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res:
bibo_abstract:
- 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 ψt the solution with
initial data ψ0. The space and time variables scale as χ ≃λ-2-κ/2, t ≃λ-2-κ with
0 < kappa; < kappa;0(d). We prove that, in the limit λ → 0, the expectation
of the Wigner distribution of ψt converges weakly to the solution of a heat equation
in the space variable x for arbitrary L2 initial data. The proof is based on a
rigorous analysis of Feynman diagrams. In the companion paper [10] the analysis
of the non-repetition diagrams was presented. In this paper we complete the proof
by estimating the recollision diagrams and showing that the main terms, i.e. the
ladder diagrams with renormalized propagator, converge to the heat equation.@eng
bibo_authorlist:
- foaf_Person:
foaf_givenName: László
foaf_name: László Erdös
foaf_surname: Erdös
foaf_workInfoHomepage: http://www.librecat.org/personId=4DBD5372-F248-11E8-B48F-1D18A9856A87
orcid: 0000-0001-5366-9603
- foaf_Person:
foaf_givenName: Manfred
foaf_name: Salmhofer, Manfred
foaf_surname: Salmhofer
- foaf_Person:
foaf_givenName: Horng
foaf_name: Yau, Horng-Tzer
foaf_surname: Yau
bibo_doi: 10.1007/s00220-006-0158-2
bibo_issue: '1'
bibo_volume: 271
dct_date: 2007^xs_gYear
dct_publisher: Springer@
dct_title: Quantum diffusion of the random Schrödinger evolution in the scaling
limit II. The recollision diagrams@
...