Fractional powers and singular perturbations of quantum differential Hamiltonians

被引：7

作者：

Michelangeli, A. ^{[1
]}

Ottolini, A. ^{[2
]}

Scandone, R. ^{[1
]}

机构：

[1] Int Sch Adv Studies SISSA, Via Bonomea 265, I-34136 Trieste, Italy

[2] Stanford Univ, Dept Math, 450 Serra Mall, Stanford, CA 94305 USA

来源：

JOURNAL OF MATHEMATICAL PHYSICS | 2018年 / 59卷 / 07期

关键词：

POINT INTERACTIONS;

D O I：

10.1063/1.5033856

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

We consider the fractional powers of singular (point-like) perturbations of the Laplacian and the singular perturbations of fractional powers of the Laplacian, and we compare two such constructions focusing on their perturbative structure for resolvents and on the local singularity structure of their domains. In application to the linear and non-linear Schrodinger equations for the corresponding operators, we outline a programme of relevant questions that deserve being investigated. Published by AIP Publishing.

引用

页数：27

共 20 条

[1] FUNDAMENTAL SOLUTION OF THE HEAT AND SCHRODINGER-EQUATIONS WITH POINT INTERACTION [J].

ALBEVERIO, S ;

BRZEZNIAK, Z ;

DABROWSKI, L .

JOURNAL OF FUNCTIONAL ANALYSIS, 1995, 130 (01) :220-254

[2]

Albeverio S., 1988, TEXTS MONOGRAPHS PHY

[3]

ALBEVERIO S, 2000, LONDON MATH SOC LECT, V271

[4]

[Anonymous], ARXIV180101694

[5]

[Anonymous], 2017, 252017MATE SISSA

[6] Tunneling in fractional quantum mechanics [J].

Capelas de Oliveira, E. ;

Vaz, Jayme, Jr. .

JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 2011, 44 (18)

[7] Dispersive estimate for the Schrodinger equation with point interactions [J].

D'Ancona, P ;

Pierfelice, V ;

Teta, A .

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2006, 29 (03) :309-323

[8] The fractional Schrodinger equation for delta potentials [J].

de Oliveira, Edmundo Capelas ;

Costa, Felix Silva ;

Vaz, Jayme, Jr. .

JOURNAL OF MATHEMATICAL PHYSICS, 2010, 51 (12)

[9]

Dell'Antonio G, 2018, ANN HENRI POINCARE, V19, P283, DOI 10.1007/s00023-017-0628-4

[10] On fractional powers of singular perturbations of the Laplacian [J].

Georgiev, Vladimir ;

Michelangeli, Alessandro ;

Scandone, Raffaele .

JOURNAL OF FUNCTIONAL ANALYSIS, 2018, 275 (06) :1551-1602

← 1 2 →