P. V. E. McClintock

Linear Response Theory in Stochastic Resonance

The susceptibility of an overdamped Markov system fluctuating in a bistable potential of general form is obtained by analytic solution of the Fokker-Planck equation (FPE) for low noise intensities. The results are discussed in the context of the LRT theory of stochastic resonance. They go over into recent results of Hu et al. [Phys. Lett. A 172 (1992) 21] obtained from the FPE for the case of a symmetrical potential, and they coincide with the LRT results of Dykman et al. [Phys. Rev. Lett. 65 (1990) 2606; JETP Lett. 52 (1990) 144; Phys. Rev. Lett. 68 (1992) 2985] obtained for the general case of bistable systems.

The breakdown of superfluidity in liquid 4He. VI, Macroscopic quantum tunnelling by vortices in isotopically pure He II

Measurements are reported of the rate v at which negative ions nucleate quantized vortices in isotopically pure superfluid 4He for electric fields E, temperatures T and pressures P within the range 103 ⩽ E ⩽ 106 V m-1, 75 ⩽ T ⩽ 500 mK, 12 ⩽ P ⩽ 23 bar (= 2.3 MPa). The form of v(E, T) differs in unexpected ways from that observed in earlier work at higher P, exhibiting: a pronounced dip in v(T) at ca. 0.3 K whose depth and precise position depends on E and P ; an exponential increase in v(T) at higher T, with an activation energy considerably smaller than the roton energy gap; and distinct structure in v(E). The experimental data are discussed and analysed in terms of the macroscopic quantum tunnelling model proposed by Muirhead et al. (Phil. Trans. R. Soc. Lond. A 311, 433 (1984)). The relatively small barrier heights of ca. 2—3 K deduced from the data on this basis are construed as confirmation that the initial vortex is a loop rather than an encircling ring. The temperature dependence of v at low pressures is interpreted in terms of a phonon-driven vortex nucleation mechanism, and values for its cross section are extracted from the data. The minima in v(T) are ascribed to phonon damping of the tunnelling process, and the kinks observed in some of the low-temperature v(E) curves are attributed to tunnelling of the system into the first excited state of the nascent vortex loop.

Branch selectivity at the bifurcation of a bistable system with external noise

Abstract Measurements of the time evolution of the statistical density as a control parameter is swept through a bifurcation point in the presence of additive noise are presented. We have used these densities to study branch selectivity, which results from a small, additive interaction, A universal time scale for all such processes is established. The results are in good agreement with a recent theory.

Branch selection in the presence of coloured noise

We have experimentally studied the effects of exponentially correlated, gaussian, additive noise on an electronic bistable system whose instability is driven by a time dependent external control parameter. The results, which indicate that the noise correlation time has little influence on the statistics of branch selection, are in substantial agreement with the predictions of a simple, physically motivated theory outlined herein.

Colored noise in the ring-laser gyroscope : theory and simulation.

We present a theoretical analysis of the effect of noise color on the mean beat frequency of a ring‐laser gyroscope based on the matrix continued‐fraction technique. The results are compared to measurements made on an electronic circuit model, and to digital simulations.

Cosmological experiments in liquid 4He: status and prospects

A recent experiment, in which a small volume of liquid 4He is expanded rapidly through the lambda transition to model the mechanism of cosmic string creation in the early universe, is reviewed. New data are presented, suggesting that, although most of the quantized vortices generated in the expansion are created (like cosmic strings) by passage through the phase transition at a finite speed, a proportion of them are probably produced through more conventional processes. Possible ways of redesigning the experiment, so as to reduce the latter extraneous vortex creation processes, are discussed.

The effect of multiplicative noise on the relaxation time of a real non-linear physical system: a comparison of experiment and theory for the random growing rate model (RGRM)

It is found that the theoretical behaviour of the relaxation time T for the random growing rate model (RGRM) under the influence of multiplicative noise of intensity Q (a monotonic decrease of T-1 towards a limiting value as Q to infinity ) differs markedly from that actually measured in electronic simulators of that system. A new electronic analogue experiment is described in which a distinct minimum in T-1(Q) has been observed for the first time, with clear evidence for an increase of T-1(Q) with Q at large Q in good qualitative agreement with an earlier analogue experiment. The discrepancy between experiment and the theoretical solutions of the (idealised) equation is attributed to the profound influence exerted by the very weak additive noise which must also, in some measure, always be present in a real physical system.

Spectral Distribution of a Double-Well Duffing Oscillator Subject to a Random Force

The power spectral density Q(ω) for an electronic circuit model of the double-well Duffing oscillator, driven by Gaussian white noise, has been measured in the limit of very low damping. Three distinct maxima and a plateau region are found in Q(ω), in excellent qualitative agreement with a recent theoretical prediction by Dykman and co-workers.

Delayed thermal relaxation of superfluid 4He at mK temperatures

Abstract It is found that the thermal relaxation of superfluid 4 He in the mK range differs substantially, depending on whether it has been heated with an oscillating grid or by the passage of a field emission current.

Noise-induced escape on time scales preceding quasistationarity: New developments in the Kramers problem

Noise-induced escape from the metastable part of a potential is considered on time scales preceding the formation of quasiequilibrium within that part of the potential. It is shown that, counterintuitively, the escape flux may then depend exponentially strongly, and in a complicated manner, on time and friction. (c) 2001 American Institute of Physics.