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https://hdl.handle.net/2142/23954
Description
Title
Theory of polaron mobility
Author(s)
Langreth, David Chapman
Issue Date
1964
Doctoral Committee Chair(s)
Kadanoff, L.P.
Department of Study
Physics
Discipline
Physics
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
polaron mobility
polaron-phonon system
quasiparticle states
Green's functions
Language
en
Abstract
"Two different methods for describing the polaron-phonon
system are formulated 0 These are: (1) description in terms of
quasiparticle states, (2) description in terms of thermodynamic
GreenYs functions~ The first approach leads naturally to an S
matrix formulation of polaron transport~ The second leads to the
Kadanoff-Baym transport equations 0 It is shown that both
approaches are equivalento By using the latter approach$ it is
shown that the low-temperature polaron drift mObility is given
rigorously by IJ. :; e'T/m * , where 'T is the polaron lifetime"" and
m* its effective masso This relationship is verified explicitly
to lowest nontrivial order in the coupling constant by using the
Kubo formula.
Various methods for calculating the low-temperature mobility
for weak and intermediate coupling are discussed and critically
compared~ These methods include: (1) perturbation theorYt (2)
the Feynman model of the polaron as applied by 'osaka, or Feynman,
Hellswarth, Iddings, and Platzman» or Schultz, (3) the Low-Pines
intermediate coupling theory augmented by Lawus scattering
theory 0 The low=temperature mobility is calculated in pertur-
02· bat ion theory to order a. 0 It is found that I-L = lJ.o (l=a/6 + 0(0, UJI
where Il o is the weak~coupling mo. bilityo This result corresponds
most closely with the expansion of Osakavs mobility formula o
Certain improvements to the mobility calculations of Schultz~
and of Low and Pines are suggested 0 When these improvements are
incorporated» both the Low~Pines and the Schultz theories come
into much better agreement with the perturbation expansion for
weak coupling, and wit.h OsakaBs theory for intermediate coupling."
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