Journal ArticleDOI
Path-integral theory of a model disordered system
TLDR
In this paper, a method for calculating the density of states and the effective mass of a model of an electron in a completely random system containing dense and weak scatterers is presented.Abstract:
A method for calculating the density of states and the effective mass of a model of an electron in a completely random system containing dense and weak scatterers, is presented. The scattering potential employed in the model is assumed to be a gaussian function. The technique used in the calculation is the path-integral method of Feynman applied to the polaron problem (1955). Special emphasis is devoted to the consideration of the asymptotic behaviours of the density of states m(E) and the effective mass m*, for two limiting values of the correlation length L. Some improvements upon the method as well as an extension to a real physical system are discussed.read more
Citations
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Journal ArticleDOI
Explicit evaluation of certain Gaussian functional integrals arising in problems of statistical physics
TL;DR: An explicit formula for a (conditional) Wiener integral, the integrand of which is an exponential of a general quadratic functional of the path, is presented in this paper.
Journal ArticleDOI
Partition function for an electron in a random potential
TL;DR: In this paper, the average partition function for an electron moving in a Gaussian random potential is computed, with a trial action like that in Feynman's polaron theory.
Journal ArticleDOI
Path integration of a two-time quadratic action
TL;DR: In this paper, path integration of a general two-time quadratic action characterising memory effects is performed within the framework of Feynman's polygonal path approach, and explicit evaluation of the propagator in exact analytical form is further carried out for the specific kernel used by the author in the polaron problem.
Journal ArticleDOI
Applications of white noise calculus to the computation of Feynman integrals
TL;DR: In this paper, the Feynman propagator in a uniform magnetic field can be explicitly computed in terms of P. Levy's stochastic area spanned by two-dimensional Brownian motion.
Book ChapterDOI
Bandgap Narrowing and Its Effects on the Properties of Moderately and Heavily Doped Germanium and Silicon
TL;DR: In this article, the effect of bandgap narrowing on the optical properties of silicon and germanium is discussed, where the authors focus on the properties of moderately and heavily doped Si and Ge.
References
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Journal ArticleDOI
Generalized cumulant expansion method
TL;DR: The notion of cumulants and cumulant functions was introduced in this paper, where a moment generating function of a set of stochastic variables defines the cumulus or the semi-invariants and the cumULant function, and the definition of average may be greatly generalized as far as the condition of the average of unity is unity.
Journal ArticleDOI
Slow Electrons in a Polar Crystal
TL;DR: In this paper, a variational principle is developed for the lowest energy of a system described by a path integral, which is applied to the problem of the interaction of an electron with a polarizable lattice, as idealized by Frohlich.
Journal ArticleDOI
Integration in Functional Spaces and its Applications in Quantum Physics
I. M. Gel'fand,A. M. Yaglom +1 more
TL;DR: Gel'fand and Yaglom as mentioned in this paper presented a survey article on the theory and applications of integration in functional spaces in problems of quantum physics, including the use of functional integration methods in quantum mechanics, quantum field theory, and quantum statistical physics.
Journal ArticleDOI
Mobility of Slow Electrons in a Polar Crystal
TL;DR: In this paper, an approximate expression for the impedance function at all frequencies, temperatures, and coupling strengths of an electron coupled to a polar lattice (a system commonly called a polaron) was obtained.
Journal ArticleDOI
Theory of Bound States in a Random Potential
J. Zittartz,James S. Langer +1 more
TL;DR: In this paper, a systematic procedure is proposed for calculation of the energy-level density of low-lying bound states in a random potential, based on a function-space formulation of the problem.