Nonequilibrium Noise Research Articles

Calculation methods for thermo-optic noise and nonequilibrium noise in the coatings of space gravitational wave detection telescope

Calculation methods for thermo-optic noise and nonequilibrium noise in the coatings of space gravitational wave detection telescope

What Can we Learn from Nonequilibrium Response of a Strange Metal?

We critically address the recent experiment by L. Chen et al. [Science 382, 907 (2023)] on nonequilibrium transport and noise in a strange metal YbRh2Si2 patterned into the nanowire shape. In the long device, resistivity, differential resistance and current noise data seem to be consistent allowing us to extract electron–phonon coupling and the temperature dependence of electron–phonon scattering length. The obtained values can be reconciled with the experimental data for the short device only assuming the significant contact resistance. We discuss its possible origin as due to the current redistribution between YbRh2Si2 and its gold covering, and reveal that this redistribution contact resistance should be proportional to the YbRh2Si2 resistivity. We also discuss some subtleties of the noise measurements. Overall, neglecting electron–phonon energy relaxation even in the shortest devices is arguable so that the observed shot noise suppression can hardly be attributed to the failure of quasiparticle concept.

Emergent organization and polarization due to active fluctuations

A general model of self-propulsion with active fluctuations is introduced. It is shown that such a nonequilibrium noise source qualitatively modifies the organization of self-propelled particles in activity landscapes, as well as their collective dynamics in the presence of quorum-sensing interactions.

Light emission in delta- T -driven mesoscopic conductors

The scattering picture of electron transport in mesoscopic conductors shows that fluctuations of the current reveal additional information on the scattering mechanism not available through the conductance alone. The electronic fluctuations are coupled to the electromagnetic field and a junction at finite bias or temperature will emit radiation. The nonsymmetrized current-current correlators characterize the emission and absorption spectrum. Recent interest is focused on the so-called delta-$T$ noise, which is the nonequilibrium noise caused by a temperature difference between the terminals. Here, we generalize the notion of delta-$T$ noise to the nonsymmetrized current-current correlator at finite frequencies. We investigate the spectral density for energy-independent scattering and for a resonant level as an example of energy-dependent scattering. We find that a temperature difference $\mathrm{\ensuremath{\Delta}}T$ leads to a partial reduction of the noise for certain frequency ranges. This is a consequence of temperature broadening in combination with a frequency shift of the involved Fermi distributions. In the case of energy-independent scattering, the lowest order is a quadratic $\ensuremath{\propto}{(\mathrm{\ensuremath{\Delta}}T)}^{2}$ correction of the thermallike noise spectrum. For the resonance, an additional contribution to the delta-$T$ noise spectrum arises that is $\ensuremath{\propto}\mathrm{\ensuremath{\Delta}}T$ to the lowest order.

Fluctuation-driven excess noise near superconducting phase transition

We discuss intrinsic mechanisms of nonequilibrium excess noise in superconducting devices and transition edge sensors. In particular, we present an overview of fluctuation-driven contributions to the current noise in the vicinity of the superconducting transition. We argue that sufficiently close to the critical temperature fluctuations of conductivity may become correlated provided that the rate of quasiparticle relaxation is slow as compared to dynamics of superconducting fluctuations. In this regime, fluctuations of conductivity adiabatically follow the fluctuations of the electron distribution. This leads to a substantial enhancement of current noise. The corresponding spectral power density of noise has a Lorentzian shape in the frequency domain while its magnitude scales proportionally to the inelastic relaxation time. It also sensitively depends on the dephasing and Ginzburg–Landau timescales. Further estimates suggest that this mechanism dominates over the conventional temperature fluctuations in the same range of parameters. To describe these effects microscopically, we use the nonequilibrium Keldysh technique in the semiclassical approximation of superconductivity with Boltzmann–Langevin random forces to account for correlations of fluctuations.

Nonequilibrium noise as a probe of pair-tunneling transport in the BCS-BEC crossover.

