In this work, we study the Rényi $\alpha$ entropies $S_{\alpha }\left(\widehat{\rho }\right)={(1-\alpha )}^{-1}ln\left\{\text{Tr}\left({\widehat{\rho }}^{\alpha }\right)\right\}$ of quantum states for $N$ bosons in the phase-space representation. With the help of the Bopp rule, we derive the entropies of Gaussian states in closed form for positive integers $\alpha =2,3,4,\cdots$ and then, with the help of the analytic continuation, acquire the closed form also for real values of $\alpha >0$. The quantity $S_2\left(\widehat{\rho }\right)$, primarily studied in the literature, will then be a special case of our finding. Subsequently we acquire the Rényi $\alpha$ entropies, with positive integers $\alpha$, in closed form also for a specific class of the non-Gaussian states (mixed states) for $N$ bosons, which may be regarded as a generalization of the eigenstates $|n\rangle$ (pure states) of a single harmonic oscillator with $n\ge 1$, in which the Wigner functions have negative values indeed. Due to the fact that the dynamics of a system consisting of $N$ oscillators is Gaussian, our result will contribute to a systematic study of the Rényi $\alpha$ entropy dynamics when the current form of a non-Gaussian state is initially prepared.

The Langevin equation greatly simplifies the mathematical expression of the effects of thermal noise by using only two terms, a dissipation term, and a random-noise term. The Langevin description was originally applied to a system in contact with a single heat reservoir; however, many recent studies have also adopted a Langevin description for systems connected to multiple heat reservoirs. This is accomplished through the introduction of a simple summation for the dissipation and random-noise terms associated with each reservoir. However, the validity of this simple addition has been the focus of only limited discussion and has raised several criticisms. Moreover, this additive description has never been either experimentally or numerically verified, rendering its validity is still an open question. Here we perform molecular dynamics simulations for a Brownian system in simultaneous contact with multiple heat reservoirs to check the validity of this additive approach. Our simulation results confirm that the effect of multiple heat reservoirs is additive in general. A very small deviation in the total amount of dissipation and associated noise is found but seems not significant within statistical errors. We find that the steady-state properties satisfy the additivity perfectly and are not affected by this deviation.

How cooperation can evolve between players is an unsolved problem of biology. Here we use Hamiltonian dynamics of models of the Ising type to describe populations of cooperating and defecting players to show that the equilibrium fraction of cooperators is given by the expectation value of a thermal observable akin to a magnetization. We apply the formalism to the public goods game with three players and show that a phase transition between cooperation and defection occurs that is equivalent to a transition in one-dimensional Ising crystals with long-range interactions. We then investigate the effect of punishment on cooperation and find that punishment plays the role of a magnetic field that leads to an “alignment” between players, thus encouraging cooperation. We suggest that a thermal Hamiltonian picture of the evolution of cooperation can generate other insights about the dynamics of evolving groups by mining the rich literature of critical dynamics in low-dimensional spin systems.

We study translocation of semiflexible polymers driven by force $f_d$ inside a nanometer-scale pore using our three-dimensional Langevin dynamics model. We show that the translocation time $\tau$ increases with increasing bending rigidity $\kappa$. Similarly, the exponent $\beta$ for the scaling of $\tau$ with polymer length $N,\tau \sim N^{\beta }$, increases with increasing $\kappa$ as well as with increasing $f_d$. By comparing waiting times between semiflexible and fully flexible polymers we show that for realistic $f_d$ translocation dynamics is to a large extent, but not completely, determined by the polymer's elastic length measured in number of Kuhn segments $N_{\mathrm{Kuhn}}$. Unlike in driven translocation of flexible polymers, friction related to the polymer segment on the trans side has a considerable effect on the resulting dynamics. This friction is intermittently reduced by buckling of the polymer segment in the vicinity of the pore opening on the trans side. We show that in the experimentally relevant regime where viscosity is higher than in computer simulation models, the probability for this buckling increases with increasing $f_d$, giving rise to a larger contribution to the trans side friction at small $f_d$. Similarly to flexible polymers, we find significant center-of-mass diffusion of the cis side polymer segment which speeds up translocation. This effect is larger for smaller $f_d$. However, this speedup is smaller than the slowing down due to the trans side friction. At large enough $N_{\mathrm{Kuhn}}$, the roles can be seen to be reversed, and the dynamics of flexible polymers can be reached. However, for example, polymers used in translocation experiments of DNA are elastically so short that the finite-length dynamics outlined here applies.

