Nonequilibrium Noise Research Articles

Mesoscopic noise and admittance of an electrically driven nano-structure

We calculate current noise and admittance of an electrically driven nano-structure in a mesoscopic capacitor plate within Floquet scattering theory. We show that the interplay between quantum statistics and coherence of electrons is important in the photo-assisted non-equilibrium noise. Current noise has two different contributions; photo-assisted non-equilibrium noise and Nyquist equilibrium noise. At low frequencies ω and temperature, the photo-assisted non-equilibrium noise dominates the Nyquist equilibrium noise as their leading terms are proportional to ω 2 and ω 3 , respectively. The Nyquist noise has peak structure as a function of the Fermi energy caused by the large delay time associated with the (photo-assisted) resonant levels. Meanwhile, the photo-assisted current noise is not simply given by the phase delay time at the Fermi level. This is because, unlike the equilibrium noise, the photo-assisted current noise is also contributed from electron states far below the Fermi level. We interpret the real admittance g ′ ( ω ) in terms of the photo-assisted phase delay time.

Possible experimental manifestations of the many-body localization

Recently, it was predicted that if all one-electron states in a noninteracting disordered system are localized, the interaction between electrons in the absence of coupling to phonons leads to a finite-temperature metal-insulator transition. Here, we show that even in the presence of a weak coupling to phonons the transition manifests itself (i) in the nonlinear conduction, leading to a bistable $I\text{\ensuremath{-}}V$ curve, and (ii) by a dramatic enhancement of the nonequilibrium current noise near the transition.

Reciprocating Motion on the Nanoscale

This paper analyzes the confined motion of a Brownian particle fluctuating between two conformational states with different potential profiles and different position-dependent rate constants of the transitions, the fluctuations arising from both thermal (equilibrium) and external (nonequilibrium) noise. The model illustrates a mechanism to transduce, on the nanoscale, the energy of nonequilibrium fluctuations into mechanical energy of reciprocating motion. Expressions for the reciprocating velocity and the efficiency of energy conversion are derived. These expressions are treated in more detail in the slow-fluctuation (quasi-equilibrium) regime, by simple perturbation theory arguments, and in the fast fluctuation limit, in terms of the potential of mean force. A notable observation is that the generalized driving force of the reciprocating motion is caused by two sources: the energy contribution due to the difference between the potential profiles of the states and the entropic contribution due to the difference between the position-dependent rate constants. Two illustrative examples are presented, where one of the two sources can be ignored and an exact solution is allowed. Among other aspects, we also discuss the ways to construct a molecular motor based on the reciprocating engine.

Nonequilibrium 1∕f noise in low-doped manganite single crystals

1 ∕ f noise in current biased La0.82Ca0.18MnO3 crystals has been investigated. The temperature dependence of the noise follows the resistivity changes with temperature, suggesting that resistivity fluctuations constitute a fixed fraction of the total resistivity, independently of the dissipation mechanism and magnetic state of the system. The noise scales as a square of the current as expected for equilibrium resistivity fluctuations. However, at 77K at bias exceeding some threshold, the noise intensity starts to decrease with increasing bias. The appearance of nonequilibrium noise is interpreted in terms of bias dependent multistep indirect tunneling.

Constructive influence of noise-flatness in correlation ratchets

The influence of noise-flatness on overdamped motion of Brownian particles in a 1D periodic system with a simple sawtooth potential subjected to both unbiased thermal noise and three-level telegraph noise is considered. The exact formula for the stationary probability flux (current) is presented. The phenomenon of multiple current reversals and some topological properties of the hypersurface of zero current in the parameter space of noises are investigated and illustrated by phase diagrams. The conditions for the existence of four current reversals versus the switching rate of nonequilibrium noise are given. An alternative interpretation of the results in terms of cross-correlation between two dichotomous noises is presented.

Effects of non-Abelian statistics on two-terminal shot noise in a quantum Hall liquid in the Pfaffian state

We study non-equilibrium noise in the tunnelling current between the edges of a quantum Hall liquid in the Pfaffian state, which is a strong candidate for the plateau at $\nu=5/2$. To first non-vanishing order in perturbation theory (in the tunneling amplitude) we find that one can extract the value of the fractional charge of the tunnelling quasiparticles. We note however that no direct information about non-abelian statistics can be retrieved at this level. If we go to higher-order in the perturbative calculation of the non-equilibrium shot noise, we find effects due to non-Abelian statistics. They are subtle, but eventually may have an experimental signature on the frequency dependent shot noise. We suggest how multi-terminal noise measurements might yield a more dramatic signature of non-Abelian statistics and develop some of the relevant formalism.