The detection of elementary carriers in transport phenomena is one of the most important keys to understand nontrivial properties of strongly correlated quantum matter. Here, we propose a method to identify the tunneling current carrier in strongly interacting fermions from nonequilibrium noise in the Bardeen-Cooper-Schrieffer to Bose-Einstein condensate crossover. The noise-to-current ratio, the Fano factor, can be a crucial probe for the current carrier. Bringing strongly correlated fermions into contact with a dilute reservoir produces a tunneling current in between. The associated Fano factor increases from one to two as the interaction becomes stronger, reflecting the fact that the dominant conduction channel changes from the quasiparticle tunneling to the pair tunneling.

Charge, spin, and heat shot noises in the absence of average currents: Conditions on bounds at zero and finite frequencies

Nonequilibrium situations where selected currents are suppressed are of interest in fields like thermoelectrics and spintronics, raising the question of how the related noises behave. We study such zero-current charge, spin, and heat noises in a two-terminal mesoscopic conductor. In the presence of voltage, spin, and temperature biases, the nonequilibrium (shot) noises of charge, spin, and heat can be arbitrarily large, even if their average currents vanish. However, as soon as a temperature bias is present, additional equilibrium (thermal-like) noise necessarily occurs. We show that this equilibrium noise sets an upper bound on the zero-current charge and spin shot noises, even if additional voltage or spin biases are present. We demonstrate that these bounds can be overcome for heat transport by breaking the spin and electron-hole symmetries, respectively. By contrast, we show that the bound on the charge noise for strictly two-terminal conductors even extends into the finite-frequency regime.

Spin-noise spectroscopy of optical light shifts

Light induced non-equilibrium spin noise spectroscopy is theoretically and experimentally shown to be an efficient technique to reveal the structure and the coherent effects in the probed transition. Indeed, using metastable helium, the spin noise spectrum is shown to exhibit a dual-peak structure around the Larmor frequency. This previously unobserved feature is due to the light shifts of the involved levels and strongly depends on the probe power, detuning, and polarization orientation. Both numerical and analytical models reproduce very well the details of the split spin noise spectra: this technique thus allows a simple and direct measurement of the light shifts, and its polarization dependence permits to reveal the level structure in a non ambiguous manner.

Anomalous transport tuned through stochastic resetting in the rugged energy landscape of a chaotic system with roughness.

Stochastic resetting causes kinetic phase transitions, whereas its underlying physical mechanism remains to be elucidated. We here investigate the anomalous transport of a particle moving in a chaotic system with a stochastic resetting and a rough potential and focus on how the stochastic resetting, roughness, and nonequilibrium noise affect the transports of the particle. We uncover the physical mechanism for stochastic resetting resulting in the anomalous transport in a nonlinear chaotic system: The particle is reset to a new basin of attraction which may be different from the initial basin of attraction from the view of dynamics. From the view of the energy landscape, the particle is reset to a new energy state of the energy landscape which may be different from the initial energy state. This resetting can lead to a kinetic phase transition between no transport and a finite net transport or between negative mobility and positive mobility. The roughness and noise also lead to the transition. Based on the mechanism, the transport of the particle can be tuned by these parameters. For example, the combination of the stochastic resetting, roughness, and noise can enhance the transport and tune negative mobility, the enhanced stability of the system, and the resonant-like activity. We analyze these results through variances (e.g., mean-squared velocity, etc.) and correlation functions (i.e., velocity autocorrelation function, position-velocity correlation function, etc.). Our results can be extensively applied in the biology, physics, and chemistry, even social system.

Scattering theory of non-equilibrium noise and delta T current fluctuations through a quantum dot

