Condensed Matter

In this paper we study the critical properties of the non-equilibrium phase transition of the Susceptible-Exposed-Infected model under the effects of long-range correlated time-varying environmental noise on the Bethe lattice. We show that temporal noise is perturbatively relevant changing the universality class from the (mean-field) dynamical percolation to the exotic infinite-noise universality class of the contact process model. Our analytical results are based on a mapping to the one-dimensional fractional Brownian motion with an absorbing wall and is confirmed by Monte Carlo simulations. Unlike the contact process, our theory also predicts that it is quite difficult to observe the associated active temporal Griffiths phase in the long-time limit. Finally, we also show an equivalence between the infinite-noise and the compact directed percolation universality classes by relating the SEI model in the presence of temporal disorder to the Domany-Kinzel cellular automaton in the limit of compact clusters.

We compute the crossover exponents of all quadratic and cubic deformations of critical field theories with permutation symmetry S q in d=6−ϵ (Landau-Potts field theories) and d=4−ϵ (hypertetrahedral models) up to three loops.We use our results to determine the ϵ -expansion of the fractal dimension of critical clusters in the most interesting cases, which include spanning trees and forests ( q→0 ), and bond percolations ( q→1 ). We also explicitly verify several expected degeneracies in the spectrum of relevant operators for natural values of q upon analytic continuation, which are linked to logarithmic corrections of CFT correlators, and use the ϵ -expansion to determine the universal coefficients of such logarithms.

A theoretical framework which unifies the conventional Mori-Zwanzig formalism and the approximate Koopman learning is presented. In this framework, the Mori-Zwanzig formalism, developed in statistical mechanics to tackle the hard problem of construction of reduced-order dynamics for high-dimensional dynamical systems, can be considered as a natural generalization of the Koopman description of the dynamical system. We next show that similar to the approximate Koopman learning methods, data-driven methods can be developed for the Mori-Zwanzig formalism with Mori's linear projection operator. We developed two algorithms to extract the key operators, the Markov and the memory kernel, using time series of a reduced set of observables in a dynamical system. We adopted the Lorenz `96 system as a test problem and solved for the operators, which exhibit complex behaviors which are unlikely to be captured by traditional modeling approaches, in Mori-Zwanzig analysis. The nontrivial Generalized Fluctuation Dissipation relationship, which relates the memory kernel with the two-time correlation statistics of the orthogonal dynamics, was numerically verified as a validation of the solved operators. We present numerical evidence that the Generalized Langevin Equation, a key construct in the Mori-Zwanzig formalism, is more advantageous in predicting the evolution of the reduced set of observables than the conventional approximate Koopman operators.

A quantum description of the surface waves in an isotropic elastic body without the use of the semiclassical quantization is proposed. The problem about the surface waves is formulated in the Lagrangian and Hamiltonian representations. Within the framework of the generalized Debye model, the contribution of the surface phonons (rayleighons) to thermodynamic functions is calculated. It is emphasized that the role of the surface phonons can be significant and even decisive in low-dimensional systems, granular and porous media, and that their contribution to the total heat capacity increases with decreasing temperature.

Symmetries in an open quantum system lead to degenerated Liouvillian that physically implies the existence of multiple steady states. In such cases, obtaining the initial condition independent stead states is highly nontrivial since any linear combination of the \emph{true} asymptotic states, which may not necessarily be a density matrix, is also a valid asymptote for the Liouvillian. Thus, in this work we consider different approaches to obtain the \emph{true} steady states of a degenerated Liouvillian. In the ideal scenario, when the open system symmetry operators are known we show how these can be used to obtain the invariant subspaces of the Liouvillian and hence the steady states. We then discuss two other approaches that do not require any knowledge of the symmetry operators. These could be a powerful tool to deal with quantum many-body complex open systems. The first approach which is based on Gramm-Schmidt orthonormalization of density matrices allows us to obtain \emph{all} the steady states, whereas the second one based on large deviations allows us to obtain the non-degenerated maximum and minimum current-carrying states. We discuss our method with the help of an open para-Benzene ring and examine interesting scenarios such as the dynamical restoration of Hamiltonian symmetries in the long-time limit and apply the method to study the eigenspacing statistics of the nonequilibrium steady state.

