Dynamical symmetries of Markov processes with multiplicative white noise

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 t...

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Detalles Bibliográficos
Publicado:	2016
Materias:	Brownian motion driven diffusive systems (theory) fluctuations (theory) stochastic processes (theory)
Acceso en línea:	https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_17425468_v2016_n5_p_Aron http://hdl.handle.net/20.500.12110/paper_17425468_v2016_n5_p_Aron
Aporte de:	Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires

id	paper:paper_17425468_v2016_n5_p_Aron
record_format	dspace
spelling	paper:paper_17425468_v2016_n5_p_Aron2023-06-08T16:27:06Z Dynamical symmetries of Markov processes with multiplicative white noise Brownian motion driven diffusive systems (theory) fluctuations (theory) stochastic processes (theory) 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. © 2016 IOP Publishing Ltd and SISSA Medialab srl. 2016 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_17425468_v2016_n5_p_Aron http://hdl.handle.net/20.500.12110/paper_17425468_v2016_n5_p_Aron
institution	Universidad de Buenos Aires
institution_str	I-28
repository_str	R-134
collection	Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic	Brownian motion driven diffusive systems (theory) fluctuations (theory) stochastic processes (theory)
spellingShingle	Brownian motion driven diffusive systems (theory) fluctuations (theory) stochastic processes (theory) Dynamical symmetries of Markov processes with multiplicative white noise
topic_facet	Brownian motion driven diffusive systems (theory) fluctuations (theory) stochastic processes (theory)
description	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. © 2016 IOP Publishing Ltd and SISSA Medialab srl.
title	Dynamical symmetries of Markov processes with multiplicative white noise
title_short	Dynamical symmetries of Markov processes with multiplicative white noise
title_full	Dynamical symmetries of Markov processes with multiplicative white noise
title_fullStr	Dynamical symmetries of Markov processes with multiplicative white noise
title_full_unstemmed	Dynamical symmetries of Markov processes with multiplicative white noise
title_sort	dynamical symmetries of markov processes with multiplicative white noise
publishDate	2016
url	https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_17425468_v2016_n5_p_Aron http://hdl.handle.net/20.500.12110/paper_17425468_v2016_n5_p_Aron
_version_	1768541865175416832

Dynamical symmetries of Markov processes with multiplicative white noise

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