Related papers: Sufficient conditions for superstability of many-b…
Integrable models form pillars of theoretical physics because they allow for full analytical understanding. Despite being rare, many realistic systems can be described by models that are close to integrable. Therefore, an important question…
A class of generalized definitions of expectation value is often employed in nonequilibrium statistical mechanics for complex systems. Here, the necessary and sufficient condition is presented for such a class to be stable under small…
In this paper we establish a necessary and sufficient stability condition for a stochastic ring network. Such networks naturally appear in a variety of applications within communication, computer, and road traffic systems. They typically…
We prove that for a wide family of non-uniformly hyperbolic maps and hyperbolic potentials we have equilibrium stability, i.e. the equilibrium states depend continuously on the dynamics and the potential. For this we deduce that the…
This article aims to investigate sufficient conditions for the stability of stochastic differential equations with a random structure, particularly in contexts involving the presence of concentration points. The proof of asymptotic…
In this paper we focus on providing sufficient conditions for some well-known stochastic orders in reliability but dealing with the discrete versions of them, filling a gap in the literature. In particular, we find conditions based on the…
We here describe the possibility of a synthetic description of the onset of Chaos in many degrees of freedom dynamical systems within the framework of the geometric description of dynamics. We show how this approach to instability helps to…
Sufficient conditions for the controllability of a conservative reduced system are given. Several examples illustrating the theory are also presented.
The exact equations of motion for microscopic density of classical many-body system with account of inter-particle retarded interactions are derived. It is shown that interactions retardation leads to irreversible behaviour of many-body…
We provide a class of inequalities for detecting entanglements in multi-mode systems. Necessary conditions for fully separable, bi-separable and sufficient conditions for fully entangled states are explicitly presented.
Linear systems governed by continuous-time difference equations cover a wide class of linear systems. From the Lyapunov-Krasovskii approach, we investigate stability for such a class of systems. Sufficient conditions, and in some particular…
We show how the stability conditions for a system of interacting fermions that conventionally involve variations of thermodynamic potentials can be rewritten in terms of one- and two-particle correlators. We illustrate the applicability of…
Recent theoretical and numerical evidence suggests that localization can survive in disordered many-body systems with very high energy density, provided that interactions are sufficiently weak. Stronger interactions can destroy…
For a quantum system to be captured by a stationary statistical ensemble, as is common in thermodynamics and statistical mechanics, it is necessary that it reaches some apparently stationary state in the first place. In this book chapter,…
Systems of strongly interacting dipoles offer an attractive platform to study many-body localized phases, owing to their long coherence times and strong interactions. We explore conditions under which such localized phases persist in the…
We summarize recent progress on one- and multi-dimensional stability of viscous shock wave solutions of compressible Navier--Stokes equations and related symmetrizable hyperbolic--parabolic systems, with an emphasis on the large-amplitude…
Superconductor stability is at the core of the design of any successful cable and magnet application. This chapter reviews the initial understanding of the stability mechanism, and reviews matters of importance for stability such as the…
Weak attractive interactions in a spin-imbalanced Fermi gas induce a multi-particle instability, binding multiple fermions together. The maximum binding energy per particle is achieved when the ratio of the number of up- and down-spin…
Superstatistics is a widely employed tool of non-equilibrium statistical physics which plays an important role in analysis of hierarchical complex dynamical systems. Yet, its "canonical" formulation in terms of a single nuisance parameter…
We illustrate a theoretical procedure determining necessary conditions for which simultaneous pure rolling kinetic constraints acting on a mechanical system can be fulfilled. We also analyze the sufficiency of these conditions by…