Derivation of the transport equation for electrons moving through random impurities

Herbert Spohn

doi:10.1007/BF01014347

Derivation of the transport equation for electrons moving through random impurities

Herbert Spohn

Princeton University

Research output: Contribution to journal › Article › peer-review

119 Scopus citations

Abstract

A single (nonrelativistic, spinless) electron subject to a constant external electric field interacts with impurities located on an infinitely extended lattice by a potential of random strength. The random strength is given by a field of Gaussian random variables. We show the existence of the averaged dynamics and prove that in the weak coupling limit, λ → 0, λ₂t=τ fixed, one obtains the usual transport equation for the velocity distribution.

Original language	English
Pages (from-to)	385-412
Number of pages	28
Journal	Journal of Statistical Physics
Volume	17
Issue number	6
DOIs	https://doi.org/10.1007/BF01014347
State	Published - Dec 1977
Externally published	Yes

Keywords

Transport equation
electrical conduction, van Hove limit
random impurities

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10.1007/BF01014347

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title = "Derivation of the transport equation for electrons moving through random impurities",

abstract = "A single (nonrelativistic, spinless) electron subject to a constant external electric field interacts with impurities located on an infinitely extended lattice by a potential of random strength. The random strength is given by a field of Gaussian random variables. We show the existence of the averaged dynamics and prove that in the weak coupling limit, λ → 0, λ2t=τ fixed, one obtains the usual transport equation for the velocity distribution.",

keywords = "Transport equation, electrical conduction, van Hove limit, random impurities",

author = "Herbert Spohn",

year = "1977",

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doi = "10.1007/BF01014347",

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PY - 1977/12

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N2 - A single (nonrelativistic, spinless) electron subject to a constant external electric field interacts with impurities located on an infinitely extended lattice by a potential of random strength. The random strength is given by a field of Gaussian random variables. We show the existence of the averaged dynamics and prove that in the weak coupling limit, λ → 0, λ2t=τ fixed, one obtains the usual transport equation for the velocity distribution.

AB - A single (nonrelativistic, spinless) electron subject to a constant external electric field interacts with impurities located on an infinitely extended lattice by a potential of random strength. The random strength is given by a field of Gaussian random variables. We show the existence of the averaged dynamics and prove that in the weak coupling limit, λ → 0, λ2t=τ fixed, one obtains the usual transport equation for the velocity distribution.

KW - Transport equation

KW - electrical conduction, van Hove limit

KW - random impurities

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U2 - 10.1007/BF01014347

DO - 10.1007/BF01014347

M3 - Article

AN - SCOPUS:0001200202

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VL - 17

SP - 385

EP - 412

JO - Journal of Statistical Physics

JF - Journal of Statistical Physics

IS - 6

ER -

Derivation of the transport equation for electrons moving through random impurities

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