NNSE618-L10-Kinetic_equation_magnetotransport

# NNSE618-L10-Kinetic_equation_magnetotransport - 1 Lecture...

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NNSE 618 Lecture #10 1 Lecture contents Kinetic equation Relaxation time approximation Magneto-transport

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NNSE 618 Lecture #10 2 Boltzmann Kinetic Equation We need to find an equation that describes the behavior of the distribution function in space and time The distribution function can change by… a spatial inflow/outflow of carriers an inflow/outflow of carriers in momentum space by means of a force scattering of carriers into or out of a particular location in position-momentum space the presence of a source or sink of carriers
NNSE 618 Lecture #10 3 Boltzmann Kinetic Equation One dimension General, multi-dimensional BKE in 7 dimensions (3 spatial, 1 time, 3 momentum—but there’s more) Collision integral: coll f f f f v F s t r p t   ˆˆ ˆ where rp coll p x y z ff f f s tt x y z p p p       vF             3 3 ' ' 2 ' ' , 1 , ' 1 k d k k W f f k k W f f t f k k k k coll

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NNSE 618 Lecture #10 4 General considerations for transport: Kinetic equation The full scattering term is almost always too complicated to allow an analytic solution Solution: simplify the BKE by converting to a scattering time representation Under relaxation time approximation (no sink): ) ( ) ( ) ( 0 k k f k f t f coll 0 1 f f f F f v t f k
NNSE 618 Lecture #10 5 Simplest Solution of the BKE Consider a spatially uniform field with no applied force

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## This note was uploaded on 11/07/2011 for the course NNSE 618 taught by Professor Sergeoktyabrsky during the Spring '11 term at SUNY Albany.

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NNSE618-L10-Kinetic_equation_magnetotransport - 1 Lecture...

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