Related papers: Survival amplitude, instantaneous energy and decay…
The XY model with quenched random phase shifts is studied by a T=0 finite size defect energy scaling method in 2d and 3d. The defect energy is defined by a change in the boundary conditions from those compatible with the true ground state…
We study a stochastic system of interacting neurons and its metastable properties. The system consists of $N$ neurons, each spiking randomly with rate depending on its membrane potential. At its spiking time, the neuron potential is reset…
The transformation of canonical decay laws of moving unstable quantum systems is studied by approximating, over intermediate times, the decay laws at rest with superpositions of exponential modes via the Prony analysis. The survival…
Late time properties of moving relativistic particles are studied. Within the proper relativistic treatment of the problem we find decay curves of such particles and we show that late time deviations of the survival probability of these…
We show that a meaningful statistical description is possible in conservative and mixing systems with zero Lyapunov exponent in which the dynamical instability is only linear in time. More specifically, (i) the sensitivity to initial…
A theory of time dependent nonlinear dispersive equations of the Schroedinger / Gross-Pitaevskii and Hartree type is developed. The short, intermediate and large time behavior is found, by deriving nonlinear Master equations (NLME),…
In a system with one conserved charge the charge diffusion is modified by non-linear self-interactions within an effective field theory (EFT) of diffusive fluctuations. We include the slowest ultraviolet (UV) mode, constructing a…
Stretched-exponential relaxation is a widely observed phenomenon found in ordered ferromagnets as well as glassy systems. One modeling approach connects this behavior to a droplet dynamics described by an effective Langevin equation for the…
Decay laws of moving unstable quantum systems with oscillating decay rates are analyzed over intermediate times. The transformations of the decay laws at rest and of the intermediate times at rest, which are induced by the change of…
Critical properties of the dynamical phase transition in the quenched generalized Bose-Anderson impurity model are studied in the mean-field limit of an infinite number of channels. The transition separates the evolution toward ground state…
We provide a scenario for a singularity-mediated turbulence based on the self-focusing non-linear Schr\"odinger equation, for which sufficiently smooth initial states leads to blow-up in finite time. Here, by adding dissipation, these…
We revisit the time-adiabatic theorem of quantum mechanics and show that it can be extended to weakly nonlinear situations, that is to nonlinear Schroedinger equations in which either the nonlinear coupling constant or, equivalently, the…
We study the existence and the rate of equilibration of weak solutions to a two-component system of non-linear diffusion-aggregation equations, with small cross diffusion effects. The aggregation term is assumed to be purely attractive, and…
Recently, Josserand et al. proposed a stochastic nonlinear Schroedinger model for finite-time singularity-mediated turbulence [Phys. Rev. Fluids 5, 054607 (2020)]. Here, we use instanton calculus to quantify the effect of extreme…
The long time behaviour of the survival probability of initial state and its dependence on the initial states are considered, for the one dimensional free quantum particle. We derive the asymptotic expansion of the time evolution operator…
The lifetime of a metastable state in the transient dynamics of an overdamped Brownian particle is analyzed, both in terms of the mean first passage time and by means of the mean growth rate coefficient. Both quantities feature non…
Kinetic equations are often appropriate to model the energy density of high frequency waves propagating in highly heterogeneous media. The limitations of the kinetic model are quantified by the statistical instability of the wave energy…
We consider N strings connected to one another and forming a particular network which is a chain of strings. We study a stabilization problem and precisley we prove that the energy of the solutions of the dissipative system decay…
We consider the problem of energy decay rates for nonlinearly damped abstract infinite dimensional systems. We prove sharp, simple and quasi-optimal energy decay rates through an indirect method, namely a weak observability estimate for the…
This paper establishes the precise asymptotic behavior, as time $t$ tends to infinity, for nontrivial, decaying solutions of genuinely nonlinear systems of ordinary differential equations. The lowest order term in these systems, when the…