Finite Trotter approximation to the averaged mean square distance in the anderson model

S. Suwanna

doi:10.1007/s10955-009-9817-y

Finite Trotter approximation to the averaged mean square distance in the anderson model

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Abstract

We prove that a finite Trotter approximation to the averaged mean square distance traveled by a particle in a disordered system on a lattice ℤ^d exhibits at most a diffusive behavior in dimensions d ≥ 3 as long as the Fourier transform of the single-site probability, is in L²(ℝ).

Original language	English
Pages (from-to)	1131-1175
Number of pages	45
Journal	Journal of Statistical Physics
Volume	136
Issue number	6
DOIs	https://doi.org/10.1007/s10955-009-9817-y
Publication status	Published - Oct 2009
Externally published	Yes

Keywords

Anderson model
Random Schrödinger operators
Trotter product formula

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10.1007/s10955-009-9817-y

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abstract = "We prove that a finite Trotter approximation to the averaged mean square distance traveled by a particle in a disordered system on a lattice ℤd exhibits at most a diffusive behavior in dimensions d ≥ 3 as long as the Fourier transform of the single-site probability, is in L2(ℝ).",

keywords = "Anderson model, Random Schr{\"o}dinger operators, Trotter product formula",

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AB - We prove that a finite Trotter approximation to the averaged mean square distance traveled by a particle in a disordered system on a lattice ℤd exhibits at most a diffusive behavior in dimensions d ≥ 3 as long as the Fourier transform of the single-site probability, is in L2(ℝ).

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KW - Random Schrödinger operators

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Finite Trotter approximation to the averaged mean square distance in the anderson model

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Keywords

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