A critical temperature for a complete signed graph of $N$ agents where the time-dependent polarization of links tends towards the Heider (structural) balance is found analytically using the heat-bath approach and the mean-field approximation as $T^c=(N-2)/a^c$, where $a^c\approx 1.71649$. The result is in perfect agreement with numerical simulations starting from the paradise state where all links are positively polarized as well as with the estimation of this temperature received earlier with much more sophisticated methods. When heating the system, one observes a discontinuous and irreversible phase transition at $T^c$ from a nearly balanced state when the mean link polarization is about $x_c=0.796388$ to a disordered and unbalanced state where the polarization vanishes. When the initial conditions for the polarization of links are random, then at low temperatures a balanced bipolar state of two mutually hostile cliques exists that decays towards the disorder and there is a discontinuous phase transition at a temperature $T^d$ that is lower than $T^c$. The system phase diagram corresponds to the so-called fold catastrophe when a stable solution of the mean-field equation collides with a separatrix, and as a result a hysteresislike loop is observed.

We study the crossing time statistic of diffusing point particles between the two ends of expanding and narrowing two-dimensional conical channels under a transverse external gravitational field. The theoretical expression for the mean first-passage time for such a system is derived under the assumption that the axial diffusion in a two-dimensional channel of smoothly varying geometry can be approximately described as a one-dimensional diffusion in an entropic potential with position-dependent effective diffusivity in terms of the modified Fick-Jacobs equation. We analyze the channel crossing dynamics in terms of the mean first-passage time, combining our analytical results with extensive two-dimensional Brownian dynamics simulations, allowing us to find the range of applicability of the one-dimensional approximation. We find that the effective particle diffusivity decreases with increasing amplitude of the external potential. Remarkably, the mean first-passage time for crossing the channel is shown to assume a minimum at finite values of the potential amplitude.

Building on the recently derived inhomogeneous mode-coupling theory, we extend the generalized mode-coupling theory of supercooled liquids to inhomogeneous environments. This provides a first-principles-based, systematic, and rigorous way of deriving high-point dynamical susceptibilities from variations of the many-body dynamic structure factors with respect to their conjugate field. This framework allows for a fully microscopic possibility to probe for collective relaxation mechanisms in supercooled liquids near the mode-coupling glass transition. The behavior of these dynamical susceptibilities is then studied in the context of simplified self-consistent relaxation models.

We derive an extended cubic-quintic nonlinear Schrödinger equation with Hamiltonian structure in a nonlinear Klein-Gordon model with cubic-quintic nonlinearity. We use the nonlinear dispersion relation to properly take into account the input of high-order nonlinear effects in the Hamiltonian perturbation approach to nonlinear modulation. We demonstrate that changing the balance between the cubic and quintic nonlinearities has a significant effect on the stability of unmodulated wave packets to long-wave modulations.

Maslov indices are an essential ingredient in the semiclassical approaches to quantum mechanics, as they are also related to the conjugate points of the corresponding trajectory, which reflects the dynamics in its neighborhood. In this paper, we show how these important topological parameters can be computed using the geometrodynamic approach to dynamics. Illustrations in two- and three-dimensional systems are presented and discussed.

In this paper, we investigate the effect of chiral-induced spin selectivity (CISS) on the radical pair mechanism of avian magnetoreception. We examine the impact of spin selectivity on the avian compass sensitivity. In this analysis, we also consider the dipolar and exchange interactions and observe their interplay with CISS. We find that CISS results in a multifold increase in avian compass sensitivity. Interestingly, we also observe that CISS can counter the deleterious effect of dipolar interaction and increase system sensitivity. The analysis has been performed for the toy model (only one nucleus) and a more general case where we consider up to six nuclei from the cryptochrome radical pair system. We observe that the CISS allows the radical pair model to have more realistic recombination rates with good sensitivity. We also do an analysis of the functional window of the avian compass reported in behavioral experiments in the functional window. We could not find a parameter set where a functional window can be observed along with CISS. We also show the effect of spin relaxation on the system and show that under relaxation, CISS shows increased compass sensitivity compared to no CISS case.

The experimental results of the complex dielectric permittivity of aliphatic ketones in dilute solutions of inert solvent cyclohexane in the gigahertz (GHz) and terahertz (THz) frequencies of the electromagnetic spectrum are examined in terms of the theory of inertial anomalous diffusion of polar molecules, considered as an assembly of molecules with interacting dipolar groups, in polar liquids. The theory is based on the generalization of the Debye rotational diffusion model of dielectric relaxation of polar molecules. The model comprises two interacting dipolar groups—one lighter and the other heavier; each has a finite moment of inertia and each experiences a finite friction with an extensive range of damping or drag coefficient and the dipole moment ratio of the two groups. The lighter group refers to the reference molecule, whereas the heavier group simulates the neighboring molecules, and the two groups interact with each other via the dipole–dipole interaction potential. The resulting approximate expression contains terms in both the Rocard form and the Сole–Сole form. The experimental data on aliphatic ketones are shown to fit extremely well with the theory, and parameters of the fit offer physical significance. An agreement of the plot of the experimental data on dielectric loss versus frequency to the formulas derived from the model offers a mathematical basis of the semiempirical equations used in the literature to fit the experimental data. Experimental results of the dielectric loss of neat polar liquid acetone in GHz and THz, as an example, are shown to fit the theory; however, the interaction potential parameter compared to its dilute solution counterpart is significantly increased, reflecting the increase in the dipole–dipole interaction energy.

