Condensed Matter

In the present study, the information entropy for smoluchowski coagulation equation is proposed based on the statistical physics. and the normalized particle size distribution is a log-normal function at equilibrium from the principle of maximum entropy and moment constraint. the parameters in the particle size distribution are determined as simple constants, the result reveals that the assumption that algebraic mean volume be unit in self-preserving hypothesis is reasonable. based on the present definition of the information entropy, the cercignani conjecture holds naturally for smoluchowski coagulation equation. Together with the fact that the conjecture is also true for Boltzmann equation, cercignani conjecture holds for any two-body collision systems, which will benefit the understanding of Brownian motion and molecule kinematic theory, such as the stability of the dissipative system, and the mathematical theory of convergence to thermodynamic equilibrium.

The hyperuniformity concept provides a unified means to classify all perfect crystals, perfect quasicrystals, and exotic amorphous states of matter according to their capacity to suppress large-scale density fluctuations. While the classification of hyperuniform point configurations has received considerable attention, much less is known about the classification of hyperuniform heterogeneous two-phase media, which include composites, porous media, foams, cellular solids, colloidal suspensions and polymer blends. The purpose of this article is to begin such a program for certain two-dimensional models of hyperuniform two-phase media by ascertaining their local volume-fraction variances σ 2 V (R) and the associated hyperuniformity order metrics B ¯ ¯ ¯ ¯ V . This is a highly challenging task because the geometries and topologies of the phases are generally much richer and more complex than point-configuration arrangements and one must ascertain a broadly applicable length scale to make key quantities dimensionless. Therefore, we focus on a certain class of two-dimensional periodic cellular networks, periodic and disordered/irregular packings, some of which maximize their effective transport and elastic properties. Among the cellular networks considered, the honeycomb networks have a minimal value of B ¯ ¯ ¯ ¯ V across all volume fractions. On the other hand, among all packings considered, the triangular-lattice packings have the smallest values of B ¯ ¯ ¯ ¯ V for the possible range of volume fractions. Among all structures studied here, the triangular-lattice packing has the minimal order metric for almost all volume fractions. Our study provides a theoretical foundation for the establishment of hyperuniformity order metrics for general two-phase media and a basis to discover new hyperuniform two-phase systems by inverse design procedures.

Seemingly different interpretations or descriptions of Einstein's model for the heat capacity of a solid can be found in textbooks and the literature. The purpose of this note is to clarify the equivalence of the different descriptions, which all lead to the same Einstein expression for the heat capacity of a solid of N atoms.

Classification of the non-equilibrium quantum many-body dynamics is a challenging problem in condensed matter physics and statistical mechanics. In this work, we study the basic question that whether a (1+1) dimensional conformal field theory (CFT) is stable or not under a periodic driving with N non-commuting Hamiltonians. Previous works showed that a Floquet (or periodically driven) CFT driven by certain S L 2 deformed Hamiltonians exhibit both non-heating (stable) and heating (unstable) phases. In this work, we show that the phase diagram depends on the types of driving Hamiltonians. In general, the heating phase is generic, but the non-heating phase may be absent in the phase diagram. For the existence of the non-heating phases, we give sufficient and necessary conditions for N=2 , and sufficient conditions for N>2 . These conditions are composed of N layers of data, with each layer determined by the types of driving Hamiltonians. Our results also apply to the single quantum quench problem with N=1 .

