Elsevier

Annals of Physics

Volume 158, Issue 2, December 1984, Pages 415-420
Annals of Physics

Semiclassical analysis of low lying elgenvalues. III. Width of the ground state band in strongly coupled solids

https://doi.org/10.1016/0003-4916(84)90125-8Get rights and content

Abstract

A smooth periodic potential, V, with one minima per unit cell, is considered. Let Δ(λ) be the width of the ground state band for −Δ + λ2V. It is rigorously proved that limλ→∞ − λ−1 ln Δ(λ) is given by the minimum action among all instantons connecting two distinct minima of V.

References (10)

  • E. Harrell

    Ann. Phys. (NY)

    (1979)
  • S. Agmon
  • R. Carmona et al.

    Cummun. Math. Phys.

    (1981)
  • E. Harrel

    Commun. Math. Phys.

    (1978)
  • B. Helffer and J. Sjöstrand, Multiple wells in the semi-classical limit, I, Commun. Partial Differential Equations, to...
There are more references available in the full text version of this article.

Cited by (44)

View all citing articles on Scopus

Research partially supported by USNSF Grant MCS-81-20833.

View full text