Narrow Results

We have investigated the effect of an external periodic driving to the macroscopic quantum tunneling of spin-1 condensates in a double-well potential. By manipulating the frequencies of the external magnetic fields, a rich set of phenomena can be studied, and dynamical localization and self-trapping in spin states can be realized using time-dependent magnetic field. We have shown that a relatively high-frequency field may induce a fast oscillation of the macroscopic quantum localization. The larger the periodic magnetic field frequency is, the faster oscillation of the spin condensate magnetization goes. By applying a lower-frequency field to the spin-condensate, one can find that the dynamical properties of the magnetization appears similar behaviors to the results of the modulations of a constant external magnetic field. A possible realization in experiments is also presented.

We demonstrate that signal-to-noise ratio (SNR) can be significantly improved by stochastic resonance in a double well potential. The overdamped dynamical system was studied using mixed signal simulation techniques. The system was driven by wideband Gaussian white noise and a periodic pulse train with variable amplitude and duty cycle. Operating the system in the non-linear response range, we obtained SNR gains much greater than unity. In addition to the classical SNR definition, the ratio of the total power of the signal to the power of the noise part was also measured and it showed better signal improvement.

It has recently been reported that in some systems showing stochastic resonance, the signal-to-noise ratio (SNR) at the output can significantly exceed that at the input; in other words, SNR gain is possible. We took two such systems, the non-dynamical Schmitt trigger and the dynamical double wellpotential, and using numerical and mixed-signal simulation techniques, we examined what SNR gains these systems can provide. In the non-linear response limit, we obtained SNR gains much greater than unity for both systems. In addition to the classical narrow-band SNR definition, we also measured the ratio of the total power of the signal to the power of the noise part, and it showed even better signal improvement. Here we present a brief review of our results, and scrutinise, for both the Schmitt-trigger and the double well potential, the behaviour of the SNR gain by stochastic resonance for different signal amplitudes and duty cycles. We also discuss the mechanism of providing gains greater than unity.

We provide a mathematical underpinning of the physically widely known phenomenon of stochastic resonance, i.e. the optimal noise-induced increase of a dynamical system's sensitivity and ability to amplify small periodic signals. The effect was first discovered in energy-balance models designed for a qualitative understanding of global glacial cycles. More recently, stochastic resonance has been rediscovered in more subtle and realistic simulations interpreting paleoclimatic data: the Dansgaard–Oeschger and Heinrich events. The underlying mathematical model is a diffusion in a periodically changing potential landscape with large forcing period. We study optimal tuning of the diffusion trajectories with the deterministic input forcing by means of the spectral power amplification measure. Our results contain a surprise: due to small fluctuations in the potential valley bottoms the diffusion — contrary to physical folklore — does not show tuning patterns corresponding to continuous time Markov chains which describe the reduced motion on the metastable states. This discrepancy can only be avoided for more robust notions of tuning, e.g. spectral amplification after elimination of the small fluctuations.

It has recently been reported that in some systems showing stochastic resonance, the signal-to-noise ratio (SNR) at the output can significantly exceed that at the input; in other words, SNR gain is possible. We took two such systems, the non-dynamical Schmitt trigger and the dynamical double well potential, and using numerical and mixed-signal simulation techniques, we examined what SNR gains these systems can provide. In the non-linear response limit, we obtained SNR gains much greater than unity for both systems. In addition to the classical narrow-band SNR definition, we also measured the ratio of the total power of the signal to the power of the noise part, and it showed even better signal improvement. Here we present a brief review of our results, and scrutinise, for both the Schmitt-trigger and the double well potential, the behaviour of the SNR gain by stochastic resonance for different signal amplitudes and duty cycles. We also discuss the mechanism of providing gains greater than unity.