We investigate ergodic time scales in single-particle tracking by introducing a covariance measure $\mathrm{\Omega }(\mathrm{\Delta };t)$ for the time-averaged relative square displacement recorded in lag-time $\mathrm{\Delta }$ at elapsed time $t$. The present model is established in the generalized Langevin equation with a power-law memory function. The ratio $\mathrm{\Omega }(\mathrm{\Delta };\mathrm{\Delta })/\mathrm{\Omega }(\mathrm{\Delta };t)$ is shown to obey a universal scaling law for long but finite times and is used to extract the effective ergodic time. We derive a finite-time-averaged Green-Kubo relation and find that, to control the deviations in measurement results from ensemble averages, the ratio $\mathrm{\Delta }/t$ must be neither too small nor close to unity. Our paper connects the experimental self-averaging property of a tracer with the theoretic velocity autocorrelation function and sheds light on the transition to ergodicity.

We consider the percolation problem of sites on an $L\times L$ square lattice with periodic boundary conditions which were unvisited by a random walk of $N=u{L}^2$ steps, i.e., are vacant. Most of the results are obtained from numerical simulations. Unlike its higher-dimensional counterparts, this problem has no sharp percolation threshold and the spanning (percolation) probability is a smooth function monotonically decreasing with $u$. The clusters of vacant sites are not fractal but have fractal boundaries of dimension 4/3. The lattice size $L$ is the only large length scale in this problem. The typical mass (number of sites $s$) in the largest cluster is proportional to $L^2$, and the mean mass of the remaining (smaller) clusters is also proportional to $L^2$. The normalized (per site) density $n_s$ of clusters of size (mass) $s$ is proportional to $s^{-\tau }$, while the volume fraction $P_k$ occupied by the $k\mathrm{th}$ largest cluster scales as $k^{-q}$. We put forward a heuristic argument that $\tau =2$ and $q=1$. However, the numerically measured values are $\tau \approx 1.83$ and $q\approx 1.20$. We suggest that these are effective exponents that drift towards their asymptotic values with increasing $L$ as slowly as $1/lnL$ approaches zero.

The thermodynamic uncertainty relation, originally derived for classical Markov-jump processes, provides a tradeoff relation between precision and dissipation, deepening our understanding of the performance of quantum thermal machines. Here, we examine the interplay of quantum system coherences and heat current fluctuations on the validity of the thermodynamics uncertainty relation in the quantum regime. To achieve the current statistics, we perform a full counting statistics simulation of the Redfield quantum master equation. We focus on steady-state quantum absorption refrigerators where nonzero coherence between eigenstates can either suppress or enhance the cooling power, compared with the incoherent limit. In either scenario, we find enhanced relative noise of the cooling power (standard deviation of the power over the mean) in the presence of system coherence, thereby corroborating the thermodynamic uncertainty relation. Our results indicate that fluctuations necessitate consideration when assessing the performance of quantum coherent thermal machines.

We study random processes with nonlocal memory and obtain solutions of the Mori-Zwanzig equation describing non-Markovian systems. We analyze the system dynamics depending on the amplitudes $\nu$ and ${\mu }_0$ of the local and nonlocal memory and pay attention to the line in the ($\nu , {\mu }_0$) plane separating the regions with asymptotically stationary and nonstationary behavior. We obtain general equations for such boundaries and consider them for three examples of nonlocal memory functions. We show that there exist two types of boundaries with fundamentally different system dynamics. On the boundaries of the first type, diffusion with memory takes place, whereas on borderlines of the second type the phenomenon of noise-induced resonance can be observed. A distinctive feature of noise-induced resonance in the systems under consideration is that it occurs in the absence of an external regular periodic force. It takes place due to the presence of frequencies in the noise spectrum, which are close to the self-frequency of the system. We analyze also the variance of the process and compare its behavior for regions of asymptotic stationarity and nonstationarity, as well as for diffusive and noise-induced-resonance borderlines between them.

We investigate experimentally a Fermi golden rule in two-edge and five-edge microwave networks with preserved time reversal invariance. A Fermi golden rule gives rates of decay of states obtained by perturbing embedded eigenvalues of graphs and networks. We show that the embedded eigenvalues are connected with the topological resonances of the analyzed systems and we find the trajectories of the topological resonances on the complex plane.

