Session Y28: Noise-Driven Dynamics I

Electrons, Spins, and Mechanics for Quantum Engines

Out-of-equilibrium phenomena in nanoscale devices can be harnessed to realise on-chip engines and refrigerators. I will show that fully suspended carbon nanotube devices have exceptional capabilities to explore thermodynamics at the nanoscale, combining electron tunnelling, spin physics, and high-frequency motion.

In these devices, and in the absence of a mechanical drive, the interplay between single electron tunnelling and mechanical motion can give rise to self-sustained oscillations. Fluctuations can make these self-oscillations irrupt, vanish, and exhibit a bistable behaviour causing hysteresis cycles. We find that self-oscillations can be stable for over 20 seconds, many orders of magnitude above electronic and mechanical characteristic timescales. I will also show that the mechanical motion of the carbon nanotube couples to single electron spins. This coupling, mediated by spin-orbit interaction, would allow for the study of fluctuations in electromechanical devices exhibiting quantum effects.   

Low fluctuations in a heated µ-resonator: first steps toward thermal noise engineering

The Fluctuation-Dissipation Theorem (FDT) is a cardinal tool of Statistical Physics. This relation yields to the Equipartition Principle, thanks to which we can link the fluctuations of an observable with the temperature of the system. In non-equilibrium situations however, such relations between fluctuations and response are not granted, and a higher noise is usually expected with respect to an equilibrium state. In this presentation, we show that the opposite phenomenon can also be experimentally observed: fluctuations smaller than in equilibrium!

In our experiment an atomic force microscope (AFM) µ-cantilever in vacuum is heated at its extremity with a laser. The heat flux sets the system in a Non-Equilibrium Steady State (NESS). We measure the thermal noise driven deflection d and quantify the amplitude of the fluctuations with an effective temperature T_eff extending the equipartition principle:

½ k_BT_eff = ½ k_n <d_n²>

with k_B the Boltzmann constant, k_n the mechanical mode stiffnesses and <d_n²> the mean square deflections. We observe a strong deficit of thermal noise with respect to the cantilever average temperature.

We will explain how a generalized FDT including the temperature field can account for these observations, when dissipation is not uniform. Further experimental evidence of the validity of this framework, down to cryogenic temperatures, will conclude the presentation. Our approach paves the way for thermal noise engineering: it can be used as a tool to probe the spatial distribution of dissipation, or on the contrary to tune the thermal noise amplitude and spectra by choosing an adequate damping field.   

Saddle avoidance of noise-induced transitions in multiscale nonequilibrium systems

In multistable dynamical systems driven by weak Gaussian noise, transitions between competing attracting states are commonly expected to pass near a saddle on the separating basin boundary. However, we show that nonequilibrium systems can behave quite differently: timescale separation can cause saddle avoidance. Using toy models from neuroscience and ecology, we analyze cases where sample transition paths deviate strongly from the minimum action path (instanton) predicted by large deviation theory, even for weak noise. As a result, the sample transition paths cross the basin boundary far away from the saddle. We attribute this to a flat Freidlin-Wentzell quasipotential and propose an approach based on the Onsager-Machlup action to accurately predict the most probable transition path. Anticipating the path of critical transitions in state space is desirable in applications ranging from brain dynamics to lasers and abrupt climate change, as it offers insight into the physical transition mechanism.   

Preserving equilibrium in stochastic models with spatially-correlated noise

In the continuum limit, spatially-correlated noise-driven stochastic partial differential equation (SPDE) models arise from considering that neighboring infinitesimally small spatial regions receive similar random perturbations. An additional benefit over white-noise-driven SPDEs is the regularization of solutions, especially in more than one spatial dimension. Nevertheless, using colored noise introduces a complication, as it disrupts the fluctuation-dissipation relationship of thermal equilibrium. In this presentation, I will discuss how the continuous spatiotemporal limit of a Metropolis-Hastings random walk can be employed to derive a stochastic partial differential equation driven by colored noise that preserves its ability to sample the equilibrium distribution, even for a system of magnetic spins. This introduces an additional geometric constraint and yields non-trivial interactions with the correlated noise, further enhancing our understanding of these intricate systems.   

Noise driven escape times in trapped ion systems

Trapped atomic ions are a promising platform for large scale quantum computation. To date, one of their biggest drawbacks has been the effects of 'anomalous motional heating' caused by electric field noise associated with trap surfaces. Precise understanding of the underlying mechanisms remains elusive, and this is a problem of considerable interest since motional heating impacts the fidelity of coherent operations and the length of time during which they can be performed. In order to shed light on these processes, we carry out simulations of first passage time distributions (FPTDs) associated with ion heating in the highly underdamped limit. These FPTDs make it possible to distinguish between correlated 'multiplicative' or 'parametric forcing' noise, and uncorrelated 'additive' noise. At long times, we find that the first passage time distribution (i.e., the distribution of times taken for the ion to gain a certain kinetic energy starting from the same initial condition) displays exponential decay for additive noise, while the decay for multiplicative noise appears to have a more complex form. In this talk, the focus is mostly on a classical model, but connections to quantum models and experimental realizations are also touched upon.   

