Repeatedly monitored quantum walks with a rate $1/\tau$ yield discrete-time trajectories which are inherently random. With these paths the first-hitting time with sharp restart is studied. We find an instability in the optimal mean hitting time, which is not found in the corresponding classical random-walk process. This instability implies that a small change in parameters can lead to a rather large change of the optimal restart time. We show that the optimal restart time versus $\tau$, as a control parameter, exhibits sets of staircases and plunges. The plunges, are due to the mentioned instability, which in turn is related to the quantum oscillations of the first-hitting time probability, in the absence of restarts. Furthermore, we prove that there are only two patterns of staircase structures, dependent on the parity of the distance between the target and the source in units of lattice constant. The global minimum of the hitting time is controlled not only by the restart time, as in classical problems, but also by the sampling time $\tau$. We provide numerical evidence that this global minimum occurs for the $\tau$ minimizing the mean hitting time, given restarts taking place after each measurement. Last, we numerically show that the instability found in this work is relatively robust against stochastic perturbations in the sampling time $\tau$.

We study how discrete-time quantum walks behave under short-range correlated noise. By considering noise as a source of inhomogeneity of quantum gates, we introduce a primitive relaxation in the assumption of uncorrelated stochastic noise: binary pair correlations manifesting in the random distribution. Using different quantum gates, we examined the transport properties for both spatial and temporal noise regimes. For spatial inhomogeneities, we unveil noise correlations driving quantum walks from the well-known exponentially localized regime to superdiffusive spreading. This scenario displays an intriguing performance in which the superdiffusive exponent is almost invariant to the degree of inhomogeneity. The time-asymptotic regime and the finite-size scaling also unveil an emergent superdiffusive behavior for quantum walks undergoing temporal noise correlation, replacing the diffusive regime exhibited when noise is random and uncorrelated. However, some quantum gates are insensitive to correlations, contrasting with the spatial noise scenario. Numerical and analytical results provide valuable insights into the underlying mechanism of superdiffusive quantum walks, including those arising from deterministic aperiodic inhomogeneities.

It is expected that conformal symmetry is an emergent property of many systems at their critical point. This imposes strong constraints on the critical behavior of a given system. Taking them into account in theoretical approaches can lead to a better understanding of the critical physics or improve approximation schemes. However, within the framework of the nonperturbative or functional renormalization group and, in particular, of one of its most used approximation schemes, the derivative expansion (DE), nontrivial constraints apply only from third order [usually denoted $O\left({\partial }^4\right)$], at least in the usual formulation of the DE that includes correlation functions involving only the order parameter. In this work we implement conformal constraints on a generalized DE including composite operators and show that new constraints already appear at second order of the DE [or $O\left({\partial }^2\right)$]. We show how these constraints can be used to fix nonphysical regulator parameters.

DNA exhibits remarkable charge transfer ability, which is crucial for its biological functions and potential electronic applications. The charge transfer process in DNA is widely recognized as primarily mediated by guanine, while the contribution of other nucleobases is negligible. Using the tight-binding models in conjunction with first-principles calculations, we investigated the charge transfer behavior of homogeneous GC and AT pairs. We found that the charge transfer rate of adenine significantly changes. With overstretching, the charge transfer rate of adenine can even surpass that of guanine, by as much as five orders of magnitude at a twist angle of around 26°. Further analysis reveals that it is attributed to the turnover of the relative coupling strength between homogeneous GC and AT base pairs, which is caused by the symmetry exchange between the two highest occupied molecular orbitals of base pairs occurring at different twist angles. Given the high degree of flexibility of DNA in vivo and in vitro conditions, these findings prompt us to reconsider the mechanism of biological functions concerning the charge transfer in DNA molecules and further open the potential of DNA as a biomaterial for electronic applications.