A class of one-dimensional, discrete-time random walk models with memory, termed “random walk with $n$ memory channels” ($\mathrm{RW}n\mathrm{MC}$), is proposed. In these models the information of $n$ ($n\in \mathbb{Z}$) previous steps from the walker's entire history is needed to decide a future step. Exact calculation of the mean and variance of position of the RW2MC ($n=2$) has been done, which shows that it can lead to asymptotic diffusive and superdiffusive behavior in different parameter regimes. A connection between $\mathrm{RW}n\mathrm{MC}$ and a Pólya-type urn model evolving by drawing $n$ balls at a time has also been reported. This connection for the RW2MC is discussed in detail and suggests the applicability of $\mathrm{RW}2\mathrm{MC}$ in many population dynamics models with multiple competing species.

Neural mass models is a general name for various models describing the collective dynamics of large neural populations in terms of averaged macroscopic variables. Recently, the so-called next-generation neural mass models have attracted a lot of attention due to their ability to account for the degree of synchrony. Being exact in the limit of infinitely large number of neurons, these models provide only an approximate description of finite-size networks. In the present Letter we study finite-size effects in the collective behavior of neural networks and prove that these effects can be captured by appropriately modified neural mass models. Namely, we show that the finite size of the network leads to the emergence of the so-called shot noise appearing as a stochastic term in the neural mass model. The power spectrum of this shot noise contains pronounced peaks, therefore its impact on the collective dynamics might be crucial due to resonance effects.

We introduce a soft fundamental measure theory functional for the purely repulsive Weeks-Chandler-Andersen (WCA) fluid. This classical density functional could serve as a reference fluid for functionals created using thermodynamic perturbation theory instead of the hard-sphere fluid. Our functional incorporates temperature-dependent parameters describing the length scale and effective softness of the particle interaction, and which reproduce the second virial coefficient of the WCA fluid. We find that this approach is comparable in accuracy to the Barker-Henderson approach combined with the White Bear density functional for the hard-sphere fluid.

We employ the second order of the derivative expansion of the nonperturbative renormalization group to study cubic (${\mathbb{Z}}_4$-symmetric) perturbations to the classical $XY$ model in dimensionality $d\in [2,4]$. In $d=3$ we provide accurate estimates of the eigenvalue $y_4$ corresponding to the leading irrelevant perturbation and follow the evolution of the physical picture upon reducing spatial dimensionality from $d=3$ towards $d=2$, where we approximately recover the onset of the Kosterlitz-Thouless physics. We analyze the interplay between the leading irrelevant eigenvalues related to $O\left(2\right)$-symmetric and ${\mathbb{Z}}_4$-symmetric perturbations and their approximate collapse for $d\to 2$. We compare and discuss different implementations of the derivative expansion in cases involving one and two invariants of the corresponding symmetry group.

We report on numerical simulation of fluid interface deformations induced by either acoustic or optical radiation pressure. This is done by solving simultaneously the scalar wave propagation equation and the two-phase flow equations using the boundary element method. Using dimensional analysis, we show that interface deformation morphogenesis is universal, i.e., depends on the same dimensionless parameters in acoustics and electromagnetics. We numerically investigate a few selected phenomena—in particular the shape of large deformations and the slenderness transition and its hysteresis—and compare with existing and novel experimental observations. Qualitative agreement between the numerical simulations and experiments is found when the mutual interaction between wave propagation and wave-induced deformations is taken into account. Our results demonstrate the leading role of the radiation pressure in morphogenesis of fluid interface deformations and the importance of the propagation-deformation interplay.

Within the time-nonlocal quantum master equation description, we develop an efficient method for calculating the noise spectrum of transport current through interacting mesoscopic systems. By introducing proper current-related density operators, we propose a practical and very efficient time-local equation of motion implementation to compute the noise spectrum, which contains the full information of emission and absorption. We obtain an analytical expression to characterize the nonequilibrium transport including Coulomb interaction and memory effect. We demonstrate the proposed method with double quantum dots systems and find good agreement with the exact results, whenever the system-reservoir coupling is smaller than the temperature.

The formation and transition of patterns of two-dimensional turbulent flows observed in various geophysical systems are commonly explained in terms of statistical mechanics. Different from ordinary systems, for a two-dimensional flow, the absolute temperature defined for a statistical equilibrium can take negative values. In a state of negative temperature, the second law of thermodynamics predicts that energy in microscopic fluctuations is irreversibly converted to a macroscopic form. This study explores the possibility of this one-way energy conversion in a two-dimensional flow using a basic conceptual model. We consider an inviscid incompressible fluid contained in a bounded domain, the shape of which is distorted by an externally imposed force. Unlike the usual fixed boundary cases, the flow energy within the domain is exchanged with the external system via pressure work through the moving lateral boundary. Concurrently, the flow field remains constrained by vorticity conservation. Beginning from a state of Kraichnan's grand-canonical ensemble, when the domain shape is distorted from one shape to another in a finite time, the Jarzynski equality is established. This equality states that, on average, the direction of a net energy flow through the boundary during a cycle of domain distortion changes with the sign of the initial temperature of the system. Numerical experiments are carried out to verify this theoretical argument and to investigate the parameter dependence of the energy exchange rate.

