Session R40: Systems with Large Fluctuations and Strong Correlations I

Kinetic roughening: how directionality changes the game

The nonequilibrium evolution of growing interfaces has attracted many experimental and theoretical studies over decades. One of the most popular theoretical approaches considers kinetic discrete models to describe particle aggregation on substrates. Albeit simple, these models are expected to contain the relevant physics. Inspired by recent advances in the production of functionalized colloidal particles, with attractive patches on their surface, we have proposed a stochastic model to study the effect of directionality and selective pairwise interactions on the kinetics of aggregation. We find a nontrivial dependence of the bulk and surface properties on the strength and flexibility of the patch-patch interactions, and on the spatial-patch distribution. For three-patch particles, sustained growth is only observed for a finite-range of the distance between patches, yielding two absorbing phase transitions and a tricritical flexibility. For four-patch particles with two distinct patches, i.e. strong and weak bonds, and sufficiently different bonding probabilities, the scaling properties of the interface crossover from the universality class of Kardar-Parisi-Zhang to the critical class of Kardar-Parisi-Zhang with quenched disorder. The latter is observed for an extended range of the parameters revealing the presence of a self-organized critical mechanism. Implications of our findings beyond functionalized particles are also discussed.   

Exactly solvable models of growing interfaces: the Arcetri models

Motivated by an analogy with the spherical model of a ferromagnet, the Arcetri models present new universality classes for the growth of interfaces, distinct from the common Edwards-Wilkinson and Kardar-Parisi-Zhang universality classes. Those models are obtained by treating and replacing the non-linear term in the noisy Burgers equation or the KPZ equation by a mean spherical condition. We studied the consequences of such constraints on the Edwards-Wilkinson (EW) interface.   

Infinite-noise criticality: Nonequilibrium phase transitions in fluctuating environments

We study the effects of time-varying environmental noise on nonequilibrium phase transitions in spreading and growth processes. Using the examples of the logistic evolution equation as well as the contact process, we show that such temporal disorder gives rise to a distinct type of critical points at which the effective noise amplitude diverges on long time scales. This leads to enormous density fluctuations characterized by an infinitely broad probability distribution at criticality. We develop a real-time renormalization-group theory that provides a general framework for the effects of temporal disorder on nonequilibrium processes. We also discuss how general this exotic critical behavior is, we illustrate the results by computer simulations, and we touch upon experimental applications of our theory.   

Random field disorder at an absorbing state transition in one and two dimensions

We investigate the behavior of nonequilibrium phase transitions under the influence of disorder that locally breaks the symmetry between two symmetrical macroscopic absorbing states. In equilibrium systems such ``random-field'' disorder destroys the phase transition in low dimensions by preventing spontaneous symmetry breaking. In contrast, we show here that random-field disorder fails to destroy the nonequilibrium phase transition of the one- and two-dimensional generalized contact process. Instead, it hampers the dynamics in the symmetry-broken phase. Specifically, the dynamics in the one-dimensional case is described by a Sinai walk of the domain walls between two different absorbing states. In the two-dimensional case, we map the dynamics onto that of the well studied low-temperature random-field Ising model. We also study the critical behavior of the nonequilibrium phase transition and characterize its universality class in one dimension. We support our results by large-scale Monte-Carlo simulations and discuss the applicability of our theory to other systems.   

Leveraging large fluctuations for stochastic control in uncertain environments

We present the development of a stochastic control strategy that leverages the environmental dynamics and uncertainty to navigate in a stochastic fluidic environment. We assume that the domain is composed of the union of a collection of disjoint regions, each bounded by Lagrangian coherent structures (LCSs). We analyze a passive particle's noise-induced transition between adjacent LCS-bounded regions and show how most probable escape trajectories with respect to the transition probability between adjacent LCS-bounded regions can be determined. Additionally, we show how the likelihood of transition can be controlled through minimal actuation. The result is an energy efficient navigation strategy that leverages the inherent uncertainty of the surrounding flow field for controlling sensors in a noisy fluidic environment. We experimentally validate the proposed control strategy and show that the single vehicle control parameter exhibits a predictable exponential scaling with respect to the escape times and is effective even in situations where the structure of the flow is not fully known and control effort is costly.   

Flux line non-equilibrium relaxation kinetics following current quenches in disordered type-II superconductors

We investigate the relaxation dynamics of magnetic vortex lines in disordered type-II superconductors following rapid changes in the external driving current by means of Langevin molecular dynamics simulations for an elastic line model. A system of driven interacting flux lines in a sample with randomly distributed point pinning centers is initially relaxed to a moving non-equilibrium steady state. The current is then instantaneously decreased, such that the final stationary state resides either still in the moving regime, or in the pinned Bragg glass phase. The ensuing non-equilibrium relaxation kinetics of the vortices is studied in detail by measuring the mean flux line gyration radius and the two-time transverse height autocorrelation function. The latter allows us to investigate the physical aging properties for quenches from the moving into the glassy phase, and to compare with non-equilibrium relaxation features obtained with different initial configurations.   