We consider the non-equilibrium zero frequency noise generated by a temperature gradient applied on a device composed of two normal leads separated by a quantum dot. We recall the derivation of the scattering theory for non-equilibrium noise for a general situation where both a bias voltage and a temperature gradient can coexist and put it in a historical perspective. We provide a microscopic derivation of zero frequency noise through a quantum dot based on a tight binding Hamiltonian, which constitutes a generalization of the seminal result obtained for the current in the context of the Keldysh formalism. For a single level quantum dot, the obtained transmission coefficient entering the scattering formula for the non-equilibrium noise corresponds to a Breit–Wigner resonance. We compute the delta-T noise as a function of the dot level position, and for a broad range of values of the dot level width, in the Breit–Wigner case, for two relevant situations which were considered recently in two separate experiments. In the regime where the two reservoir temperatures are comparable, our gradient expansion shows that the delta-T noise is dominated by its quadratic contribution, and is minimal close to resonance. In the opposite regime where one reservoir is much colder, the gradient expansion fails and we find the noise to be typically linear in temperature before saturating. In both situations, we conclude with a short discussion of the case where both a voltage bias and a temperature gradient are present, in order to address the potential competition with thermoelectric effects.

Effects of the non-Markovianity and non-Gaussianity of active environmental noises on engine performance.

An active environment is a reservoir containing active materials, such as bacteria and Janus particles. Given the self-propelled motion of these materials, powered by chemical energy, an active environment has unique, nonequilibrium environmental noise. Recently, studies on engines that harvest energy from active environments have attracted a great deal of attention because the theoretical and experimental findings indicate that these engines outperform conventional ones. Studies have explored the features of active environments essential for outperformance, such as the non-Gaussian or non-Markovian nature of the active noise. We systematically study the effects of the non-Gaussianity and non-Markovianity of active noise on engine performance. We show that non-Gaussianity is irrelevant to the performance of an engine driven by any linear force (including a harmonic trap) regardless of time dependency, whereas non-Markovianity is relevant. However, for a system driven by a general nonlinear force, both non-Gaussianity and non-Markovianity enhance engine performance. Also, the memory effect of an active reservoir should be considered when fabricating a cyclic engine.

Accumulation of Particles and Formation of a Dissipative Structure in a Nonequilibrium Bath.

The standard textbooks contain good explanations of how and why equilibrium thermodynamics emerges in a reservoir with particles that are subjected to Gaussian noise. However, in systems that convert or transport energy, the noise is often not Gaussian. Instead, displacements exhibit an -stable distribution. Such noise is commonly called Lévy noise. With such noise, we see a thermodynamics that deviates from what traditional equilibrium theory stipulates. In addition, with particles that can propel themselves, so-called active particles, we find that the rules of equilibrium thermodynamics no longer apply. No general nonequilibrium thermodynamic theory is available and understanding is often ad hoc. We study a system with overdamped particles that are subjected to Lévy noise. We pick a system with a geometry that leads to concise formulae to describe the accumulation of particles in a cavity. The nonhomogeneous distribution of particles can be seen as a dissipative structure, i.e., a lower-entropy steady state that allows for throughput of energy and concurrent production of entropy. After the mechanism that maintains nonequilibrium is switched off, the relaxation back to homogeneity represents an increase in entropy and a decrease of free energy. For our setup we can analytically connect the nonequilibrium noise and active particle behavior to entropy decrease and energy buildup with simple and intuitive formulae.

Colossal Brownian yet non-Gaussian diffusion in a periodic potential: Impact of nonequilibrium noise amplitude statistics.

Last year, Białas et al. [Phys. Rev. E 102, 042121 (2020)] studied an overdamped dynamics of nonequilibrium noise driven Brownian particle dwelling in a spatially periodic potential and discovered a novel class of Brownian, yet non-Gaussian diffusion. The mean square displacement of the particle grows linearly with time and the probability density for the particle position is Gaussian; however, the corresponding distribution for the increments is non-Gaussian. The latter property induces the colossal enhancement of diffusion, significantly exceeding the well known effect of giant diffusion. Here, we considerably extend the above predictions by investigating the influence of nonequilibrium noise amplitude statistics on the colossal Brownian, yet non-Gaussian diffusion. The tail of amplitude distribution crucially impacts both the magnitude of diffusion amplification and the Gaussianity of the position and increments statistics. Our results carry profound consequences for diffusive behavior in nonequilibrium settings such as living cells in which diffusion is a central transport mechanism.

Nonequilibrium Kondo regime current noise spectrum of quantum dot systems with the single impurity Anderson model.

