Related papers: Quantum diffusion for the Anderson model in the sc…

We consider random Schr\"odinger equations on $\bR^d$ for $d\ge 3$ with a homogeneous Anderson-Poisson type random potential. Denote by $\lambda$ the coupling constant and $\psi_t$ the solution with initial data $\psi_0$. The space and time…

We consider random Schr\"odinger equations on $\bR^d$ for $d\ge 3$ with a homogeneous Anderson-Poisson type random potential. Denote by $\lambda$ the coupling constant and $\psi_t$ the solution with initial data $\psi_0$. The space and time…

We consider random Schr\"odinger equations on $\bR^d$ or $\bZ^d$ for $d\ge 3$ with uncorrelated, identically distributed random potential. Denote by $\lambda$ the coupling constant and $\psi_t$ the solution with initial data $\psi_0$.…

We consider the Anderson tight-binding model on $\mathbb{Z}^d$, $d\geq 2$, with Gaussian noise and at low disorder $\lambda>0$. We derive a diffusive scaling limit for the entries of the resolvent $R(z)$ at imaginary part…

We investigate a single particle on a 3-dimensional, cubic lattice with a random on-site potential (3D Anderson model). We concretely address the question whether or not the dynamics of the particle is in full accord with the diffusion…

We consider a point particle moving in a random distribution of obstacles described by a potential barrier. We show that, in a weak-coupling regime, under a diffusion limit suggested by the potential itself, the probability distribution of…

This work is an extended version of the paper arXiv:0803.2669v1[math-ph], in which the main results were announced. We consider certain classical diffusion process for a wave function on the phase space. It is shown that at the time of…

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…

The scaling invariance for chaotic orbits near a transition from unlimited to limited diffusion in a dissipative standard mapping is explained via the analytical solution of the diffusion equation. It gives the probability of observing a…

We give an example of a mathematical model describing quantum mechanical processes interacting with medium. As a model, we consider the process of heat scattering of a wave function defined on the phase space. We consider the case when the…

Diffusive scaling of position moments and a central limit theorem are obtained for the mean position of a quantum particle hopping on a cubic lattice and subject to a random potential consisting of a large static part and a small part that…

We continue our study of the parabolic Anderson equation $\partial u(x,t)/\partial t = \kappa\Delta u(x,t) + \xi(x,t)u(x,t)$, $x\in\Z^d$, $t\geq 0$, where $\kappa \in [0,\infty)$ is the diffusion constant, $\Delta$ is the discrete…

We suggest the diffuse approach to the relaxation processes within the kinetic theory for the Wigner distribution function. The diffusion and drift coefficients are evaluated taking into consideration the interparticle collisions on the…

We investigate quantum persistence by analyzing amplitude and phase fluctuations of the wave function governed by the time-dependent free-particle Schr\"odinger equation. The quantum system is initialized with local random uncorrelated…

We consider a quantum particle coupled (with strength $\la$) to a spatial array of independent non-interacting reservoirs in thermal states (heat baths). Under the assumption that the reservoir correlations decay exponentially in time, we…

We consider the process of diffusion scattering of a wave function given on the phase space. In this process the heat diffusion is considered only along momenta. We write down the modified Kramers equation describing this situation. In this…

This study is concerned with the decay behaviour of a passive scalar $\theta$ in three-dimensional flows having bounded velocity gradients. Given an initially smooth scalar distribution, the decay rate $d<\theta^2>/dt$ of the scalar…

In this paper we introduce a new approach to the diffusive limit of the weakly random Schrodinger equation, first studied by L. Erdos, M. Salmhofer, and H.T. Yau. Our approach is based on a wavepacket decomposition of the evolution…

A diffusion process for charge distributions in a phase space is examined. The corresponding charge moves in a force field and under an action of a random field. There are the diffusion motions for coordinates and for momenta. In our model,…

It is common practice to approximate a weakly nonlinear wave equation through a kinetic transport equation, thus raising the issue of controlling the validity of the kinetic limit for a suitable choice of the random initial data. While for…