Two-Well System under Large Amplitude Periodic Forcing: Stochastic Synchronization, Stochastic Resonance and Stability

We study the residence time distributions and explore the possibility of observing stochastic resonance and synchonization of passages in a two-well system driven by a periodic forcing of amplitude larger than a marginal value beyond which one of the two wells become unstable and diasppear. We define and calculate hysteresis loop in the system, the area of which measures the degree of synchronization between the residence time statistics and the input signal, as a function of input noise strength. We analyse the noise induced stability obtained in such a deterministically overall unstable system and within this context discuss the above two phenomena.Comment: Mod. Phys. Lett. B 1997, in print, figures available on reques

AC driven thermal ratchets

We consider the motion of a overdamped Brownian particle in periodic asymmetric potential with space dependent friction coefficient. In the presence of external time periodic forcing, the system shows multiple current reversals on varying the amplitude of the external forcing and the temperature of the thermal bath. In the adiabatic regime we find a single reversal of current as a function of noise strength which can only be accounted due to the presence of space dependent friction coefficient. For very large forcing term, the current does not go to zero, instead it asymptotically tends to a limiting value depending on the phase shift between the potential and the friction. This fact plays an important role in obtaining multiple current reversals.Comment: 4 pages, latex/revtex, 4 eps figures. Proceedings of CMDAYS2K, held at Guru Ghasidas University, Bilaspur, Chattisgarh, India, Aug 29-31, 2

Stochastic resonance and nonlinear response in a dissipative quantum two-state system

We study the dynamics of a dissipative two-level, system driven by a monochromatic ac field, starting from the usual spin-boson Hamiltonian. The quantum Langevin equations for the spin variables are obtained. The amplitude of the coherent oscillations in the average position of the particle is studied in the high temperature limit. The system exhibits quantum stochastic resonance in qualitative agreement with earlier numerical results.Comment: PRB April 1997, figures available on reques

Mobility and stochastic resonance in spatially inhomogeneous system

The mobility of an overdamped particle, in a periodic potential tilted by a constant external field and moving in a medium with periodic friction coefficient is examined. When the potential and the friction coefficient have the same periodicity but have a phase difference, the mobility shows many interesting features as a function of the applied force, the temperature, etc. The mobility shows stochastic resonance even for constant applied force, an issue of much recent interest. The mobility also exhibits a resonance like phenomenon as a function of the field strength and noise induced slowing down of the particle in an appropriate parameter regime.Comment: 14 pages, 12 figures. Submitted to Phys. Rev.

Relation between Stochastic Resonance and Synchronization of Passages in a Double-Well System

We calculate, numerically, the residence times (and their distribution) of a Brownian particle in a two-well system under the action of a periodic, saw-tooth type, external field. We define hysteresis in the system. The hysteresis loop area is shown to be a good measure of synchronization of passages from one well to the other. We establish connection between this stochastic synchronization and stochastic resonance in the system.Comment: To appear in PRE May 1997, figures available on reques

Asymmetric motion in a double-well under the action of zero-mean Gaussian white noise and periodic forcing

Residence times of a particle in both the wells of a double-well system, under the action of zero-mean Gaussian white noise and zero-averaged but temporally asymmetric periodic forcings, are recorded in a numerical simulation. The difference between the relative mean residence times in the two wells shows monotonic variation as a function of asymmetry in the periodic forcing and for a given asymmetry the difference becomes largest at an optimum value of the noise strength. Moreover, the passages from one well to the other become less synchronous at small noise strength as the asymmetry parameter (defined below) differs from zero, but at relatively larger noise strengths the passages become more synchronous with asymmetry in the field sweep. We propose that asymmetric periodic forcing (with zero mean) could provide a simple but sensible physical model for unidirectional motion in a symmetric periodic system aided by a symmetric Gaussian white noise.Comment: Appeared in PRE March 1997, figures available on reques

Noise assisted directed motion at the molecular level - 2

The term noise is used to describe fluctuations about the mean deterministic stationary value of a physical quantity. It is now being increasingly realised that noise is an important ingredient to bring order in dynamical processes. Though it appears counterintuitive, noise seems to help in directing transport processes in biological systems at the molecular level. In Part 2 of the article, we discuss some more examples of noise assisted directed motion