In the framework of the focusing one-dimensional nonlinear Schrödinger equation, we study numerically the integrable turbulence developing from partially coherent waves (PCW), which represent superposition of uncorrelated linear waves. The long-time evolution from these initial conditions is characterized by emergence of rogue waves with heavy-tailed (non-Gaussian) statistics, and, as was established previously, the stronger deviation from Gaussianity (i.e., the higher frequency of rogue waves) is observed for narrower initial spectrum. We investigate the fundamental limiting case of very narrow initial spectrum and find that shortly after the beginning of motion the turbulence enters a quasistationary state (QSS), which is characterized by a very slow evolution of statistics and lasts for a very long time before arrival at the asymptotic stationary state. In the beginning of the QSS, the probability density function (PDF) of intensity turns out to be nearly independent of the initial spectrum and is very well approximated by a certain Bessel function that represents an integral of the product of two exponential distributions. The PDF corresponds to the maximum possible stationary value of the fourth-order moment of amplitude ${\kappa }_4=4$ and yields a probability to meet intensity above the rogue wave threshold that is higher by 1.5 orders of magnitude than that for a random superposition of linear waves. We routinely observe rogue waves with amplitudes ten times larger than the average one, and all of the largest waves that we have studied are very well approximated by the amplitude-scaled rational breather solutions of either the first (Peregrine breather) or the second orders.

Chemotherapeutic resistance via the mechanism of competitive release of resistant tumor cell subpopulations is a major problem associated with cancer treatments and one of the main causes of tumor recurrence. Often, chemoresistance is mitigated by using multidrug schedules (two or more combination therapies) that can act synergistically, additively, or antagonistically on the heterogeneous population of cells as they evolve. In this paper, we develop a three-component evolutionary game theory model to design two-drug adaptive schedules that mitigate chemoresistance and delay tumor recurrence in an evolving collection of tumor cells with two resistant subpopulations and one chemosensitive population that has a higher baseline fitness but is not resistant to either drug. Using the nonlinear replicator dynamical system with a payoff matrix of Prisoner's Dilemma (PD) type (enforcing a cost to resistance), we investigate the nonlinear dynamics of this three-component system along with an additional tumor growth model whose growth rate is a function of the fitness landscape of the tumor cell populations. A key parameter determines whether the two drugs interact synergistically, additively, or antagonistically. We show that antagonistic drug interactions generally result in slower rates of adaptation of the resistant cells than synergistic ones, making them more effective in combating the evolution of resistance. We then design evolutionary cycles (closed loops) in the three-component phase space by shaping the fitness landscape of the cell populations (i.e., altering the evolutionary stable states of the game) using appropriately designed time-dependent schedules (adaptive therapy), altering the dosages and timing of the two drugs. We describe two key bifurcations associated with our drug interaction parameter which help explain why antagonistic interactions are more effective at controlling competitive release of the resistant population than synergistic interactions in the context of an evolving tumor.

Viral transmission pathways have profound implications for public safety; it is thus imperative to establish a complete understanding of viable infectious avenues. Mounting evidence suggests SARS-CoV-2 can be transmitted via the air; however, this has not yet been demonstrated. Here we quantitatively analyze virion accumulation by accounting for aerosolized virion emission and destabilization. Reported superspreading events analyzed within this framework point towards aerosol mediated transmission of SARS-CoV-2. Virion exposure calculated for these events is found to trace out a single value, suggesting a universal minimum infective dose (MID) via aerosol that is comparable to the MIDs measured for other respiratory viruses; thus, the consistent infectious exposure levels and their commensurability to known aerosol-MIDs establishes the plausibility of aerosol transmission of SARS-CoV-2. Using filtration at a rate exceeding the destabilization rate of aerosolized SARS-CoV-2 can reduce exposure below this infective dose.

We develop a first-principles approach to compute the counting statistics in the ground state of $N$ noninteracting spinless fermions in a general potential in arbitrary dimensions $d$ (central for $d>1$). In a confining potential, the Fermi gas is supported over a bounded domain. In $d=1$, for specific potentials, this system is related to standard random matrix ensembles. We study the quantum fluctuations of the number of fermions ${\mathcal{N}}_{\mathcal{D}}$ in a domain $\mathcal{D}$ of macroscopic size in the bulk of the support. We show that the variance of ${\mathcal{N}}_{\mathcal{D}}$ grows as $N^{(d-1)/d}(A_{d}logN+B_d)$ for large $N$, and obtain the explicit dependence of $A_d,B_d$ on the potential and on the size of $\mathcal{D}$ (for a spherical domain in $d>1$). This generalizes the free-fermion results for microscopic domains, given in $d=1$ by the Dyson-Mehta asymptotics from random matrix theory. This leads us to conjecture similar asymptotics for the entanglement entropy of the subsystem $\mathcal{D}$, in any dimension, supported by exact results for $d=1$.

