Dynamical symmetries of Markov processes with multiplicative white noise

被引:25
作者
Aron, Camille [1 ,2 ]
Barci, Daniel G. [3 ]
Cugliandolo, Leticia F. [4 ]
Arenas, Zochil Gonzalez [3 ]
Lozano, Gustavo S. [4 ,5 ,6 ]
机构
[1] Princeton Univ, Dept Elect Engn, Princeton, NJ 08544 USA
[2] Katholieke Univ Leuven, Inst Theoret Fys, Leuven, Belgium
[3] Univ Estado Rio de Janeiro, Dept Fis Teor, Rua Sao Francisco Xavier 524, BR-20550013 Rio De Janeiro, RJ, Brazil
[4] Univ Paris 06, Sorbonne Univ, UMR 7589, Lab Phys Theor & Hautes Energies, Paris, France
[5] Univ Buenos Aires, FCEYN, Dept Fis, RA-1428 Buenos Aires, DF, Argentina
[6] Consejo Nacl Invest Cient & Tecn, IFIBA, Pabellon 1 Ciudad Univ, RA-1428 Buenos Aires, DF, Argentina
关键词
Brownian motion; driven di. usive systems (theory); fluctuations (theory); stochastic processes (theory); STOCHASTIC-PROCESSES; TRANSFORMATIONS; THERMODYNAMICS; INTEGRALS;
D O I
10.1088/1742-5468/2016/05/053207
中图分类号
O3 [力学];
学科分类号
08 ; 0801 ;
摘要
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.
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页数:33
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