Journal ArticleDOI
Path integral solutions for non-Markovian processes
TLDR
In this article, a path integral solution for a nonlinear stochastic flow driven by Markovian or non-Markovian colored noise ζ(t) is presented.Abstract:
For a nonlinear stochastic flow driven by Markovian or non-Markovian colored noise ζ(t) we present the path integral solution for the single-event probabilityp(x,t). The solution has the structure of a complex-valued double path integral. Explicit formulas for the action functional, i.e., the non-Markovian Onsager-Machlup functional, are derived for the case that ζ(t) is characterized by a stationary Gaussian process. Moreover, we derive explicit results for (generalized) Poissonian colored shot noise ζ(t). The use of the path integral solution is elucidated by a weak noise analysis of the WKB-type. As a simple application, we consider stochastic bistability driven by colored noise with an extremely long correlation time.read more
Citations
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Journal ArticleDOI
Introduction: 100 years of Brownian motion.
Peter Hänggi,Fabio Marchesoni +1 more
TL;DR: In the year 1905 Albert Einstein published four pap that raised him to a giant in the history of science, his first two papers on relativity theory, and his first paper on Brownian motion, which is celebrated in this Focus Issue entitled “100 Years of Brownian Motion.”
Journal ArticleDOI
Dominant pathways in protein folding.
TL;DR: A Hamilton-Jacobi variational principle is derived from the solution of the Fokker-Planck equation in terms of a path integral that is able to compute the most probable pathway of folding.
Journal ArticleDOI
Can colored noise improve stochastic resonance
TL;DR: In this paper, the effect of colored noise on the amplification of small periodic signals is studied in terms of effective, time-periodic Fokker-Planck equations, and it is shown that SR is suppressed with increasing noise color.
Journal ArticleDOI
Irreversibility in Active Matter Systems: Fluctuation Theorem and Mutual Information
TL;DR: In this article, the authors consider a Brownian particle which, in addition to being in contact with a thermal bath, is driven by fluctuating forces which stem from active processes in the system, such as self-propulsion o...
References
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Book
Quantum Mechanics and Path Integrals
TL;DR: Au sommaire as discussed by the authors developed the concepts of quantum mechanics with special examples and developed the perturbation method in quantum mechanics and the variational method for probability problems in quantum physics.
Book
Techniques and Applications of Path Integration
TL;DR: In this paper, the authors present a list of applications of the path integral formula in statistical mechanics, including the application of the Path Integral formula to Statistical Mechanics, asymptotic analysis, and the phase space path integral.
Book
Functional Integration and Semiclassical Expansions
TL;DR: In this paper, the authors define functional integrals defined as limits of discretized expressions and functional integral representations of expectation values, and define correspondence rules, functional integral methods in Fokker-Planck dynamics and product integrals.
BookDOI
Fluctuations, Instabilities, and Phase Transitions
TL;DR: In this article, the authors present a survey of the Rayleigh-Benard instability at Helium temperatures and the potential for the Taylor instability at the critical point of phase transition and Turbulence.