Passage-time calculation for the detection of weak signals via the transient dynamics of a laser

Detection of weak signals in memory thermal baths

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.

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

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 and large electric fields through the transient dynamics of a Brownian particle in an electromagnetic field

In this work we present a mechanism to detect the presence of an external electric field of either weak or large amplitude by means of the decay process from an unstable state, described by a bistable potential, of an electrically charged Brownian particle embedded in a uniform electromagnetic field. Since the detection process takes place around the initial unstable state of the bistable potential, our theoretical description is given in the linear approximation of the aforementioned potential. The decay process is characterized through the statistics of the passage time distribution calculated by means of two theoretical approaches relying on the overdamped Langevin equation: one is the quasideterministic approach valid for large times and used for the detection of weak signals, whereas the other one is the rotational approach, valid for intermediate times and adequate for the detection of large electric-field amplitudes.

Non-Markovian rotating unstable processes driven by Gaussian colored noise

In this paper the statistical properties of the mean passage time distribution are used to characterize the decay process of non-Markovian rotating unstable processes driven by Gaussian colored noise and subjected to the influence of a constant external force. The time characterization will be linear and studied in two limiting cases: large and intermediate times. General systems of two variables are studied. In both schemes we show that, for small correlation time of the noise, the non-Markovian effects are taken into account by an effective noise intensity. To compare qualitatively the non-Markovian time scale with respect to the Markovian case, we apply those results to determine the detection bandwidth of a large external signal in a laser system.

Rotating unstable Langevin-type dynamics: linear and nonlinear mean passage time distributions

To characterize the decay process of linear rotating unstable Langevin-type dynamics in the presence of constant external force, through the mean passage time distribution, two theoretical descriptions are proposed: one is called the Quasideterministic (QD) approach described in the limit of long times, and the other approach is formulated for not so long times. Both theories are matrix based and formulated in two x and y dynamical representations, y being the transformed space of coordinates by means of a time-dependent rotation matrix. In the y dynamical representation the noise as well as the external force are rotational. The QD approach is studied when the dynamics is not influenced by the external force and when it is influenced by it. In the absence of this force, the theory is given for n variables and leads to the same results as those obtained in the characterization of nonrotating unstable systems; a fact that is better understood in the space of coordinates y. In the presence of the external force, the characterization is given for two variables and it is only valid for weak amplitude forces. For large amplitudes, the dynamics is almost dominated by the deterministic rotational evolution; then the QD approach is no longer valid and therefore the other approach is required. The theory in this case is general and verified for systems of two and three variables. In the case of two variables we study a laser system and use the experimental data of this system to compare with both theoretical and simulation results. In the case of three variables, the theory foresees application in other fields, for instance, in plasma physics. We also study the time characterization of the nonlinear rotating unstable systems and show in general that the nonlinear correction to the linear case is a quantity evaluated in the deterministic limit. The same laser system studied in the linear case is used as a prototype model.

Time scales in rotating unstable Langevin-type dynamics

In this Rapid Communication we propose a different and general characterization of rotating, unstable Langevin-type dynamics in the presence of an external force in the context of two dynamical representations x and y, using the passage time distribution. Here y is the transformed space of coordinates obtained by means of a time-dependent rotation matrix. The Langevin dynamics in the new y space defines an interesting concept of external force and internal noise due to rotation. The theory is applied to the characterization of rotational unstable systems of two (such as the laser system) and three variables, and stimulates its application in other fields, for instance, in plasma physics.