Time asymmetry, nonexponential decay,and complex eigenvalues in the theory and computation of resonance states

Nicolaides, CA

dc.contributor.author	Nicolaides, CA	en
dc.date.accessioned	2014-03-01T01:52:14Z
dc.date.available	2014-03-01T01:52:14Z
dc.date.issued	2002	en
dc.identifier.issn	0020-7608	