We study statistics of occupation times for a fractional Brownian motion (fBm), which is a typical model of a non-Markov process. Due to the non-Markovian nature, recurrence times to the origin depend on the history. Numerical simulations indicate that dependence on the sum of successive recurrence times becomes weak. As a result, the distribution of the occupation time in a finite domain follows the Mittag-Leffler distribution when the Hurst exponent of the fBm is close to 1/2. We show this distributional behavior of a time-averaged observable by renewal theory. This result is an extension of the distributional limit theorem known as the Darling-Kac theorem in general Markov processes to non-Markov processes.

We discuss a model of a closed quantum evolution of two qubits where the joint Hamiltonian is so chosen such that one of the qubits acts as a bath and thermalizes the other qubit which is acting as the system. The corresponding exact master equation for the system is derived. Interestingly, for a specific choice of parameters the master equation takes the Gorini-Kossakowski-Lindblad-Sudarshan (GKLS) form, with constant coefficients representing pumping and damping of a single qubit system. Based on this model we construct an Otto cycle connected to a single qubit bath and study its thermodynamic properties. Our analysis goes beyond the conventional weak coupling scenario and illustrates the effects of finite baths, including non-Markovianity. We find closed form expressions for efficiency (coefficient of performance), power (cooling power) for the heat engine regime (refrigerator regime), and for different modifications of the joint Hamiltonian.

The dynamics across different scales in the stable atmospheric boundary layer has been investigated by means of two metrics, based on instantaneous fractal dimensions and grounded in dynamical systems theory. The wind velocity fluctuations obtained from data collected during the Cooperative Atmosphere-Surface Exchange Study–1999 experiment were analyzed to provide a local (in terms of scales) and an instantaneous (in terms of time) description of the fractal properties and predictability of the system. By analyzing the phase-space projections of the continuous turbulent, intermittent, and radiative regimes, a progressive transformation, characterized by the emergence of multiple low-dimensional clusters embedded in a high-dimensional shell and a two-lobe mirror symmetrical structure of the inverse persistence, have been found. The phase space becomes increasingly complex and anisotropic as the turbulent fluctuations become uncorrelated. The phase space is characterized by a three-dimensional structure for the continuous turbulent samples in a range of scales compatible with the inertial subrange, where the phase-space-filling turbulent fluctuations dominate the dynamics, and is low dimensional in the other regimes. Moreover, lower-dimensional structures present a stronger persistence than the higher-dimensional structures. Eventually, all samples recover a three-dimensional structure and higher persistence level at large scales, far from the inertial subrange. The two metrics obtained in the analysis can be considered as proxies for the decorrelation time and the local anisotropy in the turbulent flow.

Understanding space-charge-limited current density (SCLCD) is fundamentally and practically important for characterizing many high-power and high-current vacuum devices. Despite this, no analytic equations for SCLCD with nonzero monoenergetic initial velocity have been derived for nonplanar diodes from first principles. Obtaining analytic equations for SCLCD for nonplanar geometries is often complicated by the nonlinearity of the problem and over constrained boundary conditions. In this Letter, we use the canonical coordinates obtained by identifying Lie-point symmetries to linearize the governing differential equations to derive SCLCD for any orthogonal diode. Using this method, we derive exact analytic equations for SCLCD with a monoenergetic injection velocity for one-dimensional cylindrical, spherical, tip-to-tip (t-t), and tip-to-plate (t-p) diodes. We specifically demonstrate that the correction factor from zero initial velocity to monoenergetic emission depends only on the initial kinetic and electric potential energies and not on the diode geometry and that SCLCD is universal when plotted as a function of the canonical gap size. We also show that SCLCD for a t-p diode is a factor of four larger than a t-t diode independent of injection velocity. The results reduce to previously derived results for zero initial velocity using variational calculus and conformal mapping.

The entanglement between two weakly coupled bosonic Josephson junctions is studied in relation to the classical mixed phasespace structure of the system, containing symmetry-related regular islands separated by chaos. The symmetry-resolved entanglement spectrum and bipartite entanglement entropy of the system's energy eigenstates are calculated and compared to their expected structure for random states that exhibit complete or partial ergodicity. The entanglement spectra of chaos-supported eigenstates match the microcanonical structure of a Generalized Gibbs Ensemble due to the existence of an adiabatic invariant that restricts ergodization on the energy shell. The symmetry-resolved entanglement entropy of these quasistochastic states consists of a mean-field maximum entanglement term and a fluctuation correction due to the finite size of the constituent subsystems. The total bipartite entanglement entropy of the eigenstates correlates with their chaoticity. Island-supported eigenstates are macroscopic Schrödinger cat states for particles and excitations with substantially lower entanglement.