Recent experiments at the nanoscales confirm that thermal rectifiers, the thermal equivalent of electrical diodes, can operate in the quantum regime. We present a thorough investigation of the effect of different particle exchange statistics, coherence, and collective interactions on the quantum heat transport of rectifiers with two-terminal junctions. Using a collision model approach to describe the open system dynamics, we obtain a general expression of the nonlinear heat flow that fundamentally deviates from the Landauer formula whenever quantum statistical or coherence asymmetries are present in the bath particles. Building on this, we show that heat rectification is possible even with symmetric medium-bath couplings if the two baths differ in quantum statistics or coherence. Furthermore, the associated thermal conductance vanishes exponentially at low temperatures as in the Coulomb-blockade effect. However, at high temperatures it acquires a power-law behavior depending on the quantum statistics. Our results can be significant for heat management in hybrid open quantum systems or solid-state thermal circuits.

In this paper we study a fully connected planted spin glass named the planted XY model. Motivation for studying this system comes both from the spin glass field and the one of statistical inference where it models the angular synchronization problem. We derive the replica symmetric (RS) phase diagram in the temperature, ferromagnetic bias plane using the approximate message passing (AMP) algorithm and its state evolution (SE). While the RS predictions are exact on the Nishimori line (i.e., when the temperature is matched to the ferromagnetic bias), they become inaccurate when the parameters are mismatched, giving rise to a spin glass phase where AMP is not able to converge. To overcome the defects of the RS approximation we carry out a one-step replica symmetry-breaking (1RSB) analysis based on the approximate survey propagation (ASP) algorithm. Exploiting the state evolution of ASP, we count the number of metastable states in the measure, derive the 1RSB free entropy and find the behavior of the Parisi parameter throughout the spin glass phase.

Inspired by many examples in nature, stochastic resetting of random processes has been studied extensively in the past decade. In particular, various models of stochastic particle motion were considered where, upon resetting, the particle is returned to its initial position. Here we generalize the model of diffusion with resetting to account for situations where a particle is returned only a fraction of its distance to the origin, e.g., half way. We show that this model always attains a steady-state distribution which can be written as an infinite sum of independent, but not identical, Laplace random variables. As a result, we find that the steady-state transitions from the known Laplace form which is obtained in the limit of full resetting to a Gaussian form, which is obtained close to the limit of no resetting. A similar transition is shown to be displayed by drift diffusion whose steady state can also be expressed as an infinite sum of independent random variables. Finally, we extend our analysis to capture the temporal evolution of drift diffusion with partial resetting, providing a bottom-up probabilistic construction that yields a closed-form solution for the time-dependent distribution of this process in Fourier-Laplace space. Possible extensions and applications of diffusion with partial resetting are discussed.

Brownian motion subject to a periodic and asymmetric potential can be biased by external, nonequilibrium fluctuations, leading to directional movement of Brownian particles. Sequence-dependent flexibility variation along double-stranded DNA has been proposed as a tool to develop periodic and asymmetric potentials for DNA binding of cationic nanoparticles with sizes below tens of nanometers. Here, we propose that repetitive stretching and relaxation of a long, double-stranded DNA molecule with periodic flexibility gradient can induce nonequilibrium fluctuations that tune the amplitude of asymmetric potentials for DNA-nanoparticle binding to result in directional transport of nanometer-sized particles along DNA. Realization of the proposed Brownian ratchet was proven by Brownian dynamics simulations of coarse-grained models of a single, long DNA molecule with flexibility variation and a cationic nanoparticle.

We study the full nonequilibrium steady-state distribution $P_{\text{st}}\left(X\right)$ of the position $X$ of a damped particle confined in a harmonic trapping potential and experiencing active noise whose correlation time ${\tau }_c$ is assumed to be very short. Typical fluctuations of $X$ are governed by a Boltzmann distribution with an effective temperature that is found by approximating the noise as white Gaussian thermal noise. However, large deviations of $X$ are described by a non-Boltzmann steady-state distribution. We find that, in the limit ${\tau }_c\to 0$, they display the scaling behavior $P_{\text{st}}\left(X\right)\sim e^{-s\left(X\right)/{\tau }_c}$, where $s\left(X\right)$ is the large-deviation function. We obtain an expression for $s\left(X\right)$ for a general active noise and calculate it exactly for the particular case of telegraphic (dichotomous) noise.