Local temperatures and voltages in quantum systems far from equilibrium

We show that the local measurement of temperature and voltage for a quantum system in steady state, arbitrarily far from equilibrium, with arbitrary interactions within the system, is unique when it exists. This is interpreted as a consequence of the second law of thermodynamics. We further derive a necessary and sufficient condition for the existence of a solution. In this regard, we find that a solution occurs whenever there is no net population inversion. However, when there is a net population inversion, we may characterize the system with a (unique) negative temperature. These results provide a firm mathematical foundation for our measurement protocol, and sound meaning to such measurements in the thermodynamic sense.   

Quasiparticle explanation of "weak thermalization" regime under quench in a non-integrable quantum spin chain

Eigenstate Thermalization Hypothesis provides one picture of thermalization in a quantum system by looking at individual eigenstates. However, it is also important to consider how local observables reach equilibrium values dynamically. Quench protocol is one of the settings to study such questions. A recent numerical study [Banuls, Cirac, and Hastings, Phys. Rev. Lett. \textbf{106}, 050405 (2011)] of a nonintegrable quantum Ising model with longitudinal field under such quench setting found different behaviors under different initial quantum states. One particular case termed “weak thermalization” regime showed apparently persistent oscillations of some observables. Here we provide an explanation of such oscillations. We use perturbation theory near the ground state of the model, and identify the oscillation frequency as the quasiparticle mass. With this quasiparticle picture, we can then address the long-time behavior of the oscillations.   

How can an autonomous quantum Maxwell demon harness correlated information?

We study an autonomous quantum system, which exhibits refrigeration under an information-work tradeoff like a Maxwell demon. The system becomes correlated as a single “demon” qubit interacts sequentially with memory qubits while in contact with two heat reservoirs of different temperatures. Using strong subadditivity of the von Neumann entropy, we derive a global Clausius inequality to show thermodynamical advantages from access to correlated information. It is demonstrated, in a matrix product density operator formalism, that our demon can simultaneously realize refrigeration against a thermal gradient and erasure of information from its memory, which is impossible without correlations. The phenomenon can be even enhanced by the presence of quantum coherence.   

Fano-Andreev effect in Quantum Dots in Kondo regime

In the present work, we investigate the transport through a T-shaped double quantum dot system coupled to two normal leads and to a superconducting lead. We study the role of the superconducting lead in the quantum interferometric features of the double quantum dot and by means of a slave boson mean field approximation at low temperature regime. We inquire into the influence of intradot interactions in the electronic properties of the system as well. Our results show that Fano resonances due to Andreev bound states are exhibited in the transmission from normal to normal lead as a consequence of quantum interference and proximity effect. This Fano effect produced by Andreev bound states in a side quantum dot was called Fano-Andreev effect, which remains valid even if the electron-electron interaction are taken into account, that is, the Fano-Andreev effect is robust against e-e interactions even in Kondo regime.   

Quantum critical temperature of a modulated oscillator

We show that the rate of switching between the vibrational states of a modulated nonlinear oscillator is characterized by a quantum critical temperature $T_c\propto\hbar^2$. Above $T_c$ there emerges a quantum crossover region where the switching rate displays a steep and characteristic temperature dependence, followed by a qualitatively different temperature dependence for higher T. In contrast to the crossover between tunneling and thermal activation in equilibrium systems, here the crossover occurs between different regimes of switching activated by quantum fluctuations. The results go beyond the standard real-time instanton technique of the large-deviation theory.   

The interplay between universal scaling laws and vortex clustering in two-dimensional quantum turbulence

The relationship between vortex dynamics and the turbulent energy spectrum is an active research topic in quantum turbulence of superfluids and Bose-Einstein condensates. The energy spectra in quantum turbulence exhibit a Kolmogorov -5/3 scaling law, analogous to classical turbulence. Recent developments show that in two-dimensional quantum flows, this energy spectrum corresponds to an inverse energy cascade, which is realized by clustering of like-signed quantized vortices. We investigate numerically the statistics of quantized vortices in two-dimensional quantum turbulence using the Gross-Pitaevskii equation. We find that a universal -5/3 scaling law in the turbulent energy spectrum is intimately connected with the vortex statistics, such as number fluctuations and velocity, which also show a similar scaling behavior. The -5/3 scaling law appearing in the power spectrum of the vortex number is consistent with a scenario of isolated vortices passively advected by a turbulent superfluid velocity, which is again generated by like-signed vortex clusters. The velocity probability distribution of clustered vortices is also sensitive to spatial correlations, and exhibits a power-law tail with a -5/3 exponent that we can predict analytically from the point vortex model.   

Fluctuation loops in a noise-driven linear circuit model

Understanding the spatio-temporal structure of most probable fluctuation pathways to rarely occurring states is a central problem in the study of noise-driven, non-equilibrium dynamical systems. When the underlying system does not possess detailed balance, the optimal fluctuation pathway to a particular state and relaxation pathway from that state may combine to form a loop-like structure in the system phase space which we call a \textit{fluctuation loop}. Here, we study fluctuation loops in a linear circuit model consisting of coupled RC elements, where each element is driven by its own noise source and, generally, the effective noise strengths of different elements are not equal. Using a stochastic Hamiltonian approach, we determine the optimal fluctuation pathways, and construct corresponding fluctuation loops. Analytical results agree closely with suitably averaged simulation results based on the associated Langevin equation. To better characterize fluctuation loops, we study the time-dependent area tensor that is swept out by individual stochastic trajectories in the system phase space. At long times, the area tensor scales linearly with time, with a coefficient that precisely vanishes when the system satisfies detailed balance.