Quantum walk in stochastic environment.

We consider a quantized version of the Sinai-Derrida model for "random walk in random environment." The model is defined in terms of a Lindblad master equation. For a ring geometry (a chain with periodic boundary condition) it features a delocalization-transition as the bias in increased beyond a critical value, indicating that the relaxation becomes underdamped. Counterintuitively, the effective disorder is enhanced due to coherent hopping. We analyze in detail this enhancement and its dependence on the model parameters. The nonmonotonic dependence of the Lindbladian spectrum on the rate of the coherent transitions is highlighted.

Stochastic modeling of spreading and dissipation in mixed-chaotic systems that are driven quasistatically.

We analyze energy spreading for a system that features mixed chaotic phase space, whose control parameters (or slow degrees of freedom) vary quasistatically. For demonstration purpose we consider the restricted three-body problem, where the distance between the two central stars is modulated due to their Kepler motion. If the system featured hard chaos, one would expect diffusive spreading with coefficient that can be estimated using linear-response (Kubo) theory. But for mixed phase space the chaotic sea is multilayered. Consequently, it becomes a challenge to find a robust procedure that translates the sticky dynamics into a stochastic model. We propose a Poincaré-sequencing method that reduces the multidimensional motion into a one-dimensional random walk in impact space. We test the implied relation between stickiness and the rate of spreading.

Quantum Signatures in Quench from Chaos to Superradiance.

The driven-dissipative Dicke model features normal, superradiant, and lasing steady states that may be regular or chaotic. We report quantum signatures of chaos in a quench protocol from the lasing states. Within the framework of a classical mean-field perspective, once quenched, the system relaxes either to the normal or to the superradiant state. Quench from chaos, unlike quench from a regular lasing state, exhibits erratic dependence on control parameters. In the quantum domain, this sensitivity implies an effect that is similar to universal conductance fluctuations.

On the Effect of Practice on Exploration and Exploitation of Options and Strategies.

Insufficient exploration of one's surroundings is at the root of many real-life problems, as demonstrated by many famous biases (e.g., the status quo bias, learned helplessness). The current work focuses on the emergence of this phenomenon at the strategy level: the tendency to under-explore the set of available choice strategies. We demonstrate that insufficient exploration of strategies can also manifest as excessive exploration between options. In such cases, interventions aimed at improving choices by reducing the costs of exploration of options are likely to fail. In Study 1, participants faced an exploration task that implies an infinite number of choice strategies and a small sub-set of (near) optimal solutions. We manipulated the amount of practice participants underwent during the first, shorter game and compared their performance in a second, longer game with an identical payoff structure. Our results show that regardless of the amount of practice, participants in all experimental groups tended to under-explore the strategy space and relied on a specific strategy that implied over-exploration of the option space. That is, under-exploration of strategies was manifested as over-exploration of options. In Study 2, we added a constraint that, on a subset of practice trials, forced participants to exploit familiar options. This manipulation almost doubled the per-trial average outcome on the comparable longer second game. This suggests that forcing participants to experience the effects of different (underexplored) strategy components during practice can greatly increase the chance they make better choices later on.

Over and under commitment to a course of action in decisions from experience.

Many natural activities involve "stopping dilemmas": situations that require a repeated decision between investing effort to achieve some valued goal and stopping that effort to try something else. Previous research into these problems highlights two contradicting biases. While one class of studies suggests a tendency to stop too late (e.g., escalation of commitment), another class of studies suggests a tendency to give up too early (e.g., learned helplessness). Our paper clarifies the conditions that trigger these biases by focusing on two factors: the decision mode (ongoing decisions vs. planning in advance) and the probability each search effort will be costly. We find that experience with stopping dilemmas produces a reversed sunk-cost effect: Most participants stop too early when search is frequently costly but stop too late when search is usually rewarding. This effect can be explained by assuming that stopping decisions reflect reliance on small samples of past experiences with similar stopping dilemmas. Comparison of ongoing and planning decisions reveals an interaction: planning in advance increased search when searching was frequently costly, but decreased search when most search efforts were rewarding. This interaction can be explained by assuming a contingent re-evaluation process: Recent losses increase the tendency to reevaluate a plan to continue the search, and recent gains increase the tendency to reevaluate a plan to stop. In addition, we observe a preference for stopping strategies that imply maximal search. We assume this reflects an attempt to explore the full problem space. (PsycInfo Database Record (c) 2022 APA, all rights reserved).

Quasistatic transfer protocols for atomtronic superfluid circuits.

Quasi-static protocols for systems that feature a mixed phase-space with both chaos and quasi-regular regions are beyond the standard paradigm of adiabatic processes. We focus on many-body system of atoms that are described by the Bose-Hubbard Hamiltonian, specifically a circuit that consists of bosonic sites. We consider a sweep process: slow variation of the rotation frequency of the device (time dependent Sagnac phase). The parametric variation of phase-space topology implies that the quasi-static limit is not compatible with linear response theory. Detailed analysis is essential in order to determine the outcome of such transfer protocol, and its efficiency.

