Doubly stochastic matrices in quantum mechanics

The general set of doubly stochastic matrices of order n corresponding to ordinary nonrelativistic quantum mechanical transition probability matrices is given. Landé's discussion of the nonquantal origin of such matrices is noted. Several concrete examples are presented for elementary and composite angular momentum systems with the focus on the unitary symmetry associated with such systems in the spirit of the recent work of Bohr and Ulfbeck. Birkhoff's theorem on doubly stochastic matrices of order n is reformulated in a geometrical language suitable for application to the subset of quantum mechanical doubly stochastic matrices. Specifically, it is shown that the set of points on the unit sphere in cartesian n!-space is surjective with the set of doubly stochastic matrices of order n. The question is raised, but not answered, as to what is the subset of points of this unit sphere that correspond to the quantum mechanical transition probability matrices, and what is the symmetry group of this subset of matrices.     

Single-trigger stochastic resonance

Summary We discuss a recently discovered mechanism for stochastic resonance which involves only a single reference state with excitable dynamics and deterministic reinjection. While calculations based on an analogy with the shot effect capture the broadest features, detailed comparisons with specific dynamical systems suggest the need for certain refinements of the theory. Paper presented at the International Workshop ?Fluctuations in Physics and Biology: Stochastic Resonance, Signal Processing and Related Phenomena?, Elba, 5–10 June 1994.     

Nuclear stochastic resonance

Quantitative theory of the effect of nuclear ferromagnetism on the superconductivity of metals is proposed taking into account the electron-nuclear spin-spin interactions. At negative nuclear temperatures, when the nuclear magnetization is in opposition to an external magnetic field, nuclear ferromagnetism is favorable to superconductivity rather than suppressing it. The critical magnetic field in Be and TiH_2.07 hydrate metals may exceed the critical field of a nonmagnetic superconductor by an order of magnitude.     

Entropic stochastic resonance

We present a novel scheme for the appearance of stochastic resonance when the dynamics of a Brownian particle takes place in a confined medium. The presence of uneven boundaries, giving rise to an entropic contribution to the potential, may upon application of a periodic driving force result in an increase of the spectral amplification at an optimum value of the ambient noise level. The entropic stochastic resonance, characteristic of small-scale systems, may constitute a useful mechanism for the manipulation and control of single molecules and nanodevices.     

Non-Markovian stochastic resonance

The phenomenological linear response theory of non-Markovian stochastic resonance (SR) is put forward for stationary two-state renewal processes. In terms of a derivation of a non-Markov regression theorem we evaluate the characteristic SR-quantifiers; i.e., the spectral power amplification (SPA) and the signal-to-noise ratio (SNR), respectively. In clear contrast to Markovian-SR, a characteristic benchmark of genuine non-Markovian SR is its distinctive dependence of the SPA and SNR on small (adiabatic) driving frequencies; particularly, the adiabatic SNR becomes strongly suppressed over its Markovian counterpart. This non-Markovian SR-theory is elucidated for a fractal gating dynamics of a potassium ion channel possessing an infinite variance of closed sojourn times.     

Energetics of stochastic resonance

In this paper, we discuss the motion of a Brownian particle in a double-well potential driven by a periodic force in terms of energies delivered by the periodic and the noise forces and energy dissipated into the viscous environment. It is shown that, while the power delivered by the periodic force to the Brownian particle is controlled by the strength of the noise, the power delivered by the noise itself is independent of the amplitude and frequency of the periodic force. The implications of this result for the mechanism of stochastic resonance in an equilibrium system is that it is not energy from the noise force which enhances a small periodic force, but rather an increase of energy delivered by the periodic force, regulated by the strength of the noise. We further re-evaluate the frequency dependence of stochastic resonance in terms of energetic terms including efficiency.     

Minireview of stochastic resonance

We present an introductory overview of the subject of stochastic resonance. As researchers' interest in the phenomenon has spread from physics to biology, new questions both fundamental and practical have emerged. After reviewing some key aspects of the subject, we describe a promising candidate for exploring the possible beneficial effects of random noise in sensory transduction. (c) 1998 American Institute of Physics.     

随机共振实验

介绍了随机共振现象的基本原理、模拟电路,给出了一组实验结果,并绘制了实验曲红,分析了随机共振产生的原因。     

声学随机共振实验

在特定的非线性系统中,噪声的存在能够增强信号的响应, 这种现象为随机共振. 本文实验通过观察噪声对听觉阈限的影响,使学生了解声学中的随机共振现象.     

Lever-assisted two-noise stochastic resonance

A critical interplay of two correlated noises in a nonlinear symmetrical two-well potential system is experimentally demonstrated. One state can become completely noise free, leading to an infinite Kramers time. If an independent lever breaks the potential symmetry, stochastic resonance is recovered. In this new regime, we obtain a plateau, i.e., a high signal-to-noise ratio even for vanishing forcing signals.     

Doubly stochastic coherence via noise-induced symmetry in bistable neural models

The generation of coherent dynamics due to noise in an activator-inhibitor system describing bistable neural dynamics is investigated. We show that coherence can be induced in deterministically asymmetric regimes via symmetry restoration by multiplicative noise, together with the action of additive noise which induces jumps between the two stable steady states. The phenomenon is thus doubly stochastic, because both noise sources are necessary. This effect can be understood analytically in the frame of a small-noise expansion and is confirmed experimentally in a nonlinear electronic circuit. Finally, we show that spatial coupling enhances this coherent behavior in a form of system-size coherence resonance.     

System identification with stochastic resonance

Summary We study the impact of noise to the entrainment of underdamped nonlinear oscillators to resonant driving forces. We find that the power consumption is large at a certain noise level. In addition we find that power consumption drops significantly if the forcing function is off-resonant. We discuss possible applications for system identification. Paper presented at the International Workshop ?Fluctuations in Physics and Biology: Stochastic Resonance, Signal Processing and Related Phenomena?, Elba, 5–10 June 1994.     

Non-Gaussian,non-dynamical stochastic resonance

The classical model revealing stochastic resonance is a motion of an overdamped particle in a double-well fourth order potential when combined action of noise and external periodic driving results in amplifying of weak signals. Resonance behavior can also be observed in non-dynamical systems. The simplest example is a threshold triggered device. It consists of a periodic modulated input and noise. Every time an output crosses the threshold the signal is recorded. Such a digitally filtered signal is sensitive to the noise intensity. There exists the optimal value of the noise intensity resulting in the “most” periodic output. Here, we explore properties of the non-dynamical stochastic resonance in non-equilibrium situations, i.e. when the Gaussian noise is replaced by an α-stable noise. We demonstrate that non-equilibrium α-stable noises, depending on noise parameters, can either weaken or enhance the non-dynamical stochastic resonance.     

Brownian motors and stochastic resonance

We study the transport properties for a walker on a ratchet potential. The walker consists of two particles coupled by a bistable potential that allow the interchange of the order of the particles while moving through a one-dimensional asymmetric periodic ratchet potential. We consider the stochastic dynamics of the walker on a ratchet with an external periodic forcing, in the overdamped case. The coupling of the two particles corresponds to a single effective particle, describing the internal degree of freedom, in a bistable potential. This double-well potential is subjected to both a periodic forcing and noise and therefore is able to provide a realization of the phenomenon of stochastic resonance. The main result is that there is an optimal amount of noise where the amplitude of the periodic response of the system is maximum, a signal of stochastic resonance, and that precisely for this optimal noise, the average velocity of the walker is maximal, implying a strong link between stochastic resonance and the ratchet effect.