The drag force acting on an intruder colliding with granular media is typically influenced by the impact velocity and the penetrating depth. In this paper, the investigation was extended to the dry and immersed scenarios through coupled simulations at different penetrating velocities. The drag force regime was clarified to exhibit velocity dependence in the initial contact stage, followed by the inertial transit stage with a $F\sim z^2$ (force-depth) relationship. Subsequently, it transitioned into the depth-dependent regime in both dry and immersed cases. The underlying rheological mechanism was explored, revealing that, in both dry and immersed scenarios, the granular bulk underwent a state relaxation process, as indicated by the granular inertial number. Additionally, the presence of the ambient fluid restricted the flow dynamics of the perturbed granular material, exhibiting a similar rheology as observed in the dry case.

The normal modes, i.e., the eigensolutions to the dispersion relation equation, are the most fundamental properties of a plasma. The real part indicates the intrinsic oscillation frequency while the imaginary part the Landau damping rate. In most of the literature, the normal modes of quantum plasmas are obtained by means of small damping approximation, which is invalid for high-$k$ modes. In this paper, we solve the exact dispersion relations via the analytical continuation scheme, and, due to the multi-value nature of the Fermi-Dirac distribution, reformation of the complex Riemann surface is required. It is found that the topological shape of the root locus in quantum plasmas is quite different from classical ones, in which both real and imaginary frequencies of high-$k$ modes increase with $k$ steeper than the typical linear behavior in classical plasmas. As a result, the time-evolving behavior of a high-$k$ initial perturbation becomes ballistic-like in quantum plasmas.

Electrons are the carriers of heat and electricity in materials and exhibit abundant transport phenomena such as ballistic, diffusive, and hydrodynamic behaviors in systems with different sizes. The electron Boltzmann transport equation (eBTE) is a reliable model for describing electron transport, but it is a challenging problem to efficiently obtain the numerical solutions of the eBTE within one unified scheme involving ballistic, hydrodynamics, and/or diffusive regimes. In this work, a discrete unified gas kinetic scheme (DUGKS) in the finite-volume framework is developed based on the eBTE with the Callaway relaxation model for electron transport. By reconstructing the distribution function at the cell interface, the processes of electron drift and scattering are coupled together within a single time step. Numerical tests demonstrate that the DUGKS can be adaptively applied to multiscale electron transport, across different regimes.

We prove analytically the ballistic thermal rectification effect (BTRE) in the Corbino disk characterized by an annular shape. We derive the thermal rectification efficiency (RE) and show that it can be expressed as the product of two independent functions, the first dependent on the temperatures of the heat baths and the second on the system's geometry. It follows that a perfect BTRE can be reached with the increase of the ratios of the heat baths' temperatures and of the radius of the outer edge to the inner edge of the disk. We also show that, by introducing a potential barrier into the Corbino disk, the RE can be greatly improved. Quite remarkably, by an appropriate choice of parameters, the thermal diode effect can be reversed. Our results are robust under variation of the Corbino geometry, which may provide a flexible route to manipulate the heat flow at the nanoscale.

Using hybrid molecular dynamics/SWAP Monte Carlo (MD/SMC) simulations, we show that while the terminal relaxation times $\tau \left(\varphi \right)$ for FIRE energy minimization of soft-sphere glasses can decrease by orders of magnitude as sample equilibration proceeds and the jamming density ${\varphi }_{\mathrm{J}}$ increases, they always scale as $\tau \left(\varphi \right)\sim {({\varphi }_{\mathrm{J}}-\varphi )}^{-2}\sim {[Z_{\mathrm{iso}}-Z_{\mathrm{ms}}\left(\tau \right)]}^{-2}$, where $Z_{\mathrm{iso}}=2d$ and $Z_{\mathrm{ms}}\left(\tau \right)$ is the average coordination number of particles satisfying a minimal local mechanical stability criterion ($Z\ge d+1$) at the top of the final potential-energy-landscape (PEL) sub-basin the system encounters. This scaling allows us to collapse $\tau$ datasets that look very different when plotted as a function of $\varphi$, and to address a closely related question: how does the character of the PEL basins that dense thermal glasses most typically occupy evolve as the glasses age at constant $\varphi$ and $T$?

