on a Langevin equation of motion for a fluid particle, and assumes the fluid vertical velocity probability distribution is skewed and spatially homogeneous.
		The constraint that spatial and velocity distributions of a well-mixed tracer must be the same as those of the fluid, was used to develop the Langevin equation models and the reflection boundary conditions.
		The two Langevin equation models and three reflection methods were successfully tested using cases for which exact, analytic statistical properties of particle velocity and position are known, including well-mixed spatial and velocity distributions.
	www.osti.gov /bridge/product.biblio.jsp?osti_id=2392 (354 words)

	6.3 The Einstein-Langevin equation
		These equations can now be renormalized, that is, we can now write the bare coupling constants as renormalized coupling constants plus some suitably chosen counterterms, and take the limit
		In order to carry out such a procedure, it is convenient to distinguish between massive and massless scalar fields.
		The Einstein-Langevin equations for this particular case (and generalized to a spatially flat Robertson-Walker background) were first obtained in [58
	univie.ac.at /EMIS/journals/LRG/Articles/lrr-2004-3/articlesu11.html (528 words)

	Supersymmetry in Stochastic Processes with Higher-Order Time Derivatives
		Note that the discretized Langevin equation is assumed to be causal, meaning that given the initial value of the stochastic variable
		Once we have transformed Kramers' process into a system of coupled first-order Langevin equations (11) and (10) which is a trivial extension of the first-order equation (1) to a matrix form, there obviously exists a path integral representation analogous to (6).
		Inserting the stochastic equations (10) and (11) into the exponent of (12), we repeat the previous procedure and, choosing midpoint slicing with a=1/2 à la Stratonovich, we obtain the path integral representation of the generating functional
	www.physik.fu-berlin.de /~kleinert/kleiner_re256/k.html (2486 words)

	Langevin Equation
		Langevin equation describes system with white noise acting on
		The large time limit could be obtained from the Wiener equation
		White noise in Wiener equation is the consequence of the averaging out a fast process--in our case, velocity relaxation!
	www.plmsc.psu.edu /~www/matsc597c-1997/fluctuations/Lecture9/node1.html (69 words)

	CompSim homework 2 (Site not responding. Last check: 2007-10-08)
		The time-step dt must be chosen small enough that the approximate first-order equation is accurate.
		Solve the equation for the MSD analytically and compare with the simulated result for, say, 103, 104, 105 and 106 steps.
		The Langevin equation can be used to simulate the escape of a particle from such a potential well as a model of a molecular bond breaking.
	www.mpikg-golm.mpg.de /theory/people/julian/CompSim/Homework2.htm (412 words)

	Back reaction in semiclassical cosmology: The Einstein-Langevin equation (Site not responding. Last check: 2007-10-08)
		Using the influence functional formalism we show how to derive a generalized Einstein equation in the form of a Langevin equation for the description of the backreaction of quantum fields and their fluctuations on the dynamics of curved spacetimes.
		This approach based on statistical field theory extends the conventional theory of semiclassical gravity based on a semiclassical Einstein equation with a source given by the average value of the energy momentum tensor, thus making it possible to probe into the statistical properties of quantum fields like noise, fluctuations, entropy, decoherence and dissipation.
		Recognition of the stochastic nature of semiclassical gravity is an essential step towards the investigation of the behavior of fluctuations, instability and phase transition processes associated with the crossover to quantum gravity.
	www.physics.adelaide.edu.au /mathphysics/abstracts/gr-qc-9403043.html (253 words)

	Citebase - A stochastic golden rule and quantum Langevin equation for the low density limit
		Authors: Accardi, L. Pechen, A. Volovich, I. A rigorous derivation of quantum Langevin equation from microscopic dynamics in the low density limit is given.
		We formulate a mathematical procedure (the so-called stochastic golden rule) which allows us to determine the quantum Langevin equation in the limit of large time and small density of particles of the reservoir.
		A new derivation of quantum stochastic differential equation for the evolution operator in the low density limit is presented.
	www.citebase.org /cgi-bin/citations?id=oai:arXiv.org:math-ph/0206032 (853 words)