When chiral liquid crystals or magnets are subjected to applied fields or other anisotropic environments, the competition between favored twist and anisotropy leads to the formation of complex defect structures. In some cases, the defects are skyrmions, which have ${180}^{\circ }$ double twist going outward from the center, and hence can pack together without singularities in the orientational order. In other cases, the defects are merons, which have ${90}^{\circ }$ double twist going outward from the center; packing such merons requires singularities in the orientational order. In the liquid crystal context, a lattice of merons is equivalent to a blue phase. Here we perform theoretical and computational studies of skyrmions and merons in chiral liquid crystals and magnets. Through these studies, we calculate the phase diagrams for liquid crystals and magnets in terms of dimensionless ratios of energetic parameters. We also predict the range of metastability for liquid crystal skyrmions and show that these skyrmions can move and interact as effective particles. The results show how the properties of skyrmions and merons depend on the vector or tensor nature of the order parameter.

A uniaxially compressed thin elastic sheet that is resting on a soft adhesive substrate can form a blister, which is a small delaminated region, if the adhesion energy is sufficiently weak. To analyze the equilibrium behavior of this system, we model the substrate as a Winkler or fluid foundation. We develop a complete set of equations for the profile of the sheet at different applied pressures. We show that at the edge of delamination, the height of the sheet is equal to $\sqrt{2}{\ell }_c$, where ${\ell }_c$ is the capillary length. We then derive an approximate solution to these equations and utilize them for two applications. First, we determine the phase diagram of the system by analyzing possible transitions from the flat and wrinkled to delaminated states of the sheet. Second, we show that our solution for a blister on a soft foundation converges to the known solution for a blister on a rigid substrate that assumed a discontinuous bending moment at the blister edges. This continuous convergence into a discontinuous state marks the formation of a boundary layer around the point of delamination. The width of this layer relative to the extent length of the blister, $\ell$, scales as $w/\ell \sim {({\ell }_c/{\ell }_{ec})}^{1/2}$, where ${\ell }_{ec}$ is the elastocapillary length scale. Notably, our findings can provide guidelines for utilizing compression to remove thin biofilms from surfaces and thereby prevent the fouling of the system.

The effects of axial boundary conductivity on the formation and stability of a magnetized free Stewartson-Shercliff layer (SSL) in a short Taylor-Couette device are reported. As the axial field increases with insulating endcaps, hydrodynamic Kelvin-Helmholtz-type instabilities set in at the SSLs of the conducting fluid, resulting in a much reduced flow shear. With conducting endcaps, SSLs respond to an axial field weaker by the square root of the conductivity ratio of endcaps to fluid. Flow shear continuously builds up as the axial field increases despite the local violation of the Rayleigh criterion, leading to a large number of hydrodynamically unstable modes. Numerical simulations of both the mean flow and the instabilities are in agreement with the experimental results.

The conventional theory of combustion describes systems where all of the parameters are spatially homogeneous. On the other hand, combustion in disordered explosives has long been known to occur after local regions of the material, called hot spots, are ignited. In this article we show that a system of randomly distributed hot spots exhibits a dynamic phase transition, which, depending on parameters of the system, can be either first or second order. These two regimes are separated by a tricritical point. We also show that on the qualitative level the phase diagram of the system is universal. It is valid in two and three dimensions, in the cases when the hot spots interact either by heat or sound waves, and in a broad range of microscopic disorder models.

We investigate the quantum phase transitions of the transverse-field quantum Ising model on the triangular lattice and Sierpiński fractal lattices by employing the multipartite entanglement and quantum coherence along with the quantum renormalization group method. It is shown that the quantum criticalities of these high-dimensional models closely relate to the behaviors of the multipartite entanglement and quantum coherence. As the thermodynamic limit is approached, the first derivatives of the multipartite entanglement and quantum coherence exhibit singular behaviors, and the consistent finite-size scaling behaviors for each lattice are also obtained from the first derivatives. The multipartite entanglement and quantum coherence are demonstrated to be good indicators for detecting the quantum phase transitions in the triangular lattice and Sierpiński fractal lattices. Furthermore, the dimensions determine the relations between the critical exponents and the correlation length exponents for these lattices.

