Related papers: Sufficient conditions for superstability of many-b…

When a system has more than one stable state, how can the stability of these states be compared? This deceptively simple question has important consequences for ecosystems, because systems with alternative stable states can undergo dramatic…

We examine the conditions that give rise to metastable, persistent currents in a trapped Bose-Einstein condensate. A necessary condition for the stability of persistent currents is that the trapping potential is not a monotonically…

Driven systems offer the potential to realize a wide range of non-equilibrium phenomena that are inaccessible in static systems, such as the discrete time crystals. Time rondeau crystals with a partial temporal order have been proposed as a…

Limit theorems for a linear dynamical system with random interactions are established. These theorems enable us to characterize the dynamics of a large complex system in details and assess whether a large complex system is stable or…

Understanding how a quantum many-body state is maintained stably as a nonequilibrium steady state is of fundamental and practical importance for exploration and exploitation of open quantum systems. We establish a general equivalent…

Our recent interest is focused on establishing the necessary and sufficient conditions that guarantee a long-term stable evolution of both natural and artificial systems. Two necessary conditions, called global and local boundedness, are…

An approach to analyse the properties of a particle system is to compare it with different processes to understand when one of them is larger than other ones. The main technique for that is coupling, which may not be easy to construct. We…

In the present work we suggest a general covariant theory which can be used to study the stability of any physical system treated geometrically. Stability conditions are connected to the magnitude of the deviation vector. This theory is a…

Statistical mechanics is founded on the assumption that a system can reach thermal equilibrium, regardless of the starting state. Interactions between particles facilitate thermalization, but, can interacting systems always equilibrate…

Superfluidity in atomic Fermi gases with population imbalance has recently become an exciting research focus. There is considerable disagreement in the literature about the appropriate stability conditions for states in the phase diagram…

In this talk I will introduce the principle of stochastic stability and discussing its consequences both at equilibrium and off-equilibrium.

A well known result states that stability criterion for matchings in two-sided markets doesn't ensure uniqueness. This opens the door for a moral question with regard to the optimal stable matching from a social point of view. Here, a new…

In the stable marriage problem N men and N women have to be matched by pairs under the constraint that the resulting matching is stable. We study the statistical properties of stable matchings in the large N limit using both numerical and…

Stability is among the most important concepts in dynamical systems. Local stability is well-studied, whereas determining how "globally stable" a nonlinear system is very challenging. Over the last few decades, many different ideas have…

We consider isolated many-body quantum systems which do not thermalize, i.e., expectation values approach an (approximately) steady longtime limit which disagrees with the microcanonical prediction of equilibrium statistical mechanics. A…

Lack of knowledge about the detailed many-particle motion on the microscopic scale is a key issue in any theoretical description of a macroscopic experiment. For systems at or close to thermal equilibrium, statistical mechanics provides a…

Stability and causality are studied for linear perturbations about equilibrium in Carter's multifluid theory. Our stability analysis is grounded on the requirement that the entropy of the multifluid, plus that of the environment, must be…

A nonlinear stochastic differential equation with the order of nonlinearity higher than one, with several discrete and distributed delays and time varying coefficients is considered. It is shown that the sufficient conditions for…

Many dynamical systems arising in biology and other areas exhibit multistationarity (two or more positive steady states with the same conserved quantities). Although deciding multistationarity for a polynomial dynamical system is an…

Group behavior has received much attention as a test case of self-organization. There has been much written in recent years to investigate interactions within groups of agents. These agents can be animals moving in an interactive way, such…