Dynamical symmetries of Markov processes with multiplicative white noise
| Autor: | Leticia F. Cugliandolo, Camille Aron, Daniel G. Barci, Gustavo S. Lozano, Zochil González Arenas |
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| Jazyk: | angličtina |
| Rok vydání: | 2014 |
| Předmět: |
Statistics and Probability
Angular momentum Discretization Differential equation Ciencias Físicas FOS: Physical sciences Markov process 01 natural sciences 010305 fluids & plasmas FLUCTUATIONS (THEORY) symbols.namesake DRIVEN DIFFUSIVE SYSTEMS (THEORY) 0103 physical sciences Statistical physics 010306 general physics Condensed Matter - Statistical Mechanics Mathematics Statistical Mechanics (cond-mat.stat-mech) Stochastic process Numerical analysis Multiplicative function Statistical and Nonlinear Physics BROWNIAN MOTION Homogeneous space symbols Statistics Probability and Uncertainty CIENCIAS NATURALES Y EXACTAS STOCHASTIC PROCESSES (THEORY) Física de los Materiales Condensados |
| Popis: | We analyse various properties of stochastic Markov processes with multiplicative white noise. We take a single-variable problem as a simple example, and we later extend the analysis to the Landau-Lifshitz-Gilbert equation for the stochastic dynamics of a magnetic moment. In particular, we focus on the non-equilibrium transfer of angular momentum to the magnetization from a spin-polarised current of electrons, a technique which is widely used in the context of spintronics to manipulate magnetic moments. We unveil two hidden dynamical symmetries of the generating functionals of these Markovian multiplicative white-noise processes. One symmetry only holds in equilibrium and we use it to prove generic relations such as the fluctuation-dissipation theorems. Out of equilibrium, we take profit of the symmetry-breaking terms to prove fluctuation theorems. The other symmetry yields strong dynamical relations between correlation and response functions which can notably simplify the numerical analysis of these problems. Our construction allows us to clarify some misconceptions on multiplicative white-noise stochastic processes that can be found in the literature. In particular, we show that a first-order differential equation with multiplicative white noise can be transformed into an additive-noise equation, but that the latter keeps a non-trivial memory of the discretisation prescription used to define the former. 44 pages |
| Databáze: | OpenAIRE |
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