相关论文: Dynamical upper bounds on wavepacket spreading

We develop the wave packet decomposition to study the Schrodinger evolution with rough potential. As an application, we obtain the improved bound on the wave propagation for the generic value of a parameter.

Constraints can affect dramatically the behavior of diffusion processes. Recently, we analyzed a natural and a technological system and reported that they perform diffusion-like discrete steps displaying a peculiar constraint, whereby the…

The Lieb-Robinson bound sets a theoretical upper limit on the speed at which information can propagate in non-relativistic quantum spin networks. In its original version, it results in an exponentially exploding function of the evolution…

The proper time of an observer can be introduced as a degree of freedom in quantum cosmology, additional to the existing fields. We review two arguments for using the Schr\"odinger equation to evolve the corresponding wavefunction. We…

This thesis deals with some theoretical aspects of deterministic freak wave generation in the wave basin of a hydrodynamic laboratory. We adopt the spatial nonlinear Schr\"odinger equation as a mathematical model to describe the deformation…

In Euclidean space there is a trivial upper bound on the maximum length of a compound "walk" built up of variable-length jumps, and a considerably less trivial lower bound on its minimum length. The existence of this non-trivial lower bound…

For "static memory materials" the bulk properties depend on boundary conditions. Such materials can be realized by classical statistical systems which admit no unique equilibrium state. We describe the propagation of information from the…

The aim of this paper is to study the semi-classical behaviour of Schr\"odinger's dynamics for an one-dimesional quantum Hamiltonian with a classical hyperbolic trajectory. As in the regular case (elliptic trajectory), we prove, that for an…

We prove a maximal velocity bound for the dynamics of Markovian open quantum systems. The dynamics are described by one-parameter semi-groups of quantum channels satisfying the von Neumann-Lindblad equation. Our result says that dynamically…

The upper bounds for the rate of fluctuation growth of an observable in both open and closed quantum systems have been studied actively recently. In our recent work we showed that the rate of fluctuation growth for an observable in a closed…

We consider the evolution of a quantum particle hopping on a cubic lattice in any dimension and subject to a potential consisting of a periodic part and a random part that fluctuates stochastically in time. If the random potential evolves…

We present a rigorous study of quantum diffusion of a relativistic particle subjected to a time-dependent random potential with $\delta$ correlation in time. We find that in the asymptotic time limit the particle wave packet spreads…

We study a special kind of semiclassical limit of quantum dynamics on a circle and in a box (infinite potential well with hard walls) as the Planck constant tends to zero and time tends to infinity. The results give detailed information…

We analyze the matter wave transmission above a step potential within the framework of the cubic-nonlinear Schr\"odinger equation. We present a comprehensive analysis of the corresponding stationary problem based on an exact second-order…

We review some recent results obtained for the time evolution of wave packets for systems of equations of pseudo-differential type, including Schr{\"o}dinger ones, and discuss their application to the approximation of the associated unitary…

In this paper, we report results for the wave packet dynamics in a class of quasiperiodic chains consisting of two types of weakly coupled clusters. The dynamics are studied by means of the return probability and the mean square…

Existing models for droplet impact prescribe the spreading contact time and effective spreading velocity from asymptotic arguments, which prevents a self-consistent prediction of the maximum spreading ratio across regimes. Here, the total…

Asymptotic time evolution of a wave packet describing a non-relativistic particle incident on a potential barrier is considered, using the Wigner phase-space distribution. The distortion of the trasmitted wave packet is determined by two…

In this paper, we study the propagation of wave packets close to conical intersections with respect to a system of two Schr{\"o}dinger equations presenting a codimension 2 crossing. We focus on the dynamics that occur when the wave packets…

We study the properties of wave functions and the wave-packet dynamics in quasiperiodic tight-binding models in one, two, and three dimensions. The atoms in the one-dimensional quasiperiodic chains are coupled by weak and strong bonds…