Related papers: A stable quantum Darmois-Skitovich theorem
The paper is concerned with asymptotic stability properties of linear switched systems. Under the hypothesis that all the subsystems share a non strict quadratic Lyapunov function, we provide a large class of switching signals for which a…
We consider the simplest bosonic-type S-matrix which is usually regarded as unphysical due to the complex values of the finite volume ground state energy. While a standard quantum field theory interpretation of such a scattering theory is…
The analysis of the stability of systems' equilibria plays a central role in the study of dynamical systems and control theory. This note establishes an extension of the celebrated Krasovski\u{\i} stability theorem for functional…
This work studies the instability of stochastic scalar reaction diffusion equations, driven by a multiplicative noise that is white in time and smooth in space, near to zero, which is assumed to be a fixed point for the equation. We prove…
the stability criterion is constructed for open quantum systems which govern by quantum stochastic differential equations (QSDE) both for quantum observable flow and the stochastic density operator. We derive stability criteria (local,…
Asymptotic stability of small solitons in one dimension is proved in the framework of a discrete nonlinear Schrodinger equation with septic and higher power-law nonlinearities and an external potential supporting a simple isolated…
We give a formula of the Donaldson-Futaki invariants for certain type of semi test configurations, which essentially generalizes Ross-Thomas' slope theory. The positivity (resp. non-negativity) of those "a priori special" Donaldson-Futaki…
We study the stability/instability of the subsonic travelling waves of the Nonlinear Schr\"odinger Equation in dimension one. Our aim is to propose several methods for showing instability (use of the Grillakis-Shatah-Strauss theory, proof…
We establish a theorem concerning the normal forms by examining the newly presented concept of $\mu$-dichotomy. This work establishes the nonresonance condition based on the associated spectrum of this general nonautonomous hyperbolicity.
In this article we consider a damped version of the incompressible Navier-Stokes equations in the whole three-dimensional space with a divergence-free and time-independent external force. Within the framework of a well-prepared force and…
This work is concerned with the stable norm in word hyperbolic groups as defined by Gromov. We give a short elementary proof of one of its basic property, that is existence of a computable uniform non null lower bound for stable norm in a…
We propose a quantitative direct method to prove the local stability of a stationary solution for a rough differential equation and its regular discretization scheme. Using Doss-Sussmann technique and stopping time analysis, we provide…
The stability properties of the Einstein Static solution of General Relativity are altered when corrective terms arising from modification of the underlying gravitational theory appear in the cosmological equations. In this paper the…
By using the Wigner transform, it is shown that the nonlinear Schr$\ddot{\textmd{o}}$dinger equation can be described, in phase space, by a kinetic theory similar to the Vlasov equation which is used for describing a classical collisionless…
We consider the nonlinear Schr\"odinger equations with a potential on $\mathbb T^d$. For almost all potentials, we show the almost global stability in very high Sobolev norms. We apply an iteration of the Birkhoff normal form, as in the…
Involvement of the environment is indispensable for establishing the statistical distribution of system. We analyze the statistical distribution of a quantum system coupled strongly with a heat bath. This distribution is determined by…
In this paper, we investigate the stochastic damped Burgers equation with multiplicative noise defined on the entire real line. We demonstrate the existence and uniqueness of a mild solution to the stochastic damped Burgers equation and…
Steady-state manifolds of open quantum systems, such as decoherence-free subspaces and noiseless subsystems, are of great practical importance to the end of quantum information processing. Yet, it is a difficult problem to find steady-state…
The current series of papers is concerned with stochastic stability of monotone dynamical systems by identifying the basic dynamical units that can survive in the presence of noise interference. In the first of the series, for the…
This paper deals with stability of discrete-time switched linear systems whose all subsystems are unstable. We present sufficient conditions on the subsystems matrices such that a switched system is globally exponentially stable under a set…