We consider the motion of a harmonically trapped overdamped particle, which is submitted to a self-phoretic force, that is proportional to the gradient of a diffusive field for which the particle itself is the source. In agreement with existing results for free particles or particles in a bounded domain, we find that the system exhibits a transition between an immobile phase, where the particle stays at the center of the trap, and an oscillatory state. We perform an exact analysis giving access to the bifurcation threshold, as well as the frequency of oscillations and their amplitude near the threshold. Our analysis also characterizes the shape of two-dimensional oscillations that take place along a circle or a straight line. Our results are confirmed by numerical simulations.

The discrete stochastic dynamics of a random walker in the presence of resetting and memory is analyzed. Resetting and memory effects may compete in certain parameter regimes, and lead to significant changes in the long-time dynamics of the walker. Analytic exact results are obtained for a model memory where the walker remembers all the past events equally. In most cases, resetting effects dominate at long times and dictate the asymptotic dynamics. We discuss the full phase diagram of the asymptotic dynamics and the resulting changes due to the resetting and the memory effects.

Next-generation reservoir computing is a machine-learning approach that has been recently proposed as an effective method for predicting the dynamics of chaotic systems. So far, this approach has been applied mainly under the assumption that all components of the state vector of dynamical systems are observable. Here we study the effectiveness of this method when only a scalar time series is available for observation. As illustrations, we use the time series of Rössler and Lorenz systems, as well as the chaotic time series generated by an electronic circuit. We found that prediction is only effective if the feature vector of a nonlinear autoregression algorithm contains monomials of a sufficiently high degree. Moreover, the prediction can be improved by replacing monomials with Chebyshev polynomials. Next-generation models, built on the basis of partial observations, are suitable not only for short-term forecasting, but are also capable of reproducing the long-term climate of chaotic systems. We demonstrate the reconstruction of the bifurcation diagram of the Rössler system and the return maps of the Lorenz and electronic circuit systems.

Quantification of measurement uncertainty is crucial for robust scientific inference, yet accurate estimates of this uncertainty remain elusive for ecological measures of diversity. Here, we address this longstanding challenge by deriving a closed-form unbiased estimator for the sampling variance of Simpson's diversity index. In numerical tests the estimator consistently outperforms existing approaches, particularly for applications in which species richness exceeds sample size. We apply the estimator to quantify biodiversity loss in marine ecosystems and to demonstrate ligand-dependent contributions of T-cell-receptor chains to specificity, illustrating its versatility across fields. The novel estimator provides researchers with a reliable method for comparing diversity between samples, essential for quantifying biodiversity trends and making informed conservation decisions.

We undertake a numerical study of the ordering kinetics in the two-dimensional (2D) active Ising model (AIM), a discrete flocking model with a conserved density field coupled to a nonconserved magnetization field. We find that for a quench into the liquid-gas coexistence region and in the ordered liquid region, the characteristic length scale of both the density and magnetization domains follows the Lifshitz-Cahn-Allen growth law, $R\left(t\right)\sim t^{1/2}$, consistent with the growth law of passive systems with scalar order parameter and nonconserved dynamics. The system morphology is analyzed with the two-point correlation function and its Fourier transform, the structure factor, which conforms to the well-known Porod's law, a manifestation of the coarsening of compact domains with smooth boundaries. We also find the domain growth exponent unaffected by different noise strengths and self-propulsion velocities of the active particles. However, transverse diffusion is found to play the most significant role in the growth kinetics of the AIM. We extract the same growth exponent by solving the hydrodynamic equations of the AIM.