	Complex Langevin Equation and the Many-fermion Problem (Site not responding. Last check: 2007-10-08)
		An alternative approach to calculating expectation values in quantum many-body systems is the well-known stochastic quantization procedure, which can be extended to the case of negative and even complex probability distributions.
		In this case, the formulation of the problem in terms of a complex action does not pose any a priori problems, and the complex Langevin equation can be used to find expectation values in the space of complex auxiliary fields.
		We show how the complex Langevin method can give reliable results for cases that are intractable by the Monte-Carlo method, and demonstrate the convergence of the method by comparing to the exact results.
	www.krl.caltech.edu /~adami/langevin.html (408 words)

	Citebase - On the semiclassical Einstein-Langevin equation
		The Einstein-Langevin equation is explicitly solved around one of the simplest solutions of semiclassical gravity: Minkowski spacetime with a conformal scalar field in its vacuum state.
		This theory generalizes the semiclassical Einstein equation to an Einstein-Langevin equation with a stochastic source term arising from the fluctuations of the...
		Semiclassical Einstein-Langevin equations for arbitrary small metric perturbations conformally coupled to a massless quantum scalar field in a spatially flat cosmological background are derived.
	citebase.eprints.org /cgi-bin/citations?id=oai:arXiv.org:gr-qc/9811070 (976 words)

	THE LANGEVIN EQUATION (Site not responding. Last check: 2007-10-08)
		This volume is the second edition of the first-ever elementary book on the Langevin equation method for the solution of problems involving the Brownian motion in a potential, with emphasis on modern applications in the natural sciences, electrical engineering and so on.
		It has been substantially enlarged to cover in a succinct manner a number of new topics, such as anomalous diffusion, continuous time random walks, stochastic resonance etc, which are of major current interest in view of the large number of disparate physical systems exhibiting these phenomena.
		“This is a timely update of the theory and applications of the Langevin equation, which skillfully combines the elementary approaches with most recent developments such as anomalous diffusion and fractional kinetics.
	www.worldscibooks.com /physics/5343.html (471 words)

	The generalized Langevin equation (Site not responding. Last check: 2007-10-08)
		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.
		Molecular motion in liquids is discussed in general terms and it is concluded that these generalizations of the Langevin equation are not likely to be successful.
	stacks.iop.org /0305-4470/5/1312 (211 words)

	No Title
		Langevin approach gives rise to stochastic differential equation.
		For additive white Gaussian noise Langevin equation equivalent to Fokker-Planck equation.
		Can transform equation with Ito interpretation into one with Stratanovich interpretation or vice versa.
	www.physics.ubc.ca /~birger/lect9 (270 words)

	Application of Langevin Equation in Econometrics to the Interaction between the Exchange Rates of Japan and South Korea
		Application of Langevin Equation in Econometrics to the Interaction between the Exchange Rates of Japan and South Korea
		This articles presents and application of statistical physics to economic relationships, based on the fluctuation-dissipation theorem and the anomalous fluctuation therorem, and the Langevin equation.
		In the framework of time series which follow the Langevin equation, the interaction of two time series can be treated.
	ideas.repec.org /a/eaa/aeinde/v3y2003i3_17.html (224 words)

	Amazon.com: The Langevin Equation: With Applications to Stochastic Problems in Physics, Chemistry and Electrical ... (Site not responding. Last check: 2007-10-08)
		Amazon.com: The Langevin Equation: With Applications to Stochastic Problems in Physics, Chemistry and Electrical Engineering (World Scientific Series in Contemporary Chemical Physics Vol.
		The Langevin Equation: With Applications to Stochastic Problems in Physics, Chemistry and Electrical Engineering (World Scientific Series in Contemporary Chemical Physics Vol.
		A timely update of the theory and applications of the Langevin equation.
	www.amazon.com /exec/obidos/tg/detail/-/9812384626?v=glance (568 words)

