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We consider a recently introduced generalization of the Ising model in which individual spin strength can vary. The model is intended for analysis of ordering in systems comprising agents which, although matching in their binarity (i.e.,…
The nature of extended states in disordered tight binding models with a constant imaginary vector potential is explored. Such models, relevant to vortex physics in superconductors and to population biology, exhibit a delocalization…
In the study of closed many-body quantum systems one is often interested in the evolution of a subset of degrees of freedom. On many occasions it is possible to approach the problem by performing an appropriate decomposition into a bath and…
We consider the time evolution of entanglement in a finite two dimensional transverse Ising model. The model consists of a set of 7 localized spin-1/2 particles in a two dimensional triangular lattice coupled through nearest neighbor…
Synchronization over networks depends strongly on the structure of the coupling between the oscillators. When the coupling presents certain regularities, the dynamics can be coarse-grained into clusters by means of External Equitable…
We show that, for generative classifiers, conditional independence corresponds to linear constraints for the induced discrimination functions. Discrimination functions of undirected Markov network classifiers can thus be characterized by…
In a quantum many-body system, autocorrelation functions can determine linear responses nearby equilibrium and quantum dynamics far from equilibrium. In this letter, we bring out the connection between the operator complexity and the…
This paper is concerned with the spectral properties of matrices associated with linear filters for the estimation of the underlying trend of a time series. The interest lies in the fact that the eigenvectors can be interpreted as the…
The Ising model, in presence of an external magnetic field, is isomorphic to a model of localized interacting particles satisfying the Fermi statistics. By using this isomorphism, we construct a general solution of the Ising model which…
We study growth lemmas and questions of regularity for generators of Markov processes. The generators are allowed to have an arbitrary order of differentiability less than 2. In general, this order is represented by a function and not by a…
In this paper we consider the one dimensional spring-block model describing earthquake faulting. By using geometric singular perturbation theory and the blow-up method we provide a detailed description of the periodicity of the earthquake…
We construct a solvable spin chain model of many-body localization (MBL) with a tunable mobility edge. This simple model not only demonstrates analytically the existence of mobility edges in interacting one-dimensional (1D) disordered…
We prove two results on the mixing times of Markov chains for two-spin systems. First, we show that the Glauber dynamics mixes in polynomial time for the Gibbs distributions of antiferromagnetic two-spin systems at the critical threshold of…
Autonomous oscillations in biological systems may have a biochemical origin or result from an interplay between force-generating and visco-elastic elements. In molecular motor assemblies the force-generating elements are molecular engines…
We study topological properties of phase transition points of one-dimensional topological quantum phase transitions by assigning winding numbers defined on closed circles around the gap closing points in the parameter space of momentum and…
A multistable system generated by a Piecewise Linear (PWL) system based on the jerky equation is presented. The systems behaviour is characterised by means of the Nearest Integer or round(x) function to control the switching events and to…
We construct new solvable rational and trigonometric spin models with near-neighbors interactions by an extension of the Dunkl operator formalism. In the trigonometric case we obtain a finite number of energy levels in the center of mass…
The intensity distribution of electromagnetic polar waves in a chain of near-resonant weakly-coupled scatterers is investigated theoretically and supported by a numerical analysis. Critical scaling behavior is discovered for part of the…
This work provides a comprehensive numerical characterization of the excited spherically symmetric stationary states of the Schr\"odinger-Poisson problem. Through numerical computation of highly excited eigenstates, novel heuristic laws are…
Many-body localized (MBL) systems lie outside the framework of statistical mechanics, as they fail to equilibrate under their own quantum dynamics. Even basic features of MBL systems such as their stability to thermal inclusions and the…