The spectrum of a Schrödinger operator in a wire-like domain with a purely imaginary degenerate potential in the semiclassical limit / Y. Almog, B Helffer.

Format:

Book

Author/Creator:

Almog, Y. (Yaniv), author.

Helffer, Bernard, author.

Series:

Mémoire (Société mathématique de France) ; nouv. sér., no. 166.

Mémoires de la Société mathématique de France, 0249-633X ; Nouvelle série, Numéro 166

Language:

English

French

Subjects (All):

Schrödinger operator.

Nonselfadjoint operators.

Electric currents.

Physical Description:

vi, 94 pages : 1 illustration ; 24 cm.

Distribution:

Providence, RI : ‡b Diffusion, AMS.

Other Title:

Mémoires de la SMF 166

Place of Publication:

Paris : Société Mathématique de France, 2020.

Language Note:

Text in English, with abstract in English and French.

Summary:

"Consider a two-dimensional domain shaped like a wire, not necessarily of uniform cross section. Let V denote an electric potential driven by a voltage drop between the conducting surfaces of the wire. We consider the operator [script]A[subscript]h = -h[superscript]2[delta] + [iota]V in the semi-classical limit h --> 0. We obtain both the asymptotic behavior of the left margin of the spectrum, as well as resolvent estimates on the left side of this margin. We extend here previous results obtained for potentials for which the set where the current (or [inverted delta]V is normal to the boundary is discrete, in contrast with the present case where V is constant along the conducting surfaces."--Page 4 of printed paper wrapper.

Contents:

(from table of contents) Introduction

Lower bound

Quasimode construction

Type V1

Type V2

V1 potentials: 2D simplification

Simplified operators: V2 potentials

Upper bound

Examples of potentials satisfying (1.4).

Notes:

Series title from front cover.

Includes bibliographical references (pages 93-94). 22

ISBN:

9782856299289

2856299288

OCLC:

1228928192