Detection of weak signals through nonlinear relaxation times for a Brownian particle in an electromagnetic field

Abstract

The detection of weak signals through nonlinear relaxation times for a Brownian particle in an electromagnetic field is studied in the dynamical relaxation of the unstable state, characterized by a two-dimensional bistable potential. The detection process depends on a dimensionless quantity referred to as the receiver output, calculated as a function of the nonlinear relaxation time and being a characteristic time scale of our system. The latter characterizes the complete dynamical relaxation of the Brownian particle as it relaxes from the initial unstable state of the bistable potential to its corresponding steady state. The one-dimensional problem is also studied to complement the description.

Detection of weak signals in memory thermal baths

“…In the absence of the external force F e , the quantity x 2 (t) evolves from an initial value x 2 (0) to its corresponding steady-state value x 2 st . The NLRT is defined as [21,22,27,28] …”

“…According to the QD approach [20][21][22][23], the process h(t) plays the role of an effective initial condition and, as time increases, it becomes a Gaussian random variable (GRV). This is indeed the case since, for small values of both the noise intensity andF e ,…”

“…[22] (where the definitions of A e and A 0 are made) we can also calculate the receiver-output ratio R = A e /A 0 through the relaxation process of the bistable potential (C NL = 0) in the presence of a constant force field. According to Fig.…”

“…Recently, an alternative physical mechanism to detect weak electrical signals was given. It deals with the decay process of a charged Brownian particle under the action of constant crossed electric and magnetic fields [22]. An interesting and surprising aspect of this physical system is that its dynamic behavior is very similar to that followed by the aforementioned laser system.…”

“…The works in [29][30][31][32][33][34] provide a good description in the study of such transient stochastic dynamics. However, the one which has proved to be the most appropriate in the study of the detection of weak signals in the decay of an unstable state is the so-called quasideterministic (QD) approach [20][21][22][23][24], due to the following reasons. It has been used appropriately in connection with the MFPT and NLRT in the time characterization of such a decay process in the physical situation commented above.…”