Related papers: The third moment for the parabolic Anderson model
We study the quantum phase diagram of a three dimensional non-interacting Dirac semimetal in the presence of either quenched axial or scalar potential disorder, by calculating the average and the typical density of states as well as the…
We present the formulation of non relativistic quantum mechanics in the extended space (u,x,t) where x and t are coordinates of particles and time, and u - an additional real parameter that corresponds to generalized virial - an integral…
From transfer-matrix calculation of localization lengths and their finite-size scaling analyses, we evaluate critical exponents of the Anderson metal-insulator transition in three dimensional (3D) orthogonal class with particle-hole…
We develop a cluster dynamical mean field theory of the periodic Anderson model in three dimensions, taking a cluster of two sites as a basic reference frame. The mean field theory displays the basic features of the Doniach phase diagram: a…
We analyze numerically a forward-backward diffusion equation with a cubic-like diffusion function, -emerging in the framework of phase transitions modeling- and its "entropy" formulation determined by considering it as the singular limit of…
We derive exact asymptotics of time correlation functions for the parabolic Anderson model with homogeneous initial condition and time-independent tails that decay more slowly than those of a double exponential distribution and have a…
A boundary value problem related to a third- order parabolic equation with a small parameter is analized. This equation models the one-dimensional evolution of many dissipative media as viscoelastic fluids or solids, viscous gases,…
We consider nonlinear parabolic stochastic PDEs on a bounded Lipschitz domain driven by a Gaussian noise that is white in time and colored in space, with Dirichlet or Neumann boundary condition. We establish existence, uniqueness and moment…
We show that the random field solution to the parabolic Anderson equation $(\partial_t-\frac12 \Delta)u=u\diamond \dot{W}$ is jointly H\"older continuous in space and time.
We consider the non-linear equation $T^{-1} u+\partial_tu-\partial_x^2\pi(u)=\xi$ driven by space-time white noise $\xi$, which is uniformly parabolic because we assume that $\pi'$ is bounded away from zero and infinity. Under the further…
The parabolic Anderson problem is the Cauchy problem for the heat equation $\partial_t u(t,z)=\Delta u(t,z)+\xi(z) u(t,z)$ on $(0,\infty)\times {\mathbb Z}^d$ with random potential $(\xi(z) \colon z\in {\mathbb Z}^d)$. We consider…
We investigate the sharp density $\rho(t,x; y)$ of the solution $u(t,x)$ to stochastic partial differential equation $\frac{\partial }{\partial t} u(t,x)=\frac12 \Delta u(t,x)+u\diamond \dot W(t,x)$, where $\dot W$ is a general Gaussian…
In this paper, we introduce a natively positive approximation method based on the Feynman-Kac representation using random walks, to approximate the solution to the one-dimensional parabolic Anderson model of Skorokhod type, with either a…
The goal of the present note is to study intermittency properties for the solution to the fractional heat equation $$\frac{\partial u}{\partial t}(t,x) = -(-\Delta)^{\beta/2} u(t,x) + u(t,x)\dot{W}(t,x), \quad t>0,x \in \bR^d$$ with initial…
We study the Anderson transition in the SU(2) model and the Ando model. We report a new precise estimate of the critical exponent for the symplectic universality class of the Anderson transition. We also report numerical estimation of 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…
In this paper we use the second order equation $\frac{d^2 q}{dt^2} + (\lambda - \gamma q^2) \frac{d q}{dt} - q + q^3 = \mu q^2 \sin \omega t$ as a demonstrative example to illustrate how to apply the analysis of \cite{WO} and \cite{WOk} to…
We introduce various exchange interactions in a model Hamiltonian for Ce$^{3+}$ ions in cubic symmetry with three configurations ($f^0$,$f^1$,$f^2$). With the impurity pseudo spin $S_I=1/2$, our Hamiltonian includes: (i) One-channel…
We use two different fully vectorial microscopic models featuring nonresonant and resonant scattering, respectively, to demonstrate the Anderson localization transition for elastic waves in three-dimensional (3D) disordered solids. Critical…
Anderson localization is a universal phenomenon affecting non-interacting quantum particles in disorder. In three spatial dimensions it becomes particularly interesting to study because of the presence of a quantum phase transition from…