Aspects of the theory and computation of resonances, with applications to field-free and field-dressed atomic states

Nicolaides, CA

dc.contributor.author	Nicolaides, CA	en
dc.date.accessioned	2014-03-01T02:42:12Z
dc.date.available	2014-03-01T02:42:12Z
dc.date.issued	2003	en
dc.identifier.issn	0020-7748	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/30859
dc.subject	Complex eigenvalues	en
dc.subject	Localization	en
dc.subject	Nonexponential decay	en
dc.subject	Resonances	en
dc.subject	Time-dependence	en
dc.subject.classification	Physics, Multidisciplinary	en
dc.subject.other	POLYELECTRONIC STARK PROBLEM	en
dc.subject.other	AUTOIONIZING STATES	en
dc.subject.other	COMPLEX ENERGIES	en
dc.subject.other	TIME-DEPENDENCE	en
dc.subject.other	CONFIGURATION-INTERACTION	en
dc.subject.other	CONTINUOUS-SPECTRUM	en
dc.subject.other	EXPONENTIAL DECAY	en
dc.subject.other	PATH-INTEGRALS	en
dc.subject.other	VIRTUAL STATES	en
dc.subject.other	WIDTHS	en
dc.title	Aspects of the theory and computation of resonances, with applications to field-free and field-dressed atomic states	en
heal.type	conferenceItem	en
heal.identifier.primary	10.1023/B:IJTP.0000005952.33595.d2	en
heal.identifier.secondary	http://dx.doi.org/10.1023/B:IJTP.0000005952.33595.d2	en
heal.language	English	en
heal.publicationDate	2003	en
heal.abstract	A review of certain aspects of the theory and computation of resonance states is presented, from the point of view of the work by the author and his colleagues in atomic physics. Two issues are mainly discussed: one is the understanding and ab initio calculation of resonance states of real systems from a time-dependent point of view. The other is the derivation and application of the complex eigenvalue Schrodinger equation from a superposition of the localized wave packet 90 with the orthogonal to it scattering wave functions phi(E), when outgoing-wave boundary conditions are imposed. It is shown how two complex adjoint solutions, the hallmark of resonance state theory, correspond to the Fano solution for a resonance state on the real energy axis, obtained from the application of Hermitian quantum mechanics. The forms of the complex eigenfunctions are used for non-Hermitian calculations of resonance states in polyelectronic atoms. The question of time-asymmetry at the quantum level is tackled by observing that the time-evolution has to be considered with boundary conditions t greater than or equal to 0 and infinity > E > 0 and a complex energy distribution given by the diagonal matrix element of the Green's function with respect to Psi0. Using a model whereby the self-energy of the decaying state, A(z), is approximated by A(z) approximate to A(E-0), where E-0 = <Psi(0)\H\Psi(0)>, it is shown that time-asymmetry, if present as defined in this work, should have an effect on the as yet unobserved long-time deviation from exponential decay. Although not described explicitly, it is indicated, via the forms of the trial wave functions and via the references, how polyelectronic calculations have been carried out, for field-free resonance states as well as for resonance states that are created by the presence of an external electromagnetic field.	en
heal.publisher	KLUWER ACADEMIC/PLENUM PUBL	en
heal.journalName	International Journal of Theoretical Physics	en
dc.identifier.doi	10.1023/B:IJTP.0000005952.33595.d2	en
dc.identifier.isi	ISI:000186895900004	en
dc.identifier.volume	42	en
dc.identifier.issue	10	en
dc.identifier.spage	2145	en
dc.identifier.epage	2165	en