The study of entanglement spectra is a powerful tool to detect or elucidate universal behaviour in quantum many-body systems. We investigate the scaling of the entanglement (or Schmidt) gap δξ , i.e., the lowest laying gap of the entanglement spectrum, at a two-dimensional quantum critical point. We focus on the paradigmatic quantum spherical model, which exhibits a second-order transition, and is mappable to free bosons with an additional external constraint. We analytically show that the Schmidt gap vanishes at the critical point, although only logarithmically. For a system on a torus and the half-system bipartition, the entanglement gap vanishes as π 2 /ln(L) , with L the linear system size. The entanglement gap is nonzero in the paramagnetic phase and exhibits a faster decay in the ordered phase. The rescaled gap δξln(L) exhibits a crossing for different system sizes at the transition, although logarithmic corrections prevent a precise verification of the finite-size scaling. Interestingly, the change of the entanglement gap across the phase diagram is reflected in the zero-mode eigenvector of the spin-spin correlator. At the transition quantum fluctuations give rise to a non-trivial structure of the eigenvector, whereas in the ordered phase it is flat. We also show that the vanishing of the entanglement gap at criticality can be qualitatively but not quantitatively captured by neglecting the structure of the zero-mode eigenvector.

We study the kinetics after a low temperature quench of the one-dimensional Ising model with long range interactions between spins at distance r decaying as r ?��?. For α=0 , i.e. mean field, all spins evolve coherently quickly driving the system towards a magnetised state. In the weak long range regime with α>1 there is a coarsening behaviour with competing domains of opposite sign without development of magnetisation. For strong long range, i.e. 0<α<1 , we show that the system shows both features, with probability P α (N) of having the latter one, with the different limiting behaviours lim N?��? P α (N)=0 (at fixed α<1 ) and lim α?? P α (N)=1 (at fixed finite N ). We discuss how this behaviour is a manifestation of an underlying dynamical scaling symmetry due to the presence of a single characteristic time ? α (N)??N α .

We analyse collective motion that occurs during rare (large deviation) events in systems of active particles, both numerically and analytically. We discuss the associated dynamical phase transition to collective motion, which occurs when the active work is biased towards larger values, and is associated with alignment of particles' orientations. A finite biasing field is needed to induce spontaneous symmetry breaking, even in large systems. Particle alignment is computed exactly for a system of two particles. For many-particle systems, we analyse the symmetry breaking by an optimal-control representation of the biased dynamics, and we propose a fluctuating hydrodynamic theory that captures the emergence of polar order in the biased state.

We report on novel Brownian, yet non-Gaussian diffusion, in which the mean square displacement of the particle grows linearly with time, the probability density for the particle spreading is Gaussian-like, however, the probability density for its position increments possesses an exponentially decaying tail. In contrast to recent works in this area, this behaviour is not a consequence of either a space or time-dependent diffusivity, but is induced by external non-thermal noise acting on the particle dwelling in a periodic potential. The existence of the exponential tail in the increment statistics leads to colossal enhancement of diffusion, surpassing drastically the previously researched situation known under the label of "giant" diffusion. This colossal diffusion enhancement crucially impacts a broad spectrum of the first arrival problems, such as diffusion limited reactions governing transport in living cells.

In a recent paper by B. G. da Costa {\it et al.} [Phys. Rev. E 102, 062105(2020)], the phenomenological Langevin equation and the corresponding Fokker-Planck equation for an inhomogeneous medium with a position-dependent particle mass and position-dependent damping coefficient have been studied. The aim of this comment is to present a microscopic derivation of the Langevin equation for such a system. It is not equivalent to that in the commented paper.

The critical behavior of a hybrid spin-electron model with localized Ising spins placed on nodal sites and mobile electrons delocalized over bonds between two nodal lattice sites is analyzed by the use of a generalized decoration-iteration transformation. Our attention is primarily concentrated on a rigorous analysis of a critical temperature in canonical and grand-canonical statistical ensemble at two particular electron concentrations, corresponding to a quarter ( ρ=1 ) and a half ( ρ=2 ) filled case. It is found that the critical temperature of the investigated spin-electron system in the canonical and grand-canonical ensemble may be remarkably different and is very sensitive to the competition among the model parameters like the electron hopping amplitude ( t ), the Ising coupling between the localized spins ( J ′ ), the electrostatic potential ( V ) and the electron concentration ( ρ ). In addition, it is detected that the increasing electrostatic potential has a reduction effect upon the deviation between critical temperatures in both statistical ensembles.