A generalized collision model is developed to investigate coherent charging a single quantum battery by repeated interactions with many-atom large spins, where collective atom operators are adopted and the battery is modeled by a uniform energy ladder. For an initially empty battery, we derive analytical results of the average number of excitations and hence the charging power in the short-time limit. Our analytical results show that a faster charging and an increased amount of the power in the coherent protocol uniquely arise from the phase coherence of the atoms. Finally, we show that the charging power defined by the so-called ergotropy almost follows our analytical result, due to a nearly pure state of the battery in the short-time limit.

We introduce the spherical wedge billiard, a dynamical system consisting of a particle moving along a geodesic on a closed non-Euclidean surface of a spherical wedge. We derive the analytic form of the corresponding Poincaré map and find very complex dynamics, ranging from completely chaotic to very regular, exhibiting fractal features. Further, we show that upon changing the billiard parameter, the fixed points of the Poincaré map merge in complex ways, which has origin in the spherical aberration of the billiard mapping. We also analyze in detail the regular regime when phase space diagram is closely related to Talbot carpets.

The boundary of the lemon billiards is defined by the intersection of two circles of equal unit radius with the distance $2B$ between their centers, as introduced by Heller and Tomsovic [E. J. Heller and S. Tomsovic, Phys. Today 46, 38 (1993)]. This paper is a continuation of our recent papers on a classical and quantum ergodic lemon billiard ($B=0.5$) with strong stickiness effects [Č. Lozej et al., Phys. Rev. E 103, 012204 (2021)], as well as on the three billiards with a simple mixed-type phase space and no stickiness [Č. Lozej et al., Nonlin. Phenom. Complex Syst. 24, 1 (2021)]. Here we study two classical and quantum lemon billiards, for the cases $B=0.1953,0.083$, which are mixed-type billiards with a complex structure of phase space, without significant stickiness regions. A preliminary study of their spectra was published recently [ Č. Lozej, D. Lukman, and M. Robnik, Physics 3, 888 (2021)]. We calculate a very large number (${10}^6$) of consecutive eigenstates and their Poincaré-Husimi (PH) functions, and analyze their localization properties by studying the entropy localization measure and the normalized inverse participation ratio. We introduce an overlap index, which measures the degree of the overlap of PH functions with classically regular and chaotic regions. We observe the existence of regular states associated with invariant tori and chaotic states associated with the classically chaotic regions, and also the mixed-type states. We show that in accordance with the Berry-Robnik picture and the principle of uniform semiclassical condensation of PH functions, the relative fraction of mixed-type states decreases as a power law with increasing energy, thus, in the strict semiclassical limit, leaving only purely regular and chaotic states. Our approach offers a general phenomenological overview of the structural and localization properties of PH functions in quantum mixed-type Hamiltonian systems.

We consider the problem of inferring a matching hidden in a weighted random $k$-hypergraph. We assume that the hyperedges' weights are random and distributed according to two different densities conditioning on the fact that they belong to the hidden matching or not. We show that for $k>2$ and in the large-graph-size limit, an algorithmic first-order transition in the signal strength separates a regime in which a complete recovery of the hidden matching is feasible from a regime in which partial recovery is possible. This is in contrast to the $k=2$ case, where the transition is known to be continuous. Finally, we consider the case of graphs presenting a mixture of edges and 3-hyperedges, interpolating between the $k=2$ and the $k=3$ cases, and we study how the transition changes from continuous to first order by tuning the relative amount of edges and hyperedges.

Packings of regular convex polygons ($n$-gons) that are sufficiently dense have been studied extensively in the context of modeling physical and biological systems as well as discrete and computational geometry. Former results were mainly regarding densest lattice or double-lattice configurations. Here we consider all two-dimensional crystallographic symmetry groups (plane groups) by restricting the configuration space of the general packing problem of congruent copies of a compact subset of the two-dimensional Euclidean space to particular isomorphism classes of the discrete group of isometries. We formulate the plane group packing problem as a nonlinear constrained optimization problem. By means of the Entropic Trust Region Packing Algorithm that approximately solves this problem, we examine some known and unknown densest packings of various $n$-gons in all 17 plane groups and state conjectures about common symmetries of the densest plane group packings for every $n$-gon.

