Stochastic resonance in electrical circuits—II: Nonconventional stochastic resonance.

Stochastic resonance (SR), in which a periodic signal in a nonlinear system can be amplified by added noise, is discussed. The application of circuit modeling techniques to the conventional form of SR, which occurs in static bistable potentials, was considered in a companion paper. Here, the investigation of nonconventional forms of SR in part using similar electronic techniques is described. In the small-signal limit, the results are well described in terms of linear response theory. Some other phenomena of topical interest, closely related to SR, are also treate

Stochastic resonance in electrical circuits—I: Conventional stochastic resonance.

Stochastic resonance (SR), a phenomenon in which a periodic signal in a nonlinear system can be amplified by added noise, is introduced and discussed. Techniques for investigating SR using electronic circuits are described in practical terms. The physical nature of SR, and the explanation of weak-noise SR as a linear response phenomenon, are considered. Conventional SR, for systems characterized by static bistable potentials, is described together with examples of the data obtainable from the circuit models used to test the theory

Phase locking below rate threshold in noisy model neurons

The property of a neuron to phase-lock to an oscillatory stimulus before adapting its spike rate to the stimulus frequency plays an important role for the auditory system. We investigate under which conditions neurons exhibit this phase locking below rate threshold. To this end, we simulate neurons employing the widely used leaky integrate-and-fire (LIF) model. Tuning parameters, we can arrange either an irregular spontaneous or a tonic spiking mode. When the neuron is stimulated in both modes, a significant rise of vector strength prior to a noticeable change of the spike rate can be observed. Combining analytic reasoning with numerical simulations, we trace this observation back to a modulation of interspike intervals, which itself requires spikes to be only loosely coupled. We test the limits of this conception by simulating an LIF model with threshold fatigue, which generates pronounced anticorrelations between subsequent interspike intervals. In addition we evaluate the LIF response for harmonic stimuli of various frequencies and discuss the extension to more complex stimuli. It seems that phase locking below rate threshold occurs generically for all zero mean stimuli. Finally, we discuss our findings in the context of stimulus detection

Noise-enhanced heterodyning

A new form of heterodyning is reported, related to stochastic resonance, in which a heterodyne signal can be enhanced by adding noise

Nonconventional stochastic resonance.

It is argued, on the basis of linear response theory (LRT), that new types of stochastic resonance (SR) are to be anticipated in diverse systems, quite different from the one most commonly studied to date, which has a static double-well potential and is driven by a net force equal to the sum of periodic and stochastic terms. On this basis, three new nonconventional forms of SR are predicted, sought, found, and investigated both theoretically and by analogue electronic experiment: (a) in monostable systems; (b) in bistable systems with periodically modulated noise; and (c) in a system with coexisting periodic attractors. In each case, it is shown that LRT can provide a good quantitative description of the experimental results for sufficiently weak driving fields. It is concluded that SR is a much more general phenomenon than has hitherto been appreciated

Ab initio study of canted magnetism of finite atomic chains at surfaces

By using ab initio methods on different levels we study the magnetic ground state of (finite) atomic wires deposited on metallic surfaces. A phenomenological model based on symmetry arguments suggests that the magnetization of a ferromagnetic wire is aligned either normal to the wire and, generally, tilted with respect to the surface normal or parallel to the wire. From a first principles point of view, this simple model can be best related to the so--called magnetic force theorem calculations being often used to explore magnetic anisotropy energies of bulk and surface systems. The second theoretical approach we use to search for the canted magnetic ground state is first principles adiabatic spin dynamics extended to the case of fully relativistic electron scattering. First, for the case of two adjacent Fe atoms an a Cu(111) surface we demonstrate that the reduction of the surface symmetry can indeed lead to canted magnetism. The anisotropy constants and consequently the ground state magnetization direction are very sensitive to the position of the dimer with respect to the surface. We also performed calculations for a seven--atom Co chain placed along a step edge of a Pt(111) surface. As far as the ground state spin orientation is concerned we obtain excellent agreement with experiment. Moreover, the magnetic ground state turns out to be slightly noncollinear.Comment: 8 pages, 5 figures; presented on the International Conference on Nanospintronics Design and Realizations, Kyoto, Japan, May 2004; to appear in J. Phys.: Cond. Matte

Spin currents and spin dynamics in time-dependent density-functional theory

We derive and analyse the equation of motion for the spin degrees of freedom within time-dependent spin-density-functional theory (TD-SDFT). Results are (i) a prescription for obtaining many-body corrections to the single-particle spin currents from the Kohn-Sham equation of TD-SDFT, (ii) the existence of an exchange-correlation (xc) torque within TD-SDFT, (iii) a prescription for calculating, from TD-SDFT, the torque exerted by spin currents on the spin magnetization, (iv) a novel exact constraint on approximate xc functionals, and (v) the discovery of serious deficiencies of popular approximations to TD-SDFT when applied to spin dynamics.Comment: now includes discussion of OEP and GGA; to appear in Phys. Rev. Let

Pion-Lambda-Sigma Coupling Extracted from Hyperonic Atoms

The latest measurements of the atomic level width in Sigma-hyperonic Pb atom offer the most accurate datum in the region of low-energy Sigma-hyperon physics. Atomic widths are due to the conversion of Sigma-nucleon into Lambda-nucleon. In high angular momentum states this conversion is dominated by the one-pion exchange. A joint analysis of the data of the scattering of negative-Sigma on proton converting into a Lambda and a neutron and of the atomic widths allows to extract a pseudovector pion-hyperon-Sigma coupling constant of 0.048 with a statistical error of +-0.005 and a systematic one of +-0.004. This corresponds to a pseudoscalar coupling constant of 13.3 with a statistical uncertainty of 1.4 and a systematic one of 1.1.Comment: 12 pages, 1 figure, Use of Revtex.st

Dynamics of defect formation

A dynamic symmetry-breaking transition with noise and inertia is analyzed. Exact solution of the linearized equation that describes the critical region allows precise calculation (exponent and prefactor) of the number of defects produced as a function of the rate of increase of the critical parameter. The procedure is valid in both the overdamped and underdamped limits. In one space dimension, we perform quantitative comparison with numerical simulations of the nonlinear nonautonomous stochastic partial differential equation and report on signatures of underdamped dynamics.Comment: 4 pages, LaTeX, 4 figures. Submitted to Physical Revie