We consider the asymptotic almost sure behavior of the solution of the equation u(t, x) = u0(x) + κ ∫ t

We examine the localization properties of the 2D Anderson Hamiltonian with oo-diagonal disorder. Investigating the behavior of the participation numbers of eigenstates as well as studying their multifractal properties, we nd states in the center of the band which show critical behavior up to the system size N = 200200 considered. This result is connrmed by an independent analysis of the localiz...

In recent years, constructive field techniques and the method of renormalization group around extended singularities have been applied to the weak coupling regime of the Anderson Model. It has allowed to clarify the relationship between this model and the theory of random matrices. We review this situation and the current program to analyze in detail the density of states and Green’s functions ...

We compare different approximation schemes for investigating ferromagnetism in the periodic Anderson model. The use of several approximations allows for a detailed analysis of the implications of the respective methods, and also of the mechanisms driving the ferromagnetic transition. For the Kondo limit, our results confirm a previously proposed mechanism leading to ferromagnetic order, namely ...

In this note, we use the Feynman-Kac formula to derive a moment representation for the 2D parabolic Anderson model in small time, which is related to the intersection local time of planar Brownian motions.

Entanglement is a kind of nonlocal correlation that only exists in quantum systems. Recent studies on entanglement have been motivated by its potential applications in quantum computation, quantum teleportation and quantum communication. As the spin system is perfect to realize the quantum computer, many efforts focus on the entanglement in the Heisenberg spin model, Ising model in a transverse...

In the Anderson model on Zd, we consider a sequence of its finite volume approximation Hk k and construct a set of sequences composed of the eigenvalues and eigenfunctions of Hk in the localized region I which converge to those of H simultaneously. For its proof, Minami’s estimate turns out to be important. This result implies that, in the localized region, each eigenfunction behaves almost ind...