We characterize throughout the spectral range of an optical trap the nature of the noise that drives the Brownian motion of an overdamped trapped single microsphere and its ergodicity, comparing experimental, analytical, and simulated data. We carefully analyze noise and ergodic properties (i) using the Allan variance for characterizing the noise and (ii) exploiting a test of ergodicity tailored for experiments done over finite times. We derive these two estimators in the Ornstein-Uhlenbeck low-frequency trapped-diffusion regime and study analytically their evolution toward the high-frequency Wiener-like free-diffusion regime, in very good agreement with simulated and experimental results. This study is performed comprehensively from the free-diffusion to the trapped-diffusion regimes. It also carefully looks at the specific signatures of the estimators at the crossover between the two regimes. This analysis is important to conduct when exploiting optical traps in a metrology context.

Generalized (non-Markovian) diffusion equations with different memory kernels and subordination schemes based on random time change in the Brownian diffusion process are popular mathematical tools for description of a variety of non-Fickian diffusion processes in physics, biology, and earth sciences. Some of such processes (notably, the fluid limits of continuous time random walks) allow for either kind of description, but other ones do not. In the present work we discuss the conditions under which a generalized diffusion equation does correspond to a subordination scheme, and the conditions under which a subordination scheme does possess the corresponding generalized diffusion equation. Moreover, we discuss examples of random processes for which only one, or both kinds of description are applicable.

By characterizing the phase dynamics in coupled oscillators, we gain insights into the fundamental phenomena of complex systems. The collective dynamics in oscillatory systems are often described by order parameters, which are insufficient for identifying more specific behaviors. To improve this situation, we propose a topological approach that constructs the quantitative features describing the phase evolution of oscillators. Here, the phase data are mapped into a high-dimensional space at each time, and the topological features describing the shape of the data are subsequently extracted from the mapped points. These features are extended to time-variant topological features by adding the evolution time as an extra dimension in the topological feature space. The time-variant features provide crucial insights into the evolution of phase dynamics. Combining these features with the kernel method, we characterize the multiclustered synchronized dynamics during the early evolution stages. Finally, we demonstrate that our method can qualitatively explain chimera states. The experimental results confirmed the superiority of our method over those based on order parameters, especially when the available data are limited to the early-stage dynamics.

We investigate oscillatory phase pattern formation and amplitude control for a linearized stochastic neuron field model by simulating Mexican-hat-coupled stochastic processes. We find, for several choices of parameters, that spatial pattern formation in the temporal phases of the coupled processes occurs if and only if their amplitudes are allowed to grow unrealistically large. Stimulated by recent work on homeostatic inhibitory plasticity, we introduce static and plastic (adaptive) systemic inhibitory mechanisms to keep the amplitudes stochastically bounded. We find that systems with static inhibition exhibited bounded amplitudes but no sustained phase patterns. With plastic systemic inhibition, on the other hand, the resulting systems exhibit both bounded amplitudes and sustained phase patterns. These results demonstrate that plastic inhibitory mechanisms in neural field models can dynamically control amplitudes while allowing patterns of phase synchronization to develop. Similar mechanisms of plastic systemic inhibition could play a role in regulating oscillatory functioning in the brain.

The time-dependent Ginzburg-Landau (or Allen-Cahn) equation and the Swift-Hohenberg equation, both added with a stochastic term, are proposed to describe cloud pattern formation and cloud regime phase transitions of shallow convective clouds organized in mesoscale systems. The starting point is the Hottovy-Stechmann linear spatiotemporal stochastic model for tropical precipitation, used to describe the dynamics of water vapor and tropical convection. By taking into account that shallow stratiform clouds are close to a self-organized criticality and that water vapor content is the order parameter, it is observed that sources must have nonlinear terms in the equation to include the dynamical feedback due to precipitation and evaporation. The nonlinear terms are derived by using the known mean field of the Ising model, as the Hottovy-Stechmann linear model presents the same probability distribution. The inclusion of this nonlinearity leads to a kind of time-dependent Ginzburg-Landau stochastic equation, originally used to describe superconductivity phases. By performing numerical simulations, pattern formation is observed. These patterns are better compared with real satellite observations than the pure linear model. This is done by comparing the spatial Fourier transform of real and numerical cloud fields. However, for highly ordered cellular convective phases, considered as a form of Rayleigh-Bénard convection in moist atmospheric air, the Ginzburg-Landau model does not allow us to reproduce such patterns. Therefore, a change in the form of the small-scale flux convergence term in the equation for moist atmospheric air is proposed. This allows us to derive a Swift-Hohenberg equation. In the case of closed cellular and roll convection, the resulting patterns are much more organized than the ones obtained from the Ginzburg-Landau equation and better reproduce satellite observations as, for example, horizontal convective fields.

