Related papers: Decay Rates and Survival Probabilities in Open Qua…
The local persistence R(t), defined as the proportion of the system still in its initial state at time t, is measured for the Bak--Sneppen model. For 1 and 2 dimensions, it is found that the decay of R(t) depends on one of two classes of…
We study the destruction of dynamical localization, experimentally observed in an atomic realization of the kicked rotor, by a deterministic Hamiltonian perturbation, with a temporal periodicity incommensurate with the principal driving. We…
We study spectral properties of ergodic random Schr\"odinger operators on $L^2 (\RR^d)$. The density of states is shown to exist for a certain class of alloy type potentials with single site potentials of changing sign. The Wegner estimate…
We propose a simplified version of the Multi-Scale Analysis of tight-binding Anderson models with strongly mixing random potentials which leads directly to uniform exponential bounds on decay of eigenfunctions in arbitrarily large finite…
As was recently shown in Ref. 1, many eigenstates of a random Rydberg gas with resonant dipole-dipole interactions are highly delocalized. Although the high degree of delocalization is generic to various types of power-law interactions and…
We argue that the dynamics of particle imbalance in quadratic fermionic models is, for the majority of initial many-body product states in site occupation basis, virtually indistinguishable from the dynamics of survival probabilities of…
For a class of linear switched systems in continuous time a controllability condition implies that state feedbacks allow to achieve almost sure stabilization with arbitrary exponential decay rates. This is based on the Multiplicative…
We consider one-dimensional discrete Dirac models in vanishing random environments. In a previous work [6], we showed that these models exhibit a rich phase diagram in terms of their spectrum as a function of the rate of decay of the random…
In this paper we discuss quantitative (pointwise) decay estimates for solutions to the 3D cubic defocusing Nonlinear Schr\"odinger equation with various initial data, deterministic and random. We show that nonlinear solutions enjoy the same…
The description of an open quantum system's decay almost always requires several approximations as to remain tractable. Here, we first revisit the meaning, domain and seeming contradictions of a few of the most widely used of such…
We study the time dependence of the ionization probability of Rydberg atoms driven by a microwave field. The quantum survival probability follows the classical one up to the Heisenberg time and then decays inversely proportional to time,…
Motivated by current interest in disordered systems of interacting electrons, the effectiveness of the geometrically averaged density of states, $\rho_g(\omega)$, as an order parameter for the Anderson transition is examined. In the context…
We consider one dimensional random walks in random environment where every time the process stays at a location, it dies with a fixed probability. Under some mild assumptions it is easy to show that the survival probability goes to zero as…
Measurements of the loss rates for strontium n$^{3}$S$_{1}$ Rydberg atoms excited in a dense BEC are presented for values of principal quantum number $n$ in the range $49\lesssim n \lesssim 150$ and local atom densities of $\sim1$ to…
In this paper we consider the Anderson model with decaying randomness and show that statistics near the band edges in the absolutely continuous spectrum in dimensions $d \geq 3$ is independent of the randomness and agrees with that of the…
We investigate the probable delocalization-localization transition in open quantum systems with disorder. The disorder can induce localization in isolated quantum systems and it is generally recognized that localization is fragile under the…
We investigate light transport in three-dimensional disordered media composed of irregular dielectric particles using large scale full-wave simulations. For subwavelength particles with size parameter $kr \approx 1$ and high refractive…
The short-time behavior of quantum decay of an unstable state initially located within an interaction region of finite range is investigated using a resonant expansion of the survival amplitude. It is shown that in general the short-time…
We present two novel approaches to establish the local density of states as an order parameter field for the Anderson transition problem. We first demonstrate for 2D quantum Hall systems the validity of conformal scaling relations which are…
In an isolated single-particle quantum system a spatial disorder can induce Anderson localization. Being a result of interference, this phenomenon is expected to be fragile in the face of dissipation. Here we show that dissipation can drive…