Detection of weak signals in memory thermal baths

Abstract

The nonlinear relaxation time and the statistics of the first passage time distribution in connection with the quasideterministic approach are used to detect weak signals in the decay process of the unstable state of a Brownian particle embedded in memory thermal baths. The study is performed in the overdamped approximation of a generalized Langevin equation characterized by an exponential decay in the friction memory kernel. A detection criterion for each time scale is studied: The first one is referred to as the receiver output, which is given as a function of the nonlinear relaxation time, and the second one is related to the statistics of the first passage time distribution.

Unstable state decay in non-Markovian heat baths and weak signals detection

“…Although mathematically the form of Eqs. ( 35) and ( 36) are very similar to those obtained in [19] [see Eqs. (37) and (38)], the differences between them are basically the new contribution given by the third term of Eq.…”

“…(38) of Ref. [19], in which such a nonlinear contribution is equal to zero. In the present work the Einstein diffusion coefficient is rescaled by the factor 1/(1 − aτ ) 2 , whereas in [19], such a factor is 1/(1 − aτ ).…”

“…[19], in which such a nonlinear contribution is equal to zero. In the present work the Einstein diffusion coefficient is rescaled by the factor 1/(1 − aτ ) 2 , whereas in [19], such a factor is 1/(1 − aτ ). In this paper the external parameter β 2 = h 2 /2σ 2 , when applied to OU memory kernel, curiously becomes the same as in the Markovian case, that is β 2 M = F 2 /2aD, even when h OU and σ 2 OU are heat bath dependent.…”

“…For instance, it has recently been studied in viscoelastic fluids [4], diffusive processes -ranging from ordinary diffusion (Brownian motion) to continuous-time random walks [5,6]-, fractional Brownian motion [7,8], Lévy flights [9,10], trapped diffusion [11], geometric confinement [3,12], Ornstein-Uhlenbeck process [13,14], etc. The FPT has also been explored in non-Markovian situations including biological systems [15,16], random walks in confined media [17,18], detection of weak signals [19], among others [20,21,22,23,24,25,26,27,28,29].…”

“…In 2014, the problem of the detection of weak signals in the decay process of an unstable state in an Ornstein-Uhlenbeck (OU) heat bath, was studied in the context of a GLE [19]. Two usual theoretical criteria for the detection process were analyzed.…”