Typical eigenstates of quantum systems, whose classical limit is chaotic, are well approximated as random states. Corresponding eigenvalue spectra are modeled through an appropriate ensemble described by random matrix theory. However, a small subset of states violates this principle and displays eigenstate localization, a counterintuitive feature known to arise due to purely quantum or semiclassical effects. In the spectrum of chaotic systems, the localized and random states interact with one another and modify the spectral statistics. In this work, a $3\times 3$ random matrix model is used to obtain exact results for the ratio of spacing between a generic and localized state. We consider time-reversal-invariant as well as noninvariant scenarios. These results agree with the spectra computed from realistic physical systems that display localized eigenmodes.

We investigate both the classical and quantum dynamics for a simple kicked system (the standard map) that classically has mixed phase space. For initial conditions in a portion of the chaotic region that is close enough to the regular region, the phenomenon of sticking leads to a power-law decay with time of the classical correlation function of a simple observable. Quantum mechanically, we find the same behavior, but with a smaller exponent. We consider various possible explanations of this phenomenon, and settle on a modification of the Meiss-Ott Markov tree model that takes into account quantum limitations on the flux through a turnstile between regions corresponding to states on the tree. Further work is needed to better understand the quantum behavior.

Excitable lasers with saturable absorbers are currently investigated as potential candidates for low level spike processing tasks in integrated optical platforms. Following a small perturbation of a stable equilibrium, a single and intense laser pulse can be generated before returning to rest. Motivated by recent experiments [Selmi et al., Phys. Rev. E 94, 042219 (2016)], we consider the rate equations for a laser containing a saturable absorber (LSA) and analyze the effects of different initial perturbations. With its three steady states and following Hodgkin classification, the LSA is a Type I excitable system. By contrast to perturbations on the intensity leading to the same intensity pulse, perturbations on the gain generate pulses of different amplitudes. We explain these distinct behaviors by analyzing the slow-fast dynamics of the laser in each case. We first consider a two-variable LSA model for which the conditions of excitability can be explored in the phase plane in a transparent manner. We then concentrate on the full three variable LSA equations and analyze its solutions near a degenerate steady bifurcation point. This analysis generalizes previous results [Dubbeldam et al., Phys. Rev. E 60, 6580 (1999)] for unequal carrier density rates. Last, we discuss a fundamental difference between neuron and laser models.

Organisms can be synchronized not only to the natural 24-h light-dark cycle but also to artificial non-24-h cycles. Interestingly, when the period of the cycle is far from 24 h, organisms may show complicated behavioral patterns. For example, exposed to a 22-h light-dark cycle, in behavioral activity of rats, a phenomenon called “dissociation” emerges, i.e., one periodic component shows a 22-h period and the other shows a period close to the endogenous period of the animal (around 24 h). It has been found that these two components are regulated by two subgroups of the suprachiasmatic nucleus (SCN), respectively, with the ventrolateral part regulating the 22-h component and the dorsomedial part regulating the other component. In the present study, based on a mathematical model, we will examine how the ratio of amplitudes between these two subgroups affects the entrainment of the SCN to the external 22-h light-dark cycle. Our results show that the dissociation happens when the ratio is smaller than 1 and the maximal entrainment (synchronization) ability of the SCN to the external cycle is obtained when the ratio is larger than 1. Our finding sheds light on the dissociation between the subgroups and suggests that the heterogeneity in the amplitudes alter the entrainment ability of the SCN.

We present evidence of extreme events in two Hindmarsh-Rose (HR) bursting neurons mutually interacting via two different coupling configurations: chemical synaptic- and gap junctional-type diffusive coupling. A dragon-king-like probability distribution of the extreme events is seen for combinations of synaptic coupling where small- to medium-size events obey a power law and the larger events that cross an extreme limit are outliers. The extreme events originate due to instability in antiphase synchronization of the coupled systems via two different routes, intermittency and quasiperiodicity routes to complex dynamics for purely excitatory and inhibitory chemical synaptic coupling, respectively. For a mixed type of inhibitory and excitatory chemical synaptic interactions, the intermittency route to extreme events is only seen. Extreme events with our suggested distribution is also seen for gap junctional-type diffusive, but repulsive, coupling where the intermittency route to complexity is found. A simple electronic experiment using two diffusively coupled analog circuits of the HR neuron model, but interacting in a repulsive way, confirms occurrence of the dragon-king-like extreme events.