We study the effects of aging properties of subordinated fractional Brownian motion (FBM) with drift and in harmonic confinement, when the measurement of the stochastic process starts a time $t_a>0$ after its original initiation at $t=0$. Specifically, we consider the aged versions of the ensemble mean-squared displacement (MSD) and the time-averaged MSD (TAMSD), along with the aging factor. Our results are favorably compared with simulations results. The aging subordinated FBM exhibits a disparity between MSD and TAMSD and is thus weakly nonergodic, while strong aging is shown to effect a convergence of the MSD and TAMSD. The information on the aging factor with respect to the lag time exhibits an identical form to the aging behavior of subdiffusive continuous-time random walks (CTRW). The statistical properties of the MSD and TAMSD for the confined subordinated FBM are also derived. At long times, the MSD in the harmonic potential has a stationary value, that depends on the Hurst index of the parental (nonequilibrium) FBM. The TAMSD of confined subordinated FBM does not relax to a stationary value but increases sublinearly with lag time, analogously to confined CTRW. Specifically, short aging times $t_a$ in confined subordinated FBM do not affect the aged MSD, while for long aging times the aged MSD has a power-law increase and is identical to the aged TAMSD.

In this work the thermodynamic geometry (TG) of semiclassical fluids is analyzed. We present results for two models. The first one is a semiclassical hard-sphere (SCHS) fluid whose Helmholtz free energy is obtained from path-integral Monte Carlo simulations. It is found that, due to quantum contributions in the thermodynamic potential, the anomaly found in TG for the classical hard-sphere fluid related to the sign of the scalar curvature is now avoided in a considerable region of the thermodynamic space. The second model is a semiclassical square-well fluid, described by a SCHS repulsive interaction coupled with a classical attractive square-well contribution. The behavior of the semiclassical curvature scalar as a function of the thermal de Broglie wavelength ${\lambda }_B$ is analyzed for several attractive-potential ranges. A description of the semiclassical $R$ Widom lines, defined by the maxima of the curvature scalar, is also obtained and results are compared with the corresponding classical systems for different square-well ranges.

Navigating the intricacies of thermal management at the quantum scale is a challenge in the pursuit of advanced nanoscale technologies. To this extent, theoretical frameworks introducing minimal models mirroring the functionality of electronic current amplifiers and transistors, for instance, have been proposed. Different architectures of the subsystems composing a quantum thermal device can be considered, tacitly bringing drawbacks or advantages if properly engineered. This paper extends the prior research on thermotronics, studying a strongly coupled three-subsystem thermal device with a specific emphasis on a third excited level in the control subsystem. Our setup can be employed as a multipurpose device conditioned on the specific choice of internal parameters: heat switch, rectifier, stabilizer, and amplifier. The exploration of the detuned levels unveils a key role in the performance and working regime of the device. We observe a stable and strong amplification effect persisting over broad ranges of temperature. We conclude that considering a three-level system, as the one directly in contact with the control temperature, boosts output currents and the ability to operate our devices as a switch at various temperatures.

As the Reynolds number is increased, a laminar fluid flow becomes turbulent, and the range of time and length scales associated with the flow increases. Yet, in a turbulent reactive flow system, as we increase the Reynolds number, we observe the emergence of a single dominant timescale in the acoustic pressure fluctuations, as indicated by its loss of multifractality. Such emergence of order from chaos is intriguing. We perform experiments in a turbulent reactive flow system consisting of flame, acoustic, and hydrodynamic subsystems interacting nonlinearly. We study the evolution of short-time correlated dynamics between the acoustic field and the flame in the spatiotemporal domain of the system. The order parameter, defined as the fraction of the correlated dynamics, increases gradually from zero to one. We find that the susceptibility of the order parameter, correlation length, and correlation time diverge at a critical point between chaos and order. Our results show that the observed emergence of order from chaos is a continuous phase transition. Moreover, we provide experimental evidence that the critical exponents characterizing this transition fall in the universality class of directed percolation. Our paper demonstrates how a real-world complex, nonequilibrium turbulent reactive flow system exhibits universal behavior near a critical point.

Networks of nonlinear parametric resonators are promising candidates as Ising machines for annealing and optimization. These many-body out-of-equilibrium systems host complex phase diagrams of coexisting stationary states. The plethora of states manifest via a series of bifurcations, including bifurcations that proliferate purely unstable solutions. Here we demonstrate that the latter take a fundamental role in the stochastic dynamics of the system. Specifically, they determine the switching paths and the switching rates between stable solutions. We demonstrate experimentally the impact of the added unstable states on noise-activated switching dynamics in a network of two coupled parametric resonators.