Related papers: Analytical Treatment of Stabilization
By developing a semi-classical analysis based on the Eigenstate Thermalization Hypothesis, we determine the long time behavior of a large spin evolving with a nonlinear Hamiltonian. Despite integrable classical dynamics, we find the…
We consider the systematic force on a heavy probe induced by interaction with an overdamped diffusive medium where particles undergo a rotating force around a fixed center. The stiffness matrix summarizes the stability of the probe around…
We study the stability of the circular orbits of the electromagnetic two-body problem of classical electrodynamics. We introduce the concept of resonant dissipation, i.e. a motion that radiates the center-of-mass energy while the…
We introduce a novel method to investigate the stability of wave packet dynamics under perturbations of the Hamiltonian. Our approach relies on semiclassical approximations, but is non-perturbative. Two separate contributions to the quantum…
The effect of multiplicative stochastic perturbations on Hamiltonian systems on the plane is investigated. It is assumed that perturbations fade with time and preserve a stable equilibrium of the limiting system. The paper investigates…
In this article, we prove the exponential stabilization of the semilinear wave equation with a damping effective in a zone satisfying the geometric control condition only. The nonlinearity is assumed to be subcritical, defocusing and…
Very recently we present a theory to discuss the nature of light and show that the quantization of light energy in vacuum can be derived directly from classical electromagnetic theory. In the theory a key concept of stability of statistical…
This paper provides two results that are useful in the study of the existence and the stability properties of a periodic solution for a given dynamical system. The first result deals with scalar time-periodic systems and establishes the…
The problem of the dynamical stability of anistropic systems is studied, by proposing a criterion in terms of the adiabatic local index $\gamma$. The result has general validity and can be applied to several physical situations.…
This paper studies the stabilization for a kind of linear and impulse control systems in finite-dimensional spaces, where impulse instants appear periodically. We present several characterizations on the stabilization; show how to design…
This thesis develops exact analytical tools to study strongly correlated stochastic systems, with a focus on extreme value statistics, gap statistics, and full counting statistics in multi-particle processes. A central contribution is the…
The stability of matter composed of electrons and static nuclei is investigated for a relativistic dynamics for the electrons given by a suitably projected Dirac operator and with Coulomb interactions. In addition there is an arbitrary…
We study a two-state quantum system with a non linearity intended to describe interactions with a complex environment, arising through a non local coupling term. We study the stability of particular solutions, obtained as constrained…
The stability features of steady states of the spherically symmetric Einstein-Vlasov system are investigated numerically. We find support for the conjecture by Zeldovich and Novikov that the binding energy maximum along a steady state…
We establish the conditioned stochastic stability of equilibrium states for H\"older potentials on uniformly hyperbolic sets. While standard stochastic stability characterises measures on attractors, we analyse the statistics of transient…
We study stability and bifurcations in holomorphic families of polynomial automorphisms of C^2. We say that such a family is weakly stable over some parameter domain if periodic orbits do not bifurcate there. We first show that this defines…
In a previous paper a formalism to analyze the dynamical evolution of classical and quantum probability distributions in terms of their moments was presented. Here the application of this formalism to the system of a particle moving on a…
Necessary conditions for asymptotic stability and stabilizability of subsets for dynamical and control systems are obtained. The main necessary condition is homotopical and is in turn used to obtain a homological one. A certain extension is…
No quantum measurement can give full information on the state of a quantum system; hence any quantum feedback control problem is neccessarily one with partial observations, and can generally be converted into a completely observed control…
We establish an analytical criterion for dynamical thermalization within harmonic systems, applicable to both classical and quantum models. Specifically, we prove that thermalization of various observables, such as particle energies in…