We study the viscous dissipation in pipe flows in long channels with porous or semipermeable walls, taking into account both the dissipation in the bulk of the channel and in the pores. We give simple closed-form expressions for the dissipation in terms of the axially varying flow rate $Q\left(x\right)$ and the pressure $p\left(x\right)$, generalizing the well-known expression $\dot{W}=Q\mathrm{\Delta }p=R{Q}^2$ for the case of impenetrable walls with constant $Q$, pressure difference $\mathrm{\Delta }p$ between the ends of the pipe and resistance $R$. When the pressure $p_0$ outside the pipe is constant, the result is the straightforward generalization $\dot{W}=\mathrm{\Delta }\left[(p-p_0)Q\right]$. Finally, applications to osmotic flows are considered.

Physical understanding of how the interplay between symmetries and nonlinear effects can control the scaling and multiscaling properties in a coupled driven system, such as magnetohydrodynamic turbulence or turbulent binary fluid mixtures, remains elusive. To address this generic issue, we construct a conceptual nonlinear hydrodynamic model, parametrized jointly by the nonlinear coefficients, and the spatial scaling of the variances of the advecting stochastic velocity and the stochastic additive driving force, respectively. By using a perturbative one-loop dynamic renormalization group method, we calculate the multiscaling exponents of the suitably defined equal-time structure functions of the dynamical variable. We show that depending upon the control parameters the model can display a variety of universal scaling behaviors ranging from simple scaling to multiscaling.

We study the self-organization process induced by a nonlocal critical field, in analogy with the electric field that is derived from the global spatial profile of electric charge density during a discharge. In this nontrivial extension of standard sandpilelike models of intermittent dissipation, the charges move in a similar manner to grains of sand when the threshold condition on the field is achieved. Here we focus our attention on the long term statistics of events, so that we consider an extremely simplified model in close similarity with sandpiles, avoiding some of the extremely interesting complexities that occur in three-dimensional electric discharges. For the observed avalanches (discharges in this case) we analyze four characteristic quantities: current, charge discharged, energy discharged, and duration of the discharge. We have run several simulations to explore the parameter space and found in general that they exhibit well defined power law event statistics spanning for one to three decades in general. For some parameter values we observe the existence of large or global events, in addition to the power law statistics, some of which may be related to finite size effects due to the size of the simulation box. This is the first step in understanding the long term statistics of systems with avalanches or discharges, when the criticality is controlled by nonlocality, as there are a number systems, such as lightning discharges or heat transport in tokamaks, where this type of dynamics is expected to occur.

Nonreciprocity is of particular importance to realize one-way propagation, thus attracting intensive research interest in various fields. Thermal waves, essentially originating from periodic temperature fluctuations, are also expected to achieve one-way propagation, but the related mechanism is still lacking. To solve the problem, we introduce spatiotemporal modulation to realize thermal wave nonreciprocity. Since thermal waves are completely transient, both the convective term and the Willis term induced by spatiotemporal modulation should be considered. We also analytically study the phase difference between two spatiotemporally modulated parameters, which offers a tunable parameter to control nonreciprocity. We further define a rectification ratio based on the reciprocal of spatial decay rate and discuss nonreciprocity conditions accordingly. Finite-element simulations are performed to confirm theoretical predictions, and experimental suggestions are provided to ensure the feasibility of spatiotemporal modulation. These results have potential applications in realizing thermal detection and thermal stabilization simultaneously.

We study the quantum phase transition driven by a point impurity in a chain seamed with ring frustration. With strong coupling and light impurity, the system is in a topological extended-kink (TEK) phase, which exhibits gapless excitations in the bulk. With strong coupling and heavy impurity, the system is in a gapped kink bound state (KBS) phase. Two-point bulk and impurity correlations are defined to characterize the two phases. In the TEK phase, both the bulk and impurity correlations are long range and factorizable so that scaling functions can be parsed. The scaling functions relies on the distance scaled by the system's size. An impurity correlation length can be extracted from the impurity correlation. In the transition from TEK to KBS, the scaling function of the bulk correlation undergoes an abrupt steplike change. Meanwhile, the impurity correlation length decreases from a divergent value to a finite one. The ground state of the TEK phase retains a relatively high value of entanglement entropy due to the absence of symmetry breaking. However, spontaneous symmetry breaking occurs in the KBS phase, which induces antiferromagnetic order in the bulk and entangled spin configuration near the impurity.

We derive the general probability distribution function of stochastic work for quantum Otto engines in which both the isochoric and driving processes are irreversible due to finite time duration. The time-dependent work fluctuations, average work, and thermodynamic efficiency are explicitly obtained for a complete cycle operating with an analytically solvable two-level system. The effects of the irreversibility originating from finite-time cycle operation on the thermodynamic efficiency, work fluctuations, and relative power fluctuations are discussed.