We monitor optically the propagation of a slow interfacial mode III crack along a heterogeneous weak interface and compare it to mode I loading. Pinning and depinning of the front on local toughness asperities within the process zone are the main mechanisms for fracture roughening. Geometrical properties of the fracture fronts are derived in the framework of self-affine scale invariance and Family-Vicsek scaling. We characterize the small and large scale roughness exponents ${\zeta }_{-}=0.6$ and ${\zeta }_{+}=0.35$, the growth exponent at large scale ${\beta }_{+}=0.58$, and the power-law exponent of the local velocity distribution of the fracture fronts, $\eta =2.55$. All these analyzed properties are similar to those previously observed for mode I interfacial fractures. We also observe a common power-law decay of the probability distribution function of avalanche area. We finally observe that amplitude of front fluctuations, local rupture velocity correlation in time, and larger size of events highlight more dynamically unstable behavior of mode III crack ruptures.

In the previous studies of Rayleigh-Taylor instability, different methods were used to consider the effects of elasticity, viscosity, and magnetic fields. In this paper, a unified method, which was first used for fluids, is validated for different physical models, where the unstable mode is decomposed into an irrotational part and a rotational part, and the latter one includes the effects of nonconservative forces and constitutive relations. Previous results of solid and liquid with or without the effects of magnetic fields and finite thickness can be easily recovered after applying the corresponding interface boundary conditions. In addition, new approximate but analytical solutions of the growth rates for a semi-infinite solid-solid interface and solid-fluid interface are obtained with substantially improved accuracy in comparison with the previous ones.

The article [Phys. Rev. E 96, 032106 (2017)] recovers conservation laws and derives the H-theorem for the kinetic equation with gradient corrections. Here we show that this approach is not valid, leading to missing terms in the balance of energy and momentum and to disagreement with correlation entropy known from the Enskog equation.

Cross-beam energy transfer (CBET) is a significant energy-loss mechanism in directly driven inertial-confinement-fusion (ICF) targets. One strategy for mitigating CBET is to increase the bandwidth of the laser light, thereby disrupting the resonant three-wave interactions that underlie this nonlinear scattering process. Here, we report on numerical simulations performed with the wave-based code lpse that show a significant reduction in CBET for bandwidths of $2–5$ THz (corresponding to a normalized bandwidth of $0.2\%–0.6\%$ at a laser wavelength of $351\mathrm{nm}$) under realistic plasma conditions. Such bandwidths are beyond those available with current high-energy lasers used for ICF, but could be achieved using stimulated rotation Raman scattering in diatomic gases like nitrogen.

In the Widom-Rowlinson lattice gas, two particle species ($A, B$) diffuse freely via particle-hole exchange, subject to both on-site exclusion and prohibition of $A-B$ nearest-neighbor pairs. As an athermal system, the overall densities are the only control parameters. As the densities increase, an entropically driven phase transition occurs, leading to ordered states with $A$- and $B$-rich domains separated by hole-rich interfaces. Using Monte Carlo simulations, we analyze the effect of imposing a drive on this system, biasing particle moves along one direction. Our study parallels that for a driven Ising lattice gas, the Katz-Lebowitz-Spohn (KLS) model, which displays atypical collective behavior, e.g., structure factors with discontinuity singularities and ordered states with domains only parallel to the drive. Here, other interesting features emerge, including structure factors with kink singularities (best fitted to $\left|q\right|$), maxima at nonvanishing wave-vector values, oscillating correlation functions, and ordering into multiple striped domains perpendicular to the drive, with a preferred wavelength depending on density and drive intensity. Moreover, the (hole-rich) interfaces between the domains are statistically rough (whether driven or not), in sharp contrast with those in the KLS model, in which the drive suppresses interfacial roughness. Defining an order parameter that accounts for the emergence of multistripe states, we map out the phase diagram in the density-drive plane and present preliminary evidence for a critical phase in this driven lattice gas.

We use Glauber dynamics to study time and temperature dependence of hysteresis in the pure (without quenched disorder) Ising model on cubic, square, honeycomb lattices as well as random graphs. Results are discussed in the context of more extensive studies of hysteresis in the random field Ising model.