Analysis of certain random operators related to solid state physics

Maxim Drabkin (Autor)

Buch | Softcover

116 Seiten

2016
Südwestdeutscher Verlag für Hochschulschriften
9783838152578 (ISBN)

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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.

The author was born in Ferghana in 1984 and graduated some thirty years later at Friedrich-Alexander University of Erlangen-Nuremberg in mathematicals physics. Besides solving analytical problems author enjoys hiking tours, cooking, playing with cats and visiting beautiful cities with his wife.

Erscheinungsdatum	01.07.2016
Sprache	englisch
Maße	150 x 220 mm
Gewicht	189 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik
Schlagworte	Chern-Zahl • Dynamisches System • Elektronentransport • Ljapunov-Exponent • Schrödinger-Gleichung • Topologischer Isolator
ISBN-13	9783838152578 / 9783838152578
Zustand	Neuware