The transition from a microscopic model for the movement of many particles to a macroscopic continuum model for a density flow is studied. The microscopic model for the free flow is completely deterministic, described by an interaction potential that leads to a coherent motion where all particles move in the same direction with the same speed known as a flock. Interaction of the flock with boundaries, obstacles and other flocks leads to a temporary destruction of the coherent motion that macroscopically can be modeled through density dependent diffusion. The resulting macroscopic model is an advection-diffusion equation for the particle density whose diffusion coefficient is density dependent. Examples describing i) the interaction of material flow on a conveyor belt with an obstacle that redirects or restricts the material flow and ii) the interaction of flocks (of fish or birds) with boundaries and iii) the scattering of two flocks as they bounce off each other are discussed. In each case, the advection-diffusion equation is strictly hyperbolic before and after the interaction while the interaction phase is described by a parabolic equation. A numerical algorithm to solve the advection-diffusion equation through the transition is presented.

The existence of a constant density of two-level systems (TLS) was proposed as the basis of some intriguing universal aspects of glasses at ultra-low temperatures. Here we ask whether their existence is necessary for explaining the universal density of states quasi-localized modes (QLM) in glasses at ultra-low temperatures. A careful examination of the QLM that exist in a generic atomistic model of a glass former reveals at least two types of them, each exhibiting a different density of states, one depending on the frequency as ? 3 and the other as ? 4 . The properties of the glassy energy landscape that is responsible for the two types of modes is examined here, explaining the analytic feature responsible for the creations of (at least) two families of QLM's. Although adjacent wells certainly exist in the complex energy landscape of glasses, doubt is cast on the relevance of TLS for the universal density of QLM's.

Physical principles for designing artificial materials with energy absorbing and wave guiding properties are discussed in the present work. The idea is to insert light particles in a lattice of elastically coupled potential wells representing soft-wall versions of the so-called stochastic billiards. A planar case of a single potential well attached to the base with a linearly elastic spring and including one or few small particles was considered earlier. Here, we analyze the evolution of waves in a one-dimensional lattice of 3D potential wells with light particles inside. By assigning the initial conditions corresponding to propagating waves we found that the waves can be quickly destroyed by increasing the mass of particles while certain shapes of the potential containers provide a quasi-one-directional energy flow from the chain of containers into the chaotically moving particles by increasing the temperature of the lattice.

We consider point particles in a table made of two circular cavities connected by two rectangular channels, forming a closed loop under periodic boundary conditions. In the first channel, a bounce--back mechanism acts when the number of particles flowing in one direction exceeds a given threshold T . In that case, the particles invert their horizontal velocity, as if colliding with vertical walls. The second channel is divided in two halves parallel to the first, but located in the opposite sides of the cavities. In the second channel, motion is free. We show that, suitably tuning the sizes of cavities, of the channels and of T , non--equilibrium phase transitions take place in the N?��? limit. This induces a stationary current in the circuit, thus modeling a kind of battery, although our model is deterministic, conservative, and time reversal invariant.

In this paper, we analyze the mean first passage time (MFPT) for a single Brownian particle to find a stochastically-gated target under the additional condition that the position of the particle is reset to a fixed position $\x_r$ at a rate r . The gate switches between an open and closed state according to a two-state Markov chain and can only be detected by the searcher in the open state. One possible example of such a target is a protein switching between different conformational states. As expected, the MFPT with or without resetting is an increasing function of the fraction of time ρ 0 that the gate is closed. However, the interplay between stochastic resetting and stochastic gating has non-trivial effects with regards the optimization of the search process under resetting. First, by considering the diffusive search for a gated target at one end of an interval, we show that the fractional change in the MFPT under resetting exhibits a non-monotonic dependence on ρ 0 . In particular, the percentage reduction of the MFPT at the optimal resetting rate (when it exists) increases with ρ 0 up to some critical value, after which it decreases and eventually vanishes. Second, in the case of a spherical target in $\R^d$, the dependence of the MFPT on the spatial dimension d is significantly amplified in the presence of stochastic gating.