Negative mobility, sliding, and delocalization for stochastic networks.

We consider prototype configurations for quasi-one-dimensional stochastic networks that exhibit negative mobility, meaning that current decreases or even reversed as the bias is increased. We then explore the implications of disorder. In particular, we ask whether lower and upper bias thresholds restrict the possibility to witness nonzero current (sliding and antisliding transitions, respectively), and whether a delocalization effect manifests itself (crossover from over-damped to under-damped relaxation). In the latter context detailed analysis of the relaxation spectrum as a function of the bias is provided for both on-chain and off-chain disorder.

Quantum stochastic transport along chains.

The spreading of a particle along a chain, and its relaxation, are central themes in statistical and quantum mechanics. One wonders what are the consequences of the interplay between coherent and stochastic transitions. This fundamental puzzle has not been addressed in the literature, though closely related themes were in the focus of the Physics literature throughout the last century, highlighting quantum versions of Brownian motion. Most recently this question has surfaced again in the context of photo-synthesis. Here we consider both an infinite tight-binding chain and a finite ring within the framework of an Ohmic master equation. With added disorder it becomes the quantum version of the Sinai-Derrida-Hatano-Nelson model, which features sliding and delocalization transitions. We highlight non-monotonic dependence of the current on the bias, and a counter-intuitive enhancement of the effective disorder due to coherent hopping.

Probabilistic Hysteresis in Integrable and Chaotic Isolated Hamiltonian Systems.

We propose currently feasible experiments using small, isolated systems of ultracold atoms to investigate the effects of dynamical chaos in the microscopic onset of irreversibility. A control parameter is tuned past a critical value, then back to its initial value; hysteresis appears as a finite probability that the atoms fail to return to their initial state even when the parameter sweep is arbitrarily slow. We show that an episode of chaotic dynamics during part of the sweep time produces distinctive features in the distribution of final states that will be clearly observable in experiments.

Coherent Wave Propagation in Multimode Systems with Correlated Noise.

Imperfections in multimode systems lead to mode mixing and interferences between propagating modes. Such disorder is typically characterized by a finite correlation time (in quantum evolution) or correlation length (in paraxial evolution). We show that the long-scale dynamics of an initial excitation that spread in mode space can be tailored by the coherent dynamics on a short scale. In particular we unveil a universal crossover from exponential to power-law ballisticlike decay of the initial mode. Our results have applications to various wave physics frameworks, ranging from multimode fiber optics to quantum dots and quantum biology.

Localization due to topological stochastic disorder in active networks.

An active network is a prototype model in nonequilibrium statistical mechanics. It can represent, for example, a system with particles that have a self-propulsion mechanism. Each node of the network specifies a possible location of a particle and its orientation. The orientation (which is formally like a spin degree of freedom) determines the self-propulsion direction. The bonds represent the possibility to make transitions: to hop between locations or to switch the orientation. In systems of experimental interest (Janus particles), the self-propulsion is induced by illumination. An emergent aspect is the topological stochastic disorder (TSD). It is implied by the nonuniformity of the illumination. In technical terms the TSD reflects the local nonzero circulations (affinities) of the stochastic transitions. This type of disorder, unlike a nonhomogeneous magnetic field, is non-Hermitian and can lead to the emergence of a complex relaxation spectrum. It is therefore dramatically distinct from the conservative Anderson-type or Sinai-type disorder. We discuss the consequences of having TSD. In particular we illuminate three different routes to underdamped relaxation and show that localization plays a major role in the analysis. Implications of the bulk-edge correspondence principle are addressed too.

Semiclassical theory of strong localization for quantum thermalization.

We introduce a semiclassical theory for strong localization that may arise in the context of many-body thermalization. As a minimal model for thermalization we consider a few-site Bose-Hubbard model consisting of two weakly interacting subsystems that can exchange particles. The occupation of a subsystem (x) satisfies in the classical treatment a Fokker-Planck equation with a diffusion coefficient D(x). We demonstrate that it is possible to deduce from the classical description a quantum breaktime t^{*} and, hence, the manifestations of a strong localization effect. For this purpose it is essential to take the geometry of the energy shell into account and to make a distinction between different notions of phase-space exploration.

Adiabatic Passage through Chaos.

We study the process of nonlinear stimulated Raman adiabatic passage within a classical mean-field framework. Depending on the sign of interaction, the breakdown of adiabaticity in the interacting nonintegrable system is not related to bifurcations in the energy landscape, but rather to the emergence of quasistochastic motion that drains the followed quasistationary state. Consequently, faster sweep rate, rather than quasistatic variation of parameters, is better for adiabaticity.

From anomalies to forecasts: Toward a descriptive model of decisions under risk, under ambiguity, and from experience.

