Related papers: Predicting Steady States of One-dimensional Collis…
We establish a steady-state theory for nonlinear optical conductivity in pseudo-Hermitian systems. We derive compact formulas for the first and second order conductivity tensors in both the velocity and length gauges and prove their exact…
Understanding relaxation processes is an important unsolved problem in many areas of physics. A key challenge in studying such non-equilibrium dynamics is the scarcity of experimental tools for characterizing their complex transient states.…
Within the C*-algebraic framework of the resolvent algebra for canonical quantum systems, the structure of oscillating lattice systems with bounded nearest neighbor interactions is studied in any number of dimensions. The global dynamics of…
Theory and simulations are used to study collisionless relaxation of a gravitational $N$-body system. It is shown that when the initial one particle distribution function satisfies the virial condition -- potential energy is minus twice the…
The formation and stability of collisionless self-gravitating systems are long standing problems, which date back to the work of D. Lynden-Bell on violent relaxation and extends to the issue of virialization of dark matter (DM) halos. An…
In this paper, we are interested in investigating notions of stability for generalized linear differential equations (GLDEs). Initially, we propose and revisit several definitions of stability and provide a complete characterisation of them…
We analyze the stability under time evolution of complexifier coherent states (CCS) in one-dimensional mechanical systems. A system of coherent states is called stable if it evolves into another coherent state. It turns out that a system…
We review stability and instability results for self-gravitating matter distributions, where the matter model is a collisionless gas as described by the Vlasov equation. The focus is on the general relativistic situation, i.e., on steady…
Many scaling relations are observed for self-gravitating systems in the universe. We explore the consistent understanding of them from a simple principle based on the proposal that the collision-less dark matter fluid terns into a turbulent…
This paper provides a new unified framework for second-moment stability of discrete-time linear systems with stochastic dynamics. Relations of notions of second-moment stability are studied for the systems with general stochastic dynamics,…
In this paper we study the problem of inferring the initial conditions of a dynamical system under incomplete information. Studying several model systems, we infer the latent microstates that best reproduce an observed time series when the…
We study the linearised stability of the nakedly singular negative mass Schwarzschild solution against gravitational perturbations. There is a one parameter family of possible boundary conditions at the singularity. We give a precise…
This paper presents reduction theorems for stability, attractivity, and asymptotic stability of compact subsets of the state space of a hybrid dynamical system. Given two closed sets $\Gamma_1 \subset \Gamma_2 \subset \Re^n$, with…
Traditional centralized stability analysis struggles with scalability in large complex modern power grids. This two-part paper proposes a compositional and equilibrium-free approach to analyzing power system stability. In Part I, we prove…
A theoretical framework is presented which allows to quantitatively predict the final stationary state achieved by a non-neutral plasma during a process of collisionless relaxation. As a specific application, the theory is used to study…
We address nonautonomous initial boundary value problems for decoupled linear first-order one-dimensional hyperbolic systems, investigating the phenomenon of finite time stabilization. We establish sufficient and necessary conditions…
Many models of composite dark matter feature a first-order confinement transition in the early Universe, which would produce a stochastic background of gravitational waves that will be searched for by future gravitational-wave…
One-dimensional self-gravitating systems admit genuine thermodynamical equilibria. For systems with strictly monotonic orbital frequency profile, the Landau and Balescu-Lenard theories predict a relaxation time scaling linearly with the…
Finding the transient and steady state properties of open quantum systems is a central problem in various fields of quantum technologies. Here, we present a quantum-assisted algorithm to determine the steady states of open system dynamics.…
This paper deals with the stabilization of a class of linear infinite-dimensional systems with unbounded control operators and subject to a boundary disturbance. We assume that there exists a linear feedback law that makes the origin of the…