Author | Lang, Reinhard. author |
---|---|

Title | Spectral Theory of Random Schrรถdinger Operators [electronic resource] : A Genetic Introduction / by Reinhard Lang |

Imprint | Berlin, Heidelberg : Springer Berlin Heidelberg, 1991 |

Connect to | http://dx.doi.org/10.1007/BFb0093929 |

Descript | X, 126 p. online resource |

SUMMARY

The interplay between the spectral theory of Schr inger 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 inger 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

CONTENT

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

Mathematics
Probabilities
Physics
Mathematics
Probability Theory and Stochastic Processes
Theoretical Mathematical and Computational Physics