Nonexponential decay propagator and its differential equation for real and complex energy distributions of unstable states

Douvropoulos, TG; Nicolaides, CA

dc.contributor.author	Douvropoulos, TG	en
dc.contributor.author	Nicolaides, CA	en
dc.date.accessioned	2014-03-01T01:21:08Z
dc.date.available	2014-03-01T01:21:08Z
dc.date.issued	2004	en
dc.identifier.issn	1050-2947	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/16080
dc.subject.classification	Optics	en
dc.subject.classification	Physics, Atomic, Molecular & Chemical	en
dc.subject.other	Electron energy levels	en
dc.subject.other	Fermi level	en
dc.subject.other	Friction	en
dc.subject.other	Integral equations	en
dc.subject.other	Ionization	en
dc.subject.other	Mathematical models	en
dc.subject.other	Mathematical transformations	en
dc.subject.other	Resonance	en
dc.subject.other	Energy distributions	en
dc.subject.other	Exponential decay (ED)	en
dc.subject.other	Lorentzian function	en
dc.subject.other	Nonexponential decay (NED)	en
dc.subject.other	Quantum theory	en
dc.title	Nonexponential decay propagator and its differential equation for real and complex energy distributions of unstable states	en
heal.type	journalArticle	en
heal.identifier.primary	10.1103/PhysRevA.69.032105	en
heal.identifier.secondary	http://dx.doi.org/10.1103/PhysRevA.69.032105	en
heal.identifier.secondary	032105	en
heal.language	English	en
heal.publicationDate	2004	en
heal.abstract	The survival amplitude G(t) of a nonstationary state decaying into a purely continuous spectrum is treated in terms of an integral transform of an energy distribution with infinity>Egreater than or equal to0. We examine three such distributions. Two are real functions, the Lorentzian g(L)(E) and a modified Lorentzian G(E)=g(L)(E)E-1/2, and one is the complex version of g(L)(E),g(c)(L)(E). Real distributions are associated with Hermitian treatments while complex ones result from non-Hermitian treatments. The difference between the two has repercussions on the G(t) for nonexponential decay (NED) and on the understanding of irreversible decay at the quantum level. For all three distributions, we derive analytically amplitudes (propagators) for NED and then show that these satisfy differential equations, from which additional insight into the decay process for very long and very short times can be obtained. By making analogy with the classical Langevin equation, the terms of the differential equation that are derived when the simpler g(L)(E) and g(c)(L)(E) are employed, are interpreted using concepts such as friction and fluctuation. On the other hand, when g(L)(E) is multiplied by an energy-dependent factor, as in G(E), the results are, as expected, more complicated and the interpretability of the differential equation satisfied by the NED propagator loses clarity.	en
heal.publisher	AMERICAN PHYSICAL SOC	en
heal.journalName	Physical Review A - Atomic, Molecular, and Optical Physics	en
dc.identifier.doi	10.1103/PhysRevA.69.032105	en
dc.identifier.isi	ISI:000220605200022	en
dc.identifier.volume	69	en
dc.identifier.issue	3	en
dc.identifier.spage	032105	en
dc.identifier.epage	1	en