Resonances in the two-center Coulomb systems

Marcello Seri; Andreas Knauf; Mirko Degli Esposti; Thierry Jecko

doi:10.1142/S0129055X16500161

Resonances in the two-center Coulomb systems

Marcello Seri^*, Andreas Knauf, Mirko Degli Esposti, Thierry Jecko

^*Corresponding author for this work

Dynamical Systems, Geometry and Mathematical Physics

Research output: Contribution to journal › Review article › peer-review

2 Citations (Scopus)

37 Downloads (Pure)

Abstract

We investigate the existence of resonances for two-center Coulomb systems with arbitrary charges in two dimensions, defining them in terms of generalized complex eigenvalues of a non-selfadjoint deformation of the two-center Schrodinger operator. We construct the resolvent kernels of the operators and prove that they can be extended analytically to the second Riemann sheet. The resonances are then analyzed by means of perturbation theory and numerical methods.

Original language	English
Article number	1650016
Number of pages	55
Journal	Reviews in Mathematical Physics
Volume	28
Issue number	7
DOIs	https://doi.org/10.1142/S0129055X16500161
Publication status	Published - Aug-2016

Keywords

Resonances
two-center problem
semiclassical analysis
SPHEROIDAL WAVE-EQUATION
SCHRODINGER-OPERATORS
SEMICLASSICAL RESONANCES
EXPONENTIALLY SMALL
MATHEMATICAL-THEORY
CONVERGENCE RADII
FREE DOMAINS
MECHANICS
EIGENVALUES
ANALYTICITY

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Resonances in the two-center Coulomb systemsFinal publisher's version, 1.85 MBLicence: Taverne

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title = "Resonances in the two-center Coulomb systems",

abstract = "We investigate the existence of resonances for two-center Coulomb systems with arbitrary charges in two dimensions, defining them in terms of generalized complex eigenvalues of a non-selfadjoint deformation of the two-center Schrodinger operator. We construct the resolvent kernels of the operators and prove that they can be extended analytically to the second Riemann sheet. The resonances are then analyzed by means of perturbation theory and numerical methods.",

keywords = "Resonances, two-center problem, semiclassical analysis, SPHEROIDAL WAVE-EQUATION, SCHRODINGER-OPERATORS, SEMICLASSICAL RESONANCES, EXPONENTIALLY SMALL, MATHEMATICAL-THEORY, CONVERGENCE RADII, FREE DOMAINS, MECHANICS, EIGENVALUES, ANALYTICITY",

author = "Marcello Seri and Andreas Knauf and Esposti, {Mirko Degli} and Thierry Jecko",

year = "2016",

month = aug,

doi = "10.1142/S0129055X16500161",

language = "English",

volume = "28",

journal = "Reviews in Mathematical Physics",

issn = "0129-055X",

publisher = "World Scientific Publishing",

number = "7",

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TY - JOUR

T1 - Resonances in the two-center Coulomb systems

AU - Seri, Marcello

AU - Knauf, Andreas

AU - Esposti, Mirko Degli

AU - Jecko, Thierry

PY - 2016/8

Y1 - 2016/8

N2 - We investigate the existence of resonances for two-center Coulomb systems with arbitrary charges in two dimensions, defining them in terms of generalized complex eigenvalues of a non-selfadjoint deformation of the two-center Schrodinger operator. We construct the resolvent kernels of the operators and prove that they can be extended analytically to the second Riemann sheet. The resonances are then analyzed by means of perturbation theory and numerical methods.

AB - We investigate the existence of resonances for two-center Coulomb systems with arbitrary charges in two dimensions, defining them in terms of generalized complex eigenvalues of a non-selfadjoint deformation of the two-center Schrodinger operator. We construct the resolvent kernels of the operators and prove that they can be extended analytically to the second Riemann sheet. The resonances are then analyzed by means of perturbation theory and numerical methods.

KW - Resonances

KW - two-center problem

KW - semiclassical analysis

KW - SPHEROIDAL WAVE-EQUATION

KW - SCHRODINGER-OPERATORS

KW - SEMICLASSICAL RESONANCES

KW - EXPONENTIALLY SMALL

KW - MATHEMATICAL-THEORY

KW - CONVERGENCE RADII

KW - FREE DOMAINS

KW - MECHANICS

KW - EIGENVALUES

KW - ANALYTICITY

U2 - 10.1142/S0129055X16500161

DO - 10.1142/S0129055X16500161

M3 - Review article

SN - 0129-055X

VL - 28

JO - Reviews in Mathematical Physics

JF - Reviews in Mathematical Physics

IS - 7

M1 - 1650016

ER -

Resonances in the two-center Coulomb systems

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Keywords

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