	Citebase - Berry phase in open quantum systems: a quantum Langevin equation approach
		Berry phase in open quantum systems: a quantum Langevin equation approach
		The evolution of a two level system with a slowly varying Hamiltonian, modeled as s spin 1/2 in a slowly varying magnetic field, and interacting with a quantum environment, modeled as a bath of harmonic oscillators is analyzed using a quantum Langevin approach.
		This allows to easily obtain the dissipation time and the correction to the Berry phase in the case of an adiabatic cyclic evolution.
	www.citebase.org /cgi-bin/citations?id=oai:arXiv.org:quant-ph/0410183 (829 words)

	Langevin Equation; Coffey, W.T. (Trinity College, Dublin); Kalmykov, Yu P. (Russian Academy of Science, Moscow, ...
		Langevin Equation; Coffey, W.T. (Trinity College, Dublin); Kalmykov, Yu P. (Russian Academy of Science, Moscow, Russia); Hardback; World Retail Store - English Books
		Suitable for lecture courses on Brownian motion, this study includes coverage of the following topics: white noise; the Chapman-Kolmogorov equation - Kramers-Moyal expansion; Langevin equation; Fokker-Planck equation; Brownian motion of a free particle;
		Prices subject to change to be advised on confirmation of order.
	www.worldretailstore.com /item/BE-9810216513.html (242 words)

	THE LANGEVIN EQUATION (Site not responding. Last check: 2007-10-08)
		The book is suitable for a lecture course on the theory of Brownian motion, being based on final year undergraduate lectures given at Trinity College, Dublin.
		As the first elementary book on the Langevin equation approach to Brownian motion, this volume attempts to fill in all the missing details which students find particularly hard to comprehend from the fundamental papers contained in the Dover reprint — Selected Papers on Noise and Stochastic Processes, ed.
		Inertial Langevin Equations: Application to the Theory of Dielectric and Kerr-Effect Relaxation
	www.worldscibooks.com /physics/2256.html (260 words)

	Infinite-dimensional Langevin equation and Fokker-Planck equation, Yoshio Miyahara (Site not responding. Last check: 2007-10-08)
		[4] R. Curtain and P. Falb, Stochastic differential equations in Hubert space, J. Differential Equations, 10 (1971), 412-430.
		[6] R. Curtain, Estimation theory for abstract evolution equations excited by general white noise processes, SIAM J. Control and Optimization, 14, No. 6 (1976), 1124-1150.
		[23] A. Shimizu, Construction of a solution of linear stochastic evolution equations on a Hubert space, in Proceedings of the International Symposium on Stochastic Differential Equations, Kyoto, 1976, 385-395.
	projecteuclid.org /getRecord?id=euclid.nmj/1118786313 (394 words)

	Find in a Library: The Langevin equation : with applications in physics, chemistry, and electrical engineering (Site not responding. Last check: 2007-10-08)
		Find in a Library: The Langevin equation : with applications in physics, chemistry, and electrical engineering
		The Langevin equation : with applications in physics, chemistry, and electrical engineering
		WorldCat is provided by OCLC Online Computer Library Center, Inc. on behalf of its member libraries.
	worldcatlibraries.org /wcpa/ow/a7ab7820bbf61b72a19afeb4da09e526.html (82 words)

	Stochastic quantum Langevin equation (Site not responding. Last check: 2007-10-08)
		The stochastic representation of quantum mechanics is used to give a purely stochastic treatment of the quantum Langevin equation.
		A general coupling involving positions and velocities of the particle and harmonic modes, with arbitrary dependence on the particle's position, is dealt with.
		In particular, reselling and systematic downloading of files is prohibited.
	stacks.iop.org /0305-4470/22/537 (261 words)

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