Non-Markovian decoherence: A critique of the two-level approximation

The environmental decoherence in multilevelled systems in the context of two-level approximation is examined. It is found that the environmental temperature plays a minor role in the magnitudes of the decoherence rates whereas, the system-environment coupling and the environmental energy spectrum are dominant. Particularly, the latter is important in zero temperature quantum fluctuations and/or the nonequilibrium noise sources due to the large range of energies present in the environmental modes. Decoherence is found to be dominated by the short time nonresonant processes and this observation severely questions the use of the two-levelled models on decoherence.

Nonequilibrium statistical mechanical models for cytoskeletal assembly: Towards understanding tensegrity in cells

The cytoskeleton is not an equilibrium structure. To develop theoretical tools to investigate such nonequilibrium assemblies, we study a statistical physical model of motorized spherical particles. Though simple, it captures some of the key nonequilibrium features of the cytoskeletal networks. Variational solutions of the many-body master equation for a set of motorized particles accounts for their thermally induced Brownian motion as well as for the motorized kicking of the structural elements. These approximations yield stability limits for crystalline phases and for frozen amorphous structures. The methods allow one to compute the effects of nonequilibrium behavior and adhesion (effective cross-linking) on the mechanical stability of localized phases as a function of density, adhesion strength, and temperature. We find that nonequilibrium noise does not necessarily destabilize mechanically organized structures. The nonequilibrium forces strongly modulate the phase behavior and have comparable effect as the adhesion due to cross-linking. Modeling transitions such as these allows the mechanical properties of cytoskeleton to rapidly and adaptively change. The present model provides a statistical mechanical underpinning for a tensegrity picture of the cytoskeleton.

Nonequilibrium Noise as a Probe of the Kondo Effect in Mesoscopic Wires

We study the nonequilibrium noise in mesoscopic diffusive wires hosting magnetic impurities. We find that the shot-noise to current ratio develops a peak at intermediate source-drain biases of the order of the Kondo temperature. The enhanced impurity contribution at intermediate biases is also manifested in the effective distribution. The predicted peak represents an increased inelastic scattering rate at the nonequilibrium Kondo crossover.

Non-Markovian stochastic processes: Colored noise

We survey classical non-Markovian processes driven by thermal equilibrium or nonequilibrium (nonthermal) colored noise. Examples of colored noise are presented. For processes driven by thermal equilibrium noise, the fluctuation-dissipation relation holds. In consequence, the system has to be described by a generalized (integro-differential) Langevin equation with a restriction on the damping integral kernel: Its form depends on the correlation function of noise. For processes driven by nonequilibrium noise, there is no such a restriction: They are considered to be described by stochastic differential (Ito- or Langevin-type) equations with an independent noise term. For the latter, we review methods of analysis of one-dimensional systems driven by Ornstein-Uhlenbeck noise.

Self-Running Droplet: Emergence of Regular Motion from Nonequilibrium Noise

Spontaneous motion of an oil droplet driven by nonequilibrium chemical conditions is reported. It is shown that the droplet undergoes regular rhythmic motion under appropriately designed boundary conditions, whereas it exhibits random motion in an isotropic environment. This study is a novel manifestation on the direct energy transformation of chemical energy into regular spatial motion under isothermal conditions. A simple mathematical equation including noise reproduces the essential feature of the transition from irregularity into periodic regular motion. Our results will inspire the theoretical study on the mechanism of molecular motors in living matter, working under significant influence of thermal fluctuation.

Measuring Non-Gaussian Fluctuations through Incoherent Cooper-Pair Current

We study a Josephson junction (JJ) in the regime of incoherent Cooper-pair tunneling, capacitively coupled to a nonequilibrium noise source. The current-voltage (I-V) characteristics of the JJ are sensitive to the excess voltage fluctuations in the source, and can thus be used for wideband noise detection. Under weak driving, the odd part of the I-V can be related to the second cumulant of noise, whereas the even part is due to the third cumulant. After calibration, one can measure the Fano factors for the noise source, and get information about the frequency dependence of the noise.

Power and temperature dependence of low frequency noise in AlGaN∕GaN transmission line model structures

The low-frequency noise in AlGaN∕GaN transmission line model structures has been investigated for a wide range of ambient temperatures and dissipated powers. A deviation of low-frequency noise from a 1∕f dependence has been observed upon increasing the applied voltage. The effect correlates with the nonlinearity of current-voltage characteristics (CVC). The concept of nonequilibrium 1∕f noise has been introduced to explain 1∕f noise enhancement. A qualitative model connecting non-equilibrium noise with nonlinearity of the CVC via a common origin—nonuniform overheating of the structures—has been suggested. Furthermore, deviations of equilibrium noise from the 1∕f law at low temperatures have been observed and studied.

