##manager.scheduler.building##: Edificio Santa Maria

##manager.scheduler.room##: Auditorio San Agustin

Date: 2019-07-08 11:45 AM – 03:30 PM

Last modified: 2019-06-15

#### Abstract

Stochastic dynamics driven by multiplicative noise appears as a promissory approach for a variety of out-of-equilibrium phenomena. Multiplicative noise naturally describes inhomogeneous diffusion in which fluctuations depend on the state of the system. In this area, Langevin and Fokker-Planck formalisms are extensively used. In addition, functional path integral approaches has also been introduced, very convenient to study symmetries, phase transitions and more.

A persistent problem in this area is given by the diversity of conventions available for performing the stochastic integration. To overcome this situation, we use the* generalized Stratonovich* or *&alpha – prescription*, where &alpha is defined as a continuous parameter, 0 &le &alpha &le 1, and each of its values corresponds with a different discretization rule for the stochastic differential equation (including Itô prescription and Stratonovich one). In this context, we developed a path integral formalism and discussed the concept of time reversibility for multiplicative noise stochastic processes, deducing a specific time reversal transformation which mixes different prescriptions (JSTAT v2012, p12005, 2012; PRE v91, p042103, 2015).

In this work, we present some results derived from this functional formalism. Based on it, we computed potentials for describing non-equilibrium stationary states reached by a multiplicative Langevin dynamics and showed that our approximation procedure correctly captures the physics of noise-induced phase transitions (EPL v113, p10009, 2016). We also discuss a method to analytically compute a weak noise expansion of the transition probability for this kind of stochastic processes. Interestingly, when written in its path integral representation, its computation is equivalent to compute a propagator of a quantum particle with variable mass (arXiv:1804.02459, 2018, submitted to PRE).