Stochastic resonance

Abstract

We are taught by conventional wisdom that the transmission and detection of signals is hindered by noise. However, during the last two decades, the paradigm of stochastic resonance (SR) proved this assertion wrong: indeed, addition of the appropriate amount of noise can boost a signal and hence facilitate its detection in a noisy environment. Due to its simplicity and robustness, SR has been implemented by mother nature on almost every scale, thus attracting interdisciplinary interest from physicists, geologists, engineers, biologists and medical doctors, who nowadays use it as an instrument for their specific purposes.At the present time, there exist a lot of diversified models of SR. Taking into account the progress achieved in both theoretical understanding and practical application of this phenomenon, we put the focus of the present review not on discussing in depth technical details of different models and approaches but rather on presenting a general and clear physical picture of SR on a pedagogical level. Particular emphasis will be given to the implementation of SR in generic quantum systems-an issue that has received limited attention in earlier review papers on the topic.The major part of our presentation relies on the two-state model of SR (or on simple variants thereof), which is general enough to exhibit the main features of SR and, in fact, covers many (if not most) of the examples of SR published so far. In order to highlight the diversity of the two-state model, we shall discuss several examples from such different fields as condensed matter, nonlinear and quantum optics and biophysics. Finally, we also discuss some situations that go beyond the generic SR scenario but are still characterized by a constructive role of noise.

Enhanced vibrational energy harvesting using nonlinear stochastic resonance

“…It can be seen that the forced mechanism in stochastic resonance apparently delivers significantly more energy from the excitation Q(t) than the unforced mechanism. The forcing frequency ω required for stochastic resonance can be estimated from the Kramer's rate, the probability of transition between the potential wells [8].…”

“…If the system is trapped in either potential well, the effect of noise is merely to excite the dynamics locally, with the probability of a transition between the potential wells determined by the so-called Kramers rate [8]. For a large potential barrier between the two potential wells this probability is clearly small.…”

Stationary energy probability density of oscillators driven by a random external force

“…The effect of correlations in the random driving force on the stationary probability density and its moments were investigated [19][20][21][22], as were related problems, such as the escape from a potential well and the mean first passage time [7], stochastic resonance [23][24][25], the stability of metastable states [26], and the dynamics of excitable systems [27]. Much less attention has been paid to how the color of the noise and the nonlinearities of the potential affect the statistical properties of the particle's energy.…”

Detection of small single-cycle signals by stochastic resonance using a bistable superconducting quantum interference device

“…This interesting phenomenon is named as stochastic resonance (SR). [1][2][3][4] For example, suppose that a particle is moving in a periodically perturbed symmetric double-well potential under the influence of a Gaussian-white noise such as thermal fluctuation. Then SNR of the power spectral density of the particle's trajectory displays a broad maximum when the rate of inter-well transitions, which depends on noise strength exponentially, is comparable to the frequency of periodic signal.…”

“…[1][2][3][4][5][6][7][8][9][10][11] It has also been observed in Josephson junction-based systems, [12][13][14][15][16] which have recently attracted much interest and been applied in many fields such as quantum information. [17][18][19] However, SR has been only investigated for periodic signals that last many cycles.…”