Stochastic Resonance in 3D Ising Ferromagnets

Finite 3D Ising ferromagnets are studied in periodic magnetic fields both by computer simulations and mean-field theoretical approaches. The phenomenon of stochastic resonance is revealed. The characteristic peak obtained for the correlation function between the external oscillating magnetic field and magnetization versus the temperature of the system, is studied for various external fields and lattice sizes. Excellent agreement between simulation and theoretical results are obtained.Comment: 12 pages, 6 Postscript figures upon request, typset in Late

Stochastic Resonance in Underdamped, Bistable Systems

We carry out a detailed numerical investigation of stochastic resonance in underdamped systems in the non-perturbative regime. We point out that an important distinction between stochastic resonance in overdamped and underdamped systems lies in the lack of dependence of the amplitude of the noise-averaged trajectory on the noise strength, in the latter case. We provide qualitative explanations for the observed behavior and show that signatures such as the initial decay and long-time oscillatory behaviour of the temporal correlation function and peaks in the noise and phase averaged power spectral density, clearly indicate the manifestation of resonant behaviour in noisy, underdamped bistable systems in the weak to moderate noise regime.Comment: Revtex; (10+8)pp including 8 figure

Stochastic resonance in multi-threshold systems

We discuss the dynamical behaviour of multi-threshold systems in the presence of noise and periodic inputs. Here, the stochastic resonance phenomenon displays some peculiarities such as a clear dependence on the noise statistics and the presence of a multi-peaked characteristic curve, which are not observed in simple bistable systems. This phenomenon is described without reference to any frequency matching condition as a special case of the well-known dithering effect

AC Driven Jumps Distribution on a Periodic Substrate

A driven Brownian particle (e.g. an adatom on a surface) diffusing on a low-viscosity, periodic substrate may execute multiple jumps. In the presence of an additional periodic drive, the jump lengths and time durations become statistically modulated according to a syncronyzation mechanism reminiscent of asymmetric stochastic resonance. Here, too, bistability plays a key role, but in a dynamical sense, inasmuch as a particle switches between locked and running states.Comment: 4 pages, 4 figures, RevTeX, to be published in Surface Science Letter

Noise Limited Computational Speed

In modern transistor based logic gates, the impact of noise on computation has become increasingly relevant since the voltage scaling strategy, aimed at decreasing the dissipated power, has increased the probability of error due to the reduced switching threshold voltages. In this paper we discuss the role of noise in a two state model that mimic the dynamics of standard logic gates and show that the presence of the noise sets a fundamental limit to the computing speed. An optimal idle time interval that minimizes the error probability, is derived

Splitting of the ground state manifold of classical Heisenberg spins as couplings are varied

We construct clusters of classical Heisenberg spins with two-spin $\vec{S}_i.\vec{S}_j$-type interactions for which the ground state manifold consists of disconnected pieces. We extend the construction to lattices and couplings for which the ground state manifold splits into an exponentially large number of disconnected pieces at a sharp point as the interaction strengths are varied with respect to each other. In one such lattice we construct, the number of disconnected pieces in the ground state manifold can be counted exactly.Comment: Accepted for publication in Physica A; 6 pages, 4 figure

Controlling Nonlinear Stochastic Resonance by Harmonic Mixing

We investigate the potential for controlling the effect of nonlinear Stochastic Resonance (SR) by use of harmonic mixing signals for an overdamped Brownian dynamics in a symmetric double well potential. The periodic forcing for harmonic mixing consists of a first signal with a basic frequency $\Omega$ and a second, superimposed signal oscillating at twice the basic frequency $2\Omega$. By variation of the phase difference between these two components and the amplitude ratios of the driving the phenomenon of SR becomes a priori controllable. The harmonic mixing dynamically breaks the symmetry so that the time- and ensemble-average assumes a non-vanishing value. Independently of the noise level, the response can be suppressed by adjusting the phase difference. Nonlinear SR then exhibits resonances at higher harmonics with respect to the applied noise strength and relative phase. The scheme of nonlinear SR via harmonic mixing can be used to steer the nonlinear response and to sensitively measure the internal noise strength. We further demonstrate that the full Fokker-Planck dynamics can be well approximated by a two-state model.Comment: 13 pages, 4 figure