Nonequilibrium fluctuation-induced phenomena in Josephson junctions

Invited review: Fluctuation-induced transport. From the very small to the very large scales

The study of fluctuation-induced transport is concerned with the directed motion of particles on a substrate when subjected to a fluctuating external field. Work over the last two decades provides now precise clues on how the average transport depends on three fundamental aspects: the shape of the substrate, the correlations of the fluctuations and the mass, geometry, interaction and density of the particles. These three aspects, reviewed here,  acquire additional relevance because the same notions apply to a bewildering variety of problems at very different scales, from the small nano or micro-scale, where thermal fluctuations effects dominate,  up to very large scales including ubiquitous cooperative phenomena in granular materials. Received: 30 October 2015,  Accepted: 4 February  2016; Edited by: G. Martínez Mekler; Reviewed by: J. Mateos, Departamento de Sistemas Complejos, Instituto de Física, Universidad Nacional Autónoma de México, México.; DOI: http://dx.doi.org/10.4279/PIP.080004Cite as: G P Suárez, M Hoyuelos, D R Chialvo, Papers in Physics 8, 080004 (2016)This paper, by G P Suárez, M Hoyuelos, D R Chialvo, is licensed under the Creative Commons Attribution License 3.0.

Noise-induced multi-decrease and multi-increase of net voltage in Josephson junctions

In this paper, we investigate the net voltage in the Josephson junction subject to a thermal noise, a dc constant bias electric current and an ac time-periodic electric drive for the overdamped case and underdamped case simultaneously. It is shown that, by increasing the thermal noise strength, the net voltage can be decreased and increased several times as a function of the driving frequency. In addition, noise-enhanced stability is found for the net voltage of the junction.

Appearance of spatiotemporal noise and its effect on transport of electron pairs in a superconducting junction device

Transport of electron pairs in a superconducting junction device with spatiotemporal noise is investigated. It is shown that, in a superconducting junction device, spatiotemporal noise can appear and induce a nonzero current due to the symmetry breaking induced by the correlation of the spatiotemporal noise with the phase difference. We found that there is a negative current for the electron pairs, exhibiting a well with increasing thermal noise strength. Our results can provide a theoretical foundation for the further investigation of superconducting junctions.

Chaotic noisy transport of electron pairs in a superconducting junction device: thermal-inertia ratchets

Chaotic noisy transport of electron pairs in a superconducting junction device (thermal-inertia ratchets) is investigated. The study shows that when the temperature is low enough, the transport of the electron pairs can be mainly chaotic; when the temperature is high enough, it can be mainly stochastic. By controlling the temperature and the amplitude of the input ac signal, the current of electron pairs can be reversed.

Spontaneous symmetry breaking of population in a nonadiabatically driven atomic trap: an Ising-class phase transition

We have observed spontaneous symmetry breaking of the population of Brownian particles between two moving potentials in the spatiotemporally symmetric system. Cold atoms preferentially occupy one of the dynamic double-well potentials, produced in the parametrically driven dissipative magneto-optical trap far from equilibrium, above a critical number of atoms. We find that the population asymmetry, which may be interpreted as the biased Brownian motion, can be qualitatively described by the mean-field Ising-class phase transition. This in situ study may be useful for investigation of dynamic phase transition or temporal behavior of critical phenomena.

Directed transport of Brownian particles in a double symmetric potential

We investigate the dynamics of Brownian particles in internal state-dependent symmetric and periodic potentials. Although no space or time symmetry of the Hamiltonian is broken, we show that directed transport can appear. We demonstrate that the directed motion is induced by breaking the symmetry of the transition rates between the potentials when these are spatially shifted. Finally, we discuss the possibility of realizing our model in a system of cold particles trapped in optical lattices.

Drift by dichotomous Markov noise

We derive explicit results for the asymptotic probability density and drift velocity in systems driven by dichotomous Markov noise, including the situation in which the asymptotic dynamics crosses unstable fixed points. The results are illustrated on the problem of the rocking ratchet.

Superconducting junctions perturbed by environmental fluctuation

A superconducting junctions device is investigated in the case of the environmental perturbation. It is found that a net voltage can be produced, whose absolute value represents a phenomenon of resonance versus the additive noise strength, and may be negative, positive, and zero. By controlling the correlation between the additive and multiplicative noises, a reversal for the net voltage can be induced. The dc voltage versus the dc current is studied. It is shown that (1) with increasing the additive noise strength, the curve of the dc voltage versus the dc current is nearer and nearer to the one for the Ohmic theorem; (2) the behavior of the dc voltage versus the dc current can be manipulated by controlling the noise's strengths. In addition, we study the mean first passage time (MFPT) for the electron pair over a period of the potential, and find that the transition rate (i.e., inverse of the MFPT) can be suppressed by the positive correlations between the additive and multiplicative noises and show a minimum as the function of the noise's strengths.

Nonlinear response with dichotomous noise

Dichotomous noise appears in a wide variety of physical and mathematical models. It has escaped attention that the standard results for the long time properties cannot be applied when unstable fixed points are crossed in the asymptotic regime. We show how calculations have to be modified to deal with these cases and present as a first application full analytic results for hypersensitive transport.

Transport of particles for a spatially periodic stochastic system with correlated noises

The transport of particles for a spatially periodic stochastic system driven by two multiplicative noises and one additive noise (between which there are correlations) is investigated for the overdamped and underdamped cases. It is shown that (i) the probability current can be positive, zero, or negative; (ii) the movement of the particles represents the phenomenon of resonance as a function of the additive noise strength. For the underdamped case, the particles with different mass can be separated by controlling the system or the noise parameters. In particular, a reversal of the flux can be induced by controlling the correlations between the additive and multiplicative noises.

Nonequilibrium response spectroscopy of voltage-sensitive ion channel gating

We describe a new electrophysiological technique called nonequilibrium response spectroscopy, which involves application of rapidly fluctuating (as high as 14 kHz) large-amplitude voltage clamp waveforms to ion channels. As a consequence of the irreversible (in the sense of Carnot) exchange of energy between the fluctuating field and the channel protein, the gating response is exquisitely sensitive to features of the kinetics that are difficult or impossible to adequately resolve by means of traditional stepped potential protocols. Here we focus on the application of dichotomous (telegraph) noise voltage fluctuations, a broadband Markovian colored noise that fluctuates between two values. Because Markov kinetic models of channel gating can be embedded within higher-dimensional Markov models that take into account the effects of the voltage fluctuations, many features of the response of the channels can be calculated algebraically. This makes dichotomous noise and its generalizations uniquely suitable for model selection and kinetic analysis. Although we describe its application to macroscopic ionic current measurements, the nonequilibrium response method can also be applied to gating and single channel current recording techniques. We show how data from the human cardiac isoform (hH1a) of the Na+ channel expressed in mammalian cells can be acquired and analyzed, and how these data reveal hidden aspects of the molecular kinetics that are not revealed by conventional methods.