Spectral theory of random Schrödinger operators : a genetic introduction / Reinhard Lang.

Author
Lang, Reinhard [Browse]
Format
Book
Language
English
Εdition
1st ed. 1991.
Published/​Created
  • Berlin, Heidelberg : Springer-Verlag, [1991]
  • ©1991
Description
1 online resource (X, 126 p.)

Details

Subject(s)
Series
  • Lecture notes in mathematics (Berlin) ; Volume 1498. [More in this series]
  • Lecture Notes in Mathematics ; Volume 1498
Summary note
The interplay between the spectral theory of Schr|dinger operators and probabilistic considerations forms the main theme of these notes, written for the non-specialist reader and intended to provide a brief and elementaryintroduction to this field. An attempt is made to show basic ideas in statu nascendi and to follow their evaluation from simple beginnings through to more advanced results. The term "genetic" in the title refers to this proceedure. The author concentrates on 2 topics which, in the history of the subject, have been of major conceptual importance - on the one hand the Laplacian is a random medium and the left end of its spectrum (leading to large deviation problems for Brownian motion and the link to thenotion of entropy) and on the other, Schr|dinger operators with general ergodic potentials in one-dimensional space. Ideas and concepts are explained in the simplest, possible setting and by means of a few characteristic problems with heuristic arguments preceding rigorous proofs.
Notes
Bibliographic Level Mode of Issuance: Monograph
Source of description
Description based on print version record.
Language note
English
Contents
  • Two simple examples
  • The general heuristic picture
  • Some known results and open problems
  • Explanation of Theorem 1 and introduction to an extended Boltzmann theory of entropy
  • Explanation of Theorem 2 and introduction to an extended Floquet-Weyl theory
  • Conclusion.
ISBN
3-540-46627-4
OCLC
1066198996
Doi
  • 10.1007/BFb0093929
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