Bookcover of Analysis of certain random operators related to solid state physics
Booktitle:

Analysis of certain random operators related to solid state physics

Südwestdeutscher Verlag für Hochschulschriften (2016-06-03 )

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ISBN-13:

978-3-8381-5257-8

ISBN-10:
3838152573
EAN:
9783838152578
Book language:
English
Blurb/Shorttext:
The presented book is about the random Kronig-Penney model and other related quantum mechanical models. The main objects in consideration are random mostly one dimensional and discrete Schrödinger operators and their spectral properties. From the physical point of view the most interesting objects in these models are conductivity and charge transport in disordered solid media. These show different behavior than the ordered systems. For the Kronig-Penney model lower bounds on the growth of the time-averaged q-th moment of the position operator X are obtained, as well as the perturbative analysis of the Lyapunov exponent and the integrated density of states. On the technical level the theory of the products of random matrices is used. It is known, that the products of random matrices exhibit Gaussian fluctuations around almost surely convergent Lyapunov exponents. For the 2x2 matrices the variance is calculated perturbatively. Furthermore for the random Bogoliubov-de Gennes model operators the localization in the spectral gap is proven.
Publishing house:
Südwestdeutscher Verlag für Hochschulschriften
Website:
https://www.svh-verlag.de
By (author) :
Maxim Drabkin
Number of pages:
116
Published on:
2016-06-03
Stock:
Available
Category:
Theory of probability, stochastics, mathematical statistics
Price:
59.00 €
Keywords:
Chern-Zahl, Dynamisches System, Elektronentransport, Ljapunov-Exponent, Schrödinger-Gleichung, Topologischer Isolator

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