We investigate the nonequilibrium current noise spectrum of single impurity Anderson model quantum dot systems on the basis of the accurate dissipation equation of motion evaluations. By comparing between the equilibrium and nonequilibrium cases and between the non-Kondo and Kondo regimes, we identify the current noise spectrum of the nonequilibrium Kondo features that actually appear in the entire region of ω ∈ [-eV,eV]. It is well known that the primary Kondo characteristics at ω = ±eV = ±(μL -μR) display asymmetrical upturns and remarkable peaks in S(ω) and dS(ω)/dω, respectively. These features are originated from the Rabi interference of the transport current dynamics, with the Kondo oscillation frequency of |eV|. Moreover, we also identify the minor but very distinguishable inflections, crossing over from ω = -eV to ω = +eV. This uncovered feature would be related to the interference between two Kondo resonance channels.

Active noise-driven particles under space-dependent friction in one dimension.

We study a Langevin equation describing the stochastic motion of a particle in one dimension with coordinate x, which is simultaneously exposed to a space-dependent friction coefficient γ(x), a confining potential U(x) and nonequilibrium (i.e., active) noise. Specifically, we consider frictions γ(x)=γ_{0}+γ_{1}|x|^{p} and potentials U(x)∝|x|^{n} with exponents p=1,2 and n=0,1,2. We provide analytical and numerical results for the particle dynamics for short times and the stationary probability density functions (PDFs) for long times. The short-time behavior displays diffusive and ballistic regimes while the stationary PDFs display unique characteristic features depending on the exponent values (p,n). The PDFs interpolate between Laplacian, Gaussian, and bimodal distributions, whereby a change between these different behaviors can be achieved by a tuning of the friction strengths ratio γ_{0}/γ_{1}. Our model is relevant for molecular motors moving on a one-dimensional track and can also be realized for confined self-propelled colloidal particles.

Active motion of passive asymmetric dumbbells in a non-equilibrium bath

Persistent motion of passive asymmetric bodies in non-equilibrium media has been experimentally observed in a variety of settings. However, fundamental constraints on the efficiency of such motion are not fully explored. Understanding such limits, and ways to circumvent them, is important for efficient utilization of energy stored in agitated surroundings for purposes of taxis and transport. Here, we examine such issues in the context of erratic movements of a passive asymmetric dumbbell driven by non-equilibrium noise. For uncorrelated (white) noise, we find a (non-Boltzmann) joint probability distribution for the velocity and orientation, which indicates that the dumbbell preferentially moves along its symmetry axis. The dumbbell thus behaves as an Ornstein-Uhlenbeck walker, a prototype of active matter. Exploring the efficiency of this active motion, we show that in the over-damped limit, the persistence length l of the dumbbell is bound from above by half its mean size, while the propulsion speed v∥ is proportional to its inverse size. The persistence length can be increased by exploiting inertial effects beyond the over-damped regime, but this improvement always comes at the price of smaller propulsion speeds. This limitation is explained by noting that the diffusivity of a dumbbell, related to the product v∥l, is always less than that of its components, thus severely constraining the usefulness of passive dumbbells as active particles.

Colossal Brownian yet non-Gaussian diffusion induced by nonequilibrium noise.

We report on Brownian, yet non-Gaussian diffusion, in which the mean square displacement of the particle grows linearly with time, and the probability density for the particle spreading is Gaussian like, but the probability density for its position increments possesses an exponentially decaying tail. In contrast to recent works in this area, this behavior is not a consequence of either a space- or time-dependent diffusivity, but is induced by external nonthermal noise acting on the particle dwelling in a periodic potential. The existence of the exponential tail in the increment statistics leads to colossal enhancement of diffusion, drastically surpassing the previously researched situation known as "giant" diffusion. This colossal diffusion enhancement crucially impacts a broad spectrum of the first arrival problems, such as diffusion limited reactions governing transport in living cells.

