Towards the quantum Brownian motion
| dc.creator | Erdos, Laszlo | |
| dc.creator | Salmhofer, Manfred | |
| dc.creator | Yau, Horng-Tzer | |
| dc.date | 2005-03-01 | |
| dc.date | 2006-02-06 | |
| dc.date.accessioned | 2026-07-07T06:38:35Z | |
| dc.date.available | 2026-07-07T06:38:35Z | |
| dc.description | We consider random Schrödinger equations on $\bR^d$ or $\bZ^d$ for $d\ge 3$ with uncorrelated, identically distributed random potential. Denote by $λ$ the coupling constant and $ψ_t$ the solution with initial data $ψ_0$. Suppose that the space and time variables scale as $x\sim λ^{-2 -κ/2}, t \sim λ^{-2 -κ}$ with $0< κ\leq κ_0$, where $κ_0$ is a sufficiently small universal constant. We prove that the expectation value of the Wigner distribution of $ψ_t$, $\bE W_{ψ_{t}} (x, v)$, converges weakly to a solution of a heat equation in the space variable $x$ for arbitrary $L^2$ initial data in the weak coupling limit $λ\to 0$. The diffusion coefficient is uniquely determined by the kinetic energy associated to the momentum $v$. | |
| dc.description | Self-contained overview (Conference proceedings). The complete proof is archived in math-ph/0502025. Some typos corrected and new references added in the updated version | |
| dc.identifier | https://arxiv.org/abs/math-ph/0503001 | |
| dc.identifier | http://arxiv.org/abs/math-ph/0503001 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/100788 | |
| dc.subject | Mathematical Physics | |
| dc.subject | 60J65, 81T18, 82C10, 82C44 | |
| dc.title | Towards the quantum Brownian motion | |
| dc.type | text |