Search
Now showing items 1-10 of 12
Local Semicircle Law and Complete Delocalization for Wigner Random Matrices
(Springer Nature, 2008)
We consider N × N Hermitian random matrices with independent identical distributed entries. The matrix is normalized so that the average spacing between consecutive eigenvalues is of order 1/N. Under suitable assumptions ...
Quantum Diffusion for the Anderson Model in the Scaling Limit
(Springer Nature, 2007)
We consider random Schrödinger equations on ℤdZd for d ≥ 3 with identically distributed random potential. Denote by λ the coupling constant and ψt the solution with initial data ψ0. The space and time variables scale as ...
Towards the Quantum Brownian Motion
(Springer Berlin Heidelberg, 2006)
We consider random Schr\"odinger equations on $\bR^d$ or $\bZ^d$ for d≥3 with uncorrelated, identically distributed random potential. Denote by λ the coupling constant and ψt the solution with initial data ψ0. Suppose that ...
Linear Boltzmann equation as the weak coupling limit of a random Schrödinger equation
(Wiley-Blackwell, 2000)
We study the time evolution of a quantum particle in a Gaussian random environment. We show that in the weak coupling limit the Wigner distribution of the wave function converges to a solution of a linear Boltzmann equation ...
Quantum Diffusion of the Random Schrödinger Evolution in the Scaling Limit II. The Recollision Diagrams
(Springer Nature, 2007)
We consider random Schrödinger equations on {mathbb{R}d} for d≥ 3 with a homogeneous Anderson-Poisson type random potential. Denote by λ the coupling constant and ψ t the solution with initial data ψ0. The space and time ...
On the Quantum Boltzmann Equation
(Springer Nature, 2004)
We give a nonrigorous derivation of the nonlinear Boltzmann equation from the Schrödinger evolution of interacting fermions. The argument is based mainly on the assumption that a quasifree initial state satisfies a property ...
Nonlinear Hartree Equation as the Mean Field Limit of Weakly Coupled Fermions
(Elsevier BV, 2004)
We consider a system of N weakly interacting fermions with a real analytic pair interaction. We prove that for a general class of initial data there exists a fixed time T such that the difference between the one particle ...
Quantum diffusion of the random Schrödinger evolution in the scaling limit
(International Press of Boston, 2008)
We consider random Schrödinger equations on Rd for d ≽ 3 with a homogeneous Anderson–Poisson type random potential. Denote by λ the coupling constant and ψtψt the solution with initial data ψ0ψ0 . The space and time ...
Gross-Pitaevskii Equation as the Mean Field Limit of Weakly Coupled Bosons
(Springer Nature, 2005)
We consider the dynamics of N boson systems interacting through a pair potential N−1Va(xi−xj) where Va(x)=a−3V(x/a). We denote the solution to the N-particle Schrödinger equation by ΨN, t. Recall that the Gross-Pitaevskii ...
Derivation of the cubic non-linear Schrödinger equation from quantum dynamics of many-body systems
(Springer Nature, 2006)
We prove rigorously that the one-particle density matrix of three dimensional interacting Bose systems with a short-scale repulsive pair interaction converges to the solution of the cubic non-linear Schrödinger equation ...