Theory of nonequilibrium noise in general multiterminal superconducting hybrid devices: Application to multiple Cooper pair resonances

We consider the out-of-equilibrium behavior of a general class of mesoscopic devices composed of several superconducting or/and normal metal leads separated by quantum dots. Starting from a microscopic Hamiltonian description, we provide a nonperturbative approach to quantum electronic transport in the tunneling amplitudes between dots and leads: using the equivalent of a path integral formulation, the lead degrees of freedom are integrated out in order to compute both the current and the current correlations (noise) in this class of systems, in terms of the dressed Green's function matrix of the quantum dots. In order to illustrate the efficiency of this formalism, we apply our results to the ``all superconducting Cooper pair beam splitter,'' a device composed of three superconducting leads connected via two quantum dots, where crossed Andreev reflection operates Cooper pair splitting. Commensurate voltage differences between the three leads allow us to obtain expressions for the current and noise as a function of the Keldysh Nambu Floquet dressed Green's function of the dot system. This voltage configuration allows the occurrence of nonlocal processes involving multiple Cooper pairs which ultimately lead to the presence of nonzero DC currents in an out-of-equilibrium situation. We investigate in detail the results for the noise obtained numerically in the specific case of opposite voltages, where the transport properties are dominated by the so called ``quartet processes,'' involving the coherent exchange of two Cooper pairs among all three superconducting terminals. We show that these processes are noiseless in the nonresonant case, and that this property is also observed for other voltage configurations. When the dots are in a resonant regime, the noise characteristics change qualitatively, with the appearance of giant Fano factors.

Transport properties of strongly coupled electron–phonon liquids

In this work we consider the hydrodynamic behavior of a coupled electron–phonon fluid, focusing on electronic transport under the conditions of strong phonon drag. This regime occurs when the rate of phonon equilibration due to e.g. umklapp scattering is much slower than the rate of normal electron–phonon collisions. Then phonons and electrons form a coupled out-of-equilibrium state where the total quasi-momentum of the electron–phonon fluid is conserved. A joint flow-velocity emerges as a collective hydrodynamic variable. We derive the equation of motion for this fluid from the underlying microscopic kinetic theory and elucidate its effective viscosity and thermal conductivity. In particular, we derive decay times of arbitrary harmonics of the distribution function and reveal its corresponding super-diffusive relaxation on the Fermi surface. We further consider several applications of this theory to magneto-transport properties in the Hall-bar and Corbino-disk geometries, relevant to experiments. In our analysis we allow for general boundary conditions that cover the crossover from no-slip to no-stress flows. Our approach also covers a crossover from the Stokes to the Ohmic regime under the conditions of the Gurzhi effect. In addition, we consider the frequency dependence of the surface impedance and non-equilibrium noise. For the latter, we notice that in the diffusive regime, a Fokker–Planck approximation, applied to the electron–phonon collision integral in the Eliashberg form, reduces it to a differential operator with Burgers type nonlinearity. As a result, the non-equilibrium distribution function has a shock-wave structure in the energy domain. The consequence of this behavior for the Fano factor of the noise is investigated. In conclusion we discuss connections and limitations of our results in the context of recent electron–phonon drag measurements in Dirac and Weyl semimetals, and layout directions for further extensions and developments.

Anisotropic dynamics of a self-assembled colloidal chain in an active bath.

Anisotropic macromolecules exposed to non-equilibrium (active) noise are very common in biological systems, and an accurate understanding of their anisotropic dynamics is therefore crucial. Here, we experimentally investigate the dynamics of isolated chains assembled from magnetic microparticles at a liquid-air interface and moving in an active bath consisting of motile E. coli bacteria. We investigate both the internal chain dynamics and the anisotropic center-of-mass dynamics through particle tracking. We find that both the internal and center-of-mass dynamics are greatly enhanced compared to the passive case, i.e., a system without bacteria, and that the center-of-mass diffusion coefficient D features a non-monotonic dependence as a function of the chain length. Furthermore, our results show that the relationship between the components of D parallel and perpendicular with respect to the direction of the applied magnetic field is preserved in the active bath compared to the passive case, with a higher diffusion in the parallel direction, in contrast to previous findings in the literature. We argue that this qualitative difference is due to subtle differences in the experimental geometry and conditions and the relative roles played by long-range hydrodynamic interactions and short-range collisions.