Graphene heat engine

Nano-electromechanical systems (NEMS) have become an important platform in recent times for applications of nonlinear and non-equilibrium phenomena [1]. Recently, it has been demonstrated that squeezed states of NEMS modes can be used as two heat baths to construct a Carnot cycle towards development of a nano-mechanical heat engine [2]. With two quadratures acting as two temperature baths, practical applications of such  heat engines can be challenging, since it is often difficult to phase sensitivity couple one mode of system to the engine. Here we propose using a novel scheme of parametrically driving graphene resonators [3], at a frequency which is an order of magnitude lower than the fundamental mode of graphene.  With increasing drive strength, we find generation of sideband on the Thermal mode of graphene, cooling down the mode to 51 K. Furthermore, we find that with sudden turn-off of the drive, the temperature equilibrates at a time scale which is orders of magnitude faster than the time scale over which the frequency of the fundamental graphene modes shift. We use the shifted frequency, along with changing thermal phonons as two paths to close a Carnot cycle that operates with an efficiency of 83%. Dispersion of graphene allows us to switch the sense of direction of the cycles, thereby converting the engine to a refrigerator. We expect these results to be applicable in a wide range of nano-scale devices which seeks efficient conversion from thermal phonons to mechanical work at rf frequencies.   

Dissipative timescales from coarse-graining irreversibility

A goal of stochastic thermodynamics research is the development of methods to identify the degrees of freedom responsible for energy dissipation in nonequilibrium steady-states. To complement these efforts, we present a method for estimating the time-scale of dissipative processes modeled as steady-state Markov jump processes on discrete-state spaces. The method exploits an inequality between the entropy production and the irreversibility–the statistical breaking of time-reversal symmetry. We show that when there is a time-scale separation between the dissipative and non-dissipative processes, the irreversibility as a function of the coarse-graining time gives rise to a sigmoid-like profile with a drop off at a coarse-graining time that is inversely proportional to the rate of dissipation. From these observations we derive a functional form that estimates the irreversibility in this highly dissipative regime. Using this functional form as a fitting ansatz, we then propose a method to measure this dissipative time-scale from time-series data, and benchmark it using synthetic data. This method thus lends itself to experimental applications where the rate of dissipative processes are of interest and unknown.   

Topologically-constrained fluctuations and thermodynamics regulate nonequilibrium response

A fruitful technique to infer the physical properties of a system, in and out of equilibrium, is to observe how it responds to external perturbations. Near equilibrium, the Fluctuation-Dissipation Theorem is a powerful tool for rationalizing our observations about response by equating them to fluctuations. Its relevance has driven significant interest in developing similar equalities valid far from equilibrium, leading to critical theoretical insights into the characteristics of nonequilibrium response. Recently a different perspective has been conceptualized, where instead of seeking general fluctuation-response equalities the goal is to identify fundamental limits to nonequilibrium response. Building upon this approach, we prove a novel fluctuation-response inequality and show that an arbitrary nonequilibrium response is constrained by fluctuations of a topological variable and enhanced by nonequilibrium driving. Our fluctuation-response inequality notably requires no kinetic information beyond the state space structure. When applied to models of receptor binding, this prediction reveals that sensitivity is bounded by the steepness of a Hill function with a Hill coefficient enhanced beyond the structural thermodynamic limit by the chemical driving.   

Harnessing viscoelasticity to suppress irreversibility build-up in a colloidal Stirling engine

Typically, the rate at which a heat engine can produce useful work is constrained by the build-up of irreversibility with increasing operating speed. Here, using a recently developed reservoir engineering technique, we designed and quantified the performance of a colloidal Stirling engine operating in a viscoelastic bath. While the bath acts like a viscous fluid in the quasistatic limit, and the engine's performance agrees with equilibrium predictions, on reducing the cycle time to the bath's structural relaxation time, the increasingly elastic response of the bath aids suppress the build-up of irreversibility. We show that the elastic energy stored during the isothermal compression step of the Stirling cycle facilitates quick equilibration in the isothermal expansion step. This results in equilibrium-like efficiencies even for cycle times shorter than the equilibration time of the colloidal particle.   

Jamming from Stochastic Dynamics with Interactive Noise

Random close packing of spheres has been studied using dynamical models such as biased random organization (BRO) and gradient descent. In this study, we develop a continuous-time stochastic model of particle dynamics called Stochastic Dynamics with Interactive Noise (SDIN). This model incorporates repulsive interactions and athermal noise stemming from particle interactions. Due to the anisotropic and inhomogeneous nature of the particles' microenvironment, we model fluctuations using multiplicative, anisotropic noise. We then demonstrate that SDIN approximates both biased random organization (BRO) and mini-batch gradient descent (MGD) in the limit of small step size (or learning rate), hence BRO and MGD are equivalent in this limit, and they converge to the same random close packing fraction. Furthermore, we show that the behavior of MGD near the critical (jamming) point is consistent with the Manna universality class and exhibits hyperuniformity at the jamming point.   

Energy Harvesting in a 2-dimensional Anisotropic Temperature field

We consider overdamped Brownian particles with two degrees of freedom (DoF), confined in a time-varying quadratic potential and subject to anisotropic fluctuations. We quantify maximal work extraction via an isoperimetric problem where the Wasserstein length of cyclic trajectory quantifies dissipation and a surface integral over the enclosing curve in the manifold of thermodynamic states (thermodynamic cycle) quantifies extracted work. The efficiency can likewise be bounded by an isoperimetric inequality, providing universal speed limits to work extraction. The analyis extends earlier results that pertain to the case where the entropy of thermodynamic states is kept constant along the cycle. Our present analysis, that addresses the general case, shows that by exploring variation in entropy dissipation along the cycle can be reduced, as compared to the constant-entropy case. Thereby, we characterize optimal trajectories that attain maximal work output and efficiency in complete generality.