Quantum diffusion for the Anderson model in the scaling limit
| dc.creator | Erdos, Laszlo | |
| dc.creator | Salmhofer, Manfred | |
| dc.creator | Yau, Horng-Tzer | |
| dc.date | 2005-02-07 | |
| dc.date | 2007-03-26 | |
| dc.date.accessioned | 2026-07-07T07:53:37Z | |
| dc.date.available | 2026-07-07T07:53:37Z | |
| dc.description | We consider random Schrödinger equations on $\bZ^d$ for $d\ge 3$ with identically distributed random potential. Denote by $λ$ the coupling constant and $ψ_t$ the solution with initial data $ψ_0$. The space and time variables scale as $x\sim λ^{-2 -κ/2}, t \sim λ^{-2 -κ}$ with $0< κ< κ_0(d)$. We prove that, in the limit $λ\to 0$, the expectation of the Wigner distribution of $ψ_t$ converges weakly to a solution of a heat equation in the space variable $x$ for arbitrary $L^2$ initial data. The diffusion coefficient is uniquely determined by the kinetic energy associated to the momentum $v$. This work is an extension to the lattice case of our previous result in the continuum \cite{ESYI}, \cite{ESYII}. Due to the non-convexity of the level surfaces of the dispersion relation, the estimates of several Feynman graphs are more involved. | |
| dc.description | 70 pages, 7 figures The earlier version of the paper was divided into two independent articles. The current version contains the main body of the proof. The proof of the key "Four denominator lemma" is presented separately in math-ph/0604039. Several errors and misprints are corrected. On March 4, 2007, the paper was updated according to the improvement of in the paper [8] (math-ph/0512014) and the threshold exponent kappa was improved. References were updated on March 6. On March 26 a typo was corrected in (7.17) that has led to different exponents in several error terms | |
| dc.identifier | https://arxiv.org/abs/math-ph/0502025 | |
| dc.identifier | http://arxiv.org/abs/math-ph/0502025 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/126292 | |
| dc.subject | Mathematical Physics | |
| dc.subject | 60J65, 81T18, 82C10, 82C44 | |
| dc.title | Quantum diffusion for the Anderson model in the scaling limit | |
| dc.type | text |