Anomalous mobility of Brownian particles in a tilted symmetric sawtooth potential

Overdamped motion of Brownian particles in a 1D periodic system with a simple symmetric sawtooth potential subjected to both unbiased thermal noise and spatially nonhomogeneous three-level colored noise is considered analytically. Upon application of a tilting force the particles exhibit anomalous transport properties, namely, absolute negative mobility, negative differential mobility, and the phenomenon of hypersensitive differential response. It is established that the mobility (differential mobility included) depends nonmonotonically on the parameters (switching rate, amplitude, and temperature) of nonequilibrium and thermal noises. The necessary conditions for various anomalous transport properties are found.

Fano factor reduction on the 0.7 conductance structure of a ballistic one-dimensional wire.

We have measured the nonequilibrium current noise in a ballistic one-dimensional wire which exhibits an additional conductance plateau at 0.7x2e(2)/h. The Fano factor shows a clear reduction on the 0.7 structure, and eventually vanishes upon applying a strong parallel magnetic field. These results provide experimental evidence that the 0.7 structure is associated with two conduction channels that have different transmission probabilities.

Equilibrium and non-equilibrium 1/f noise in AlGaN/GaN TLM structures

The low frequency noise of AlGaN/GaN transmission line model (TLM) structures has been investigated in a wide temperature range. Deviation of low frequency noise from 1/f dependence has been observed. The results indicate that the structure become more non-linear upon increasing of power. The observed features have been explained as a result of non-equilibrium condition in TLM structures, equilibrium and non-equilibrium noise cases have been studied. The non-equilibrium fluctuations in gateless TLM structures were analysed taking into account the influence of the positive surface charge, formed by polarization effects on dynamics of non-uniform potential redistribution along the channel.

Comprehensive study of noise processes in electrode electrolyte interfaces

A general circuit model is derived for the electrical noise of electrode–electrolyte systems, with emphasis on its implications for electrochemical sensors. The noise power spectral densities associated with all noise sources introduced in the model are also analytically calculated. Current and voltage fluctuations in typical electrode–electrolyte systems are demonstrated to originate from either thermal equilibrium noise created by conductors, or nonequilibrium excess noise caused by charge transfer processes produced by electrochemical interactions. The power spectral density of the thermal equilibrium noise is predicted using the fluctuation-dissipation theorem of thermodynamics, while the excess noise is assessed in view of charge transfer kinetics, along with mass transfer processes in the electrode proximity. The presented noise model not only explains previously reported noise spectral densities such as thermal noise in sensing electrodes, shot noise in electrochemical batteries, and 1/f noise in corrosive interfaces, it also provides design-oriented insight into the fabrication of low-noise micro- and nanoelectrochemical sensors.

Cosmological constant and vacuum energy

In systems possessing a spatial or dynamical symmetry breaking, thermal Brownian motion combined with unbiased, non-equilibrium noise gives rise to a channelling of chance that can be used to exercise control over systems at the micro- and even on the nano-scale. This theme is known as the “Brownian motor” concept. The constructive role of (the generally overdamped) Brownian motion is exemplified for a noise-induced transport of particles within various set-ups. We first present the working principles and characteristics with a proof-of-principle device, a diffusive temperature Brownian motor. Next, we consider very recent applications based on the phenomenon of signal mixing. The latter is particularly simple to implement experimentally in order to optimize and selectively control a rich variety of directed transport behaviors. The subtleties and also the potential for Brownian motors operating in the quantum regime are outlined and some state-of-the-art applications, together with future roadways, are presented.

Where is the shot noise of a quantum point contact?

Reznikov et al. [Phys. Rev. Lett. 75, 3340 (1995)]] have presented definitive observations of nonequilibrium noise in a quantum point contact. Especially puzzling is the "anomalous" peak structure of the excess noise measured at constant current; to date it remains unexplained. We show that their experiment directly reveals the deep link between conservation principles in the electron gas and its low-dimensional, mesoscopic behavior. The keys to that connection are gauge invariance and the compressibility sum rule. These are central not only to the experiment of Reznikov et al., but to the very nature of all mesoscopic transport.

Mechanism of hypersensitive transport in tilted sharp ratchets.

The noise-flatness-induced hypersensitive transport of overdamped Brownian particles in a tilted ratchet system driven by multiplicative nonequilibrium three-level Markovian noise and additive white noise is considered. At low temperatures, the enhancement of current is very sensitive to the applied small static tilting force. It is established that the enhancement of mobility depends nonmonotonically on the parameters (flatness, correlation time) of multiplicative noise. The optimal values of noise parameters maximizing the mobility are found.