Experimental studies of choice behavior document distinct, and sometimes contradictory, deviations from maximization. For example, people tend to overweight rare events in 1-shot decisions under risk, and to exhibit the opposite bias when they rely on past experience. The common explanations of these results assume that the contradicting anomalies reflect situation-specific processes that involve the weighting of subjective values and the use of simple heuristics. The current article analyzes 14 choice anomalies that have been described by different models, including the Allais, St. Petersburg, and Ellsberg paradoxes, and the reflection effect. Next, it uses a choice prediction competition methodology to clarify the interaction between the different anomalies. It focuses on decisions under risk (known payoff distributions) and under ambiguity (unknown probabilities), with and without feedback concerning the outcomes of past choices. The results demonstrate that it is not necessary to assume situation-specific processes. The distinct anomalies can be captured by assuming high sensitivity to the expected return and 4 additional tendencies: pessimism, bias toward equal weighting, sensitivity to payoff sign, and an effort to minimize the probability of immediate regret. Importantly, feedback increases sensitivity to probability of regret. Simple abstractions of these assumptions, variants of the model Best Estimate and Sampling Tools (BEAST), allow surprisingly accurate ex ante predictions of behavior. Unlike the popular models, BEAST does not assume subjective weighting functions or cognitive shortcuts. Rather, it assumes the use of sampling tools and reliance on small samples, in addition to the estimation of the expected values. (PsycINFO Database Record

Lognormal-like statistics of a stochastic squeeze process.

We analyze the full statistics of a stochastic squeeze process. The model's two parameters are the bare stretching rate w and the angular diffusion coefficient D. We carry out an exact analysis to determine the drift and the diffusion coefficient of log(r), where r is the radial coordinate. The results go beyond the heuristic lognormal description that is implied by the central limit theorem. Contrary to the common "quantum Zeno" approximation, the radial diffusion is not simply D_{r}=(1/8)w^{2}/D but has a nonmonotonic dependence on w/D. Furthermore, the calculation of the radial moments is dominated by the far non-Gaussian tails of the log(r) distribution.

Resistor-network anomalies in the heat transport of random harmonic chains.

We consider thermal transport in low-dimensional disordered harmonic networks of coupled masses. Utilizing known results regarding Anderson localization, we derive the actual dependence of the thermal conductance G on the length L of the sample. This is required by nanotechnology implementations because for such networks Fourier's law G∝1/L^{α} with α=1 is violated. In particular we consider "glassy" disorder in the coupling constants and find an anomaly which is related by duality to the Lifshitz-tail regime in the standard Anderson model.

Relaxation rate of a stochastic spreading process in a closed ring.

The relaxation process of a diffusive ring becomes underdamped if the bias (so-called affinity) exceeds a critical threshold value, also known as the delocalization transition. This is related to the spectral properties of the pertinent stochastic kernel. We find the dependence of the relaxation rate on the affinity and on the length of the ring. Additionally we study the implications of introducing a weak link into the circuit and illuminate some subtleties that arise while taking the continuum limit of the discrete model.

Path integral approach to the quantum fidelity amplitude.

The Loschmidt echo is a measure of quantum irreversibility and is determined by the fidelity amplitude of an imperfect time-reversal protocol. Fidelity amplitude plays an important role both in the foundations of quantum mechanics and in its applications, such as time-resolved electronic spectroscopy. We derive an exact path integral formula for the fidelity amplitude and use it to obtain a series of increasingly accurate semiclassical approximations by truncating an exact expansion of the path integral exponent. While the zeroth-order expansion results in a remarkably simple, yet non-trivial approximation for the fidelity amplitude, the first-order expansion yields an alternative derivation of the so-called 'dephasing representation,' circumventing the use of a semiclassical propagator as in the original derivation. We also obtain an approximate expression for fidelity based on the second-order expansion, which resolves several shortcomings of the dephasing representation. The rigorous derivation from the path integral permits the identification of sufficient conditions under which various approximations obtained become exact.

Percolation, sliding, localization and relaxation in topologically closed circuits.

Considering a random walk in a random environment in a topologically closed circuit, we explore the implications of the percolation and sliding transitions for its relaxation modes. A complementary question regarding the "delocalization" of eigenstates of non-hermitian Hamiltonians has been addressed by Hatano, Nelson, and followers. But we show that for a conservative stochastic process the implied spectral properties are dramatically different. In particular we determine the threshold for under-damped relaxation, and observe "complexity saturation" as the bias is increased.

Thermalization of Bipartite Bose-Hubbard Models.

We study the time evolution of a bipartite Bose-Hubbard model prepared far from equilibrium. When the classical dynamics is chaotic, we observe ergodization of the number distribution and a constant increase of the entanglement entropy between the constituent subsystems until it saturates to thermal equilibrium values. No thermalization is obtained when the system is launched in quasi-integrable phase space regions.