The structures of dilute electrolyte solutions close to nonuniformly charged planar substrates are systematically studied within the entire spectrum of microscopic to macroscopic length scales by means of a unified classical density functional theory approach. This is in contrast to previous investigations, which are applicable either to short or to long length scales. It turns out that interactions with microscopic ranges, e.g., due to the hard cores of the fluid molecules and ions, have a negligible influence on the formation of nonuniform lateral structures of the electrolyte solutions. This partly justifies the Debye-Hückel approximation schemes applied in previous studies of that system. In general, a coupling between the lateral and the normal fluid structures leads to the phenomenology that, upon increasing the distance from the substrate, fewer details of the lateral nonuniformities contribute to the fluid structure, such that ultimately only large-scale surface features remain relevant. It can be expected that this picture also applies to other fluids characterized by several length scales.

The Leidenfrost effect is a phenomenon in which a liquid, poured onto a glowing surface significantly hotter than the liquid's boiling point, produces a layer of vapor that prevents the liquid from rapid evaporation. Rather than making physical contact, a drop of water levitates above the surface. The temperature above which the phenomenon occurs is called the Leidenfrost temperature. The reason for the existence of the Leidenfrost temperature, which is much higher than the boiling point of the liquid, is not fully understood and predicted. For water we prove that the Leidenfrost temperature corresponds to a bifurcation in the solutions of equations describing evaporation of a nonequilibrium liquid-vapor interface. For water, the theoretical values of obtained Leidenfrost temperature, and that of the liquid-vapor interface which is smaller than the boiling point of liquid, fit the experimental results found in the literature.

The collisionless ion-Weibel instability is a leading candidate mechanism for the formation of collisionless shocks in many astrophysical systems, where the typical distance between particle collisions is much larger than the system size. Multiple laboratory experiments aimed at studying this process utilize laser-driven $(\mathrm{I}\gtrsim {10}^{15}$ $\mathrm{W}/{\mathrm{cm}}^2)$, counterstreaming plasma flows $(\mathrm{V}\lesssim 2000 \mathrm{km}/\mathrm{s})$ to create conditions unstable to Weibel-filamentation and growth. This technique intrinsically produces temporally varying plasma conditions at the midplane of the interaction where Weibel-driven B fields are generated and studied. Experiments discussed herein demonstrate robust formation of Weibel-driven B fields under multiple plasma conditions using CH, Al, and Cu plasmas. Linear theory based on benchmarked radiation-hydrodynamic FLASH calculations is compared with Fourier analyses of proton images taken $\sim$5–6 linear growth times into the evolution. The new analyses presented here indicate that the low-density, high-velocity plasma-conditions present during the first linear-growth time $(\sim 300–500 \mathrm{ps})$ sets the spectral characteristics of Weibel filaments during the entire evolution. It is shown that the dominant wavelength $(\sim 300\mu \mathrm{m})$ at saturation persists well into the nonlinear phase, consistent with theory under these experimental conditions. However, estimates of B-field strength, while difficult to determine accurately due to the path-integrated nature of proton imaging, are shown to be in the $\sim 10–30 \mathrm{T}$ range, an order of magnitude above the expected saturation limit in homogenous plamas but consistent with enhanced B fields in the midplane due to temporally varying plasma conditions in experiments.

This paper addresses the construction of numerical boundary conditions for simulating rogue wave solutions in the nonlinear Schrödinger equation. While three kinds of commonly used boundary conditions require a big enough computational domain to reproduce solutions faithfully in the central domain, we propose transparent boundary conditions for the Peregrine soliton and Kuznetsov-Ma breather solutions, respectively. For both solutions, these boundary conditions require a smaller computational domain than other boundary conditions to attain the best accuracy of the Crank-Nicolson scheme and selected mesh size, which will be referred to as the “acceptable accuracy” below. In particular, the computational domain with these boundary conditions is only $1/16$ as small as others in the simulations of the Peregrine soliton solution. As a result, they reduce both the memory requirement and the computing time for the Peregrine soliton solution.

The onset of rigidity in interacting liquids, as they undergo a transition to a disordered solid, is associated with a rearrangement of the low-frequency vibrational spectrum. In this Letter, we derive scaling forms for the singular dynamical response of disordered viscoelastic networks near both jamming and rigidity percolation. Using effective-medium theory, we extract critical exponents, invariant scaling combinations, and analytical formulas for universal scaling functions near these transitions. Our scaling forms describe the behavior in space and time near the various onsets of rigidity, for rigid and floppy phases and the crossover region, including diverging length scales and timescales at the transitions.

The properties of the ground state of the simplest frustrated system, the dilute Ising chain in a magnetic field, are rigorously investigated over the entire range of concentrations of charged nonmagnetic impurities. Analytical methods are proposed for calculating the residual entropy of frustrated states, including states at phase boundaries, which are based on the Markov property of the system and involve solving a linear optimization problem for energy and a nonlinear optimization problem for entropy. These methods allow obvious generalizations for one-dimensional pseudospin models with anisotropic interactions. We calculate the composition, entropy, and magnetization for the ground state phases. We prove the absence of pseudotransitions in the dilute Ising chain, since the residual entropy of states at phase boundaries is always higher than the entropy of adjacent phases. The concentration dependencies of magnetization at the phase boundaries are obtained, and unlike linear dependencies for adjacent phases, they have nonlinear behavior. Field-induced transitions between ground states and entropy jumps associated with them are also considered, and in particular, it is shown that the field-induced transition from an antiferromagnetic state to a frustrated one is accompanied by charge ordering.

We analyze the effect of impurity on the work output and efficiency of quantum Otto and quantum Carnot heat cycles, modeled as a single quantum particle in an infinite square well potential, which is the working substance. We solve this quantum mechanical system perturbatively up to first and second order in strength of the impurity for strong- and weak-coupling regimes, respectively. We derive the analytical expressions of work and efficiency for the strong-coupling regime to the first order in the strength parameter. The threshold value of the strength parameter in weak coupling is obtained up to which the numerical result agrees with the perturbative result for a repulsive and attractive impurity. To our surprise, an embedded impurity unlocks new operational phases in the system, such as a quantum heat engine, quantum refrigerator, and quantum cold pump. In addition, the efficiency of the quantum Otto heat engine is seen to reach Carnot efficiency for some parameter regimes. The cooling power and coefficient of performance of the quantum refrigerator and quantum cold pump are nontrivially affected by the impurity.

A large number of processes in the mesoscopic world occur out of equilibrium, where the time evolution of a system becomes immensely important since it is driven principally by dissipative effects. Nonequilibrium steady states (NESS) represent a crucial category in such systems, where relaxation timescales are comparable to the operational timescales. In this study, we employ a model NESS stochastic system, which is comprised of a colloidal microparticle optically trapped in a viscous fluid, externally driven by a temporally correlated noise, and show that time-integrated observables such as the entropic current, the work done on the system or the work dissipated by it, follow the three Lévy arcsine laws [A. C. Barato et al., Phys. Rev. Lett. 121, 090601 (2018)], in the large time limit. We discover that cumulative distributions converge faster to arcsine distributions when it is near equilibrium and the rate of entropy production is small, because in that case the entropic current has weaker temporal autocorrelation. We study this phenomenon by changing the strength of the added noise as well as by perturbing our system with a flow field produced by a microbubble at close proximity to the trapped particle. We confirm our experimental findings with theoretical simulations of the systems. Our work provides an interesting insight into the NESS statistics of the meso-regime, where stochastic fluctuations play a pivotal role.

The modulational instability (MI) phenomenon is addressed in a nonlocal medium under controllable saturation. The linear stability analysis of a plane-wave solution is used to derive an expression for the growth rate of MI that is exploited to parametrically discuss the possibility for the plane wave to disintegrate into nonlinear localized light patterns. The influence of the nonlocal parameter, the saturation coefficient, and the saturation index are mainly explored in the context of a Gaussian nonlocal response. It is pointed out that the instability spectrum, which tends to be quenched by the high nonlocality parameter, gets amplified under the right choices of the saturation parameters, especially the saturation index. Via direct numerical simulations, confirmations of analytical predictions are given, where competing nonlocal and saturable nonlinearities enable the emergence of trains of patterns as manifestations of MI. The comprehensive parametric analysis carried out throughout the numerical experiment reveals the robustness of the obtained rogue waves of A- and B-type Akhmediev breathers, as the nonlinear signature of MI, providing the saturation index as a suitable tool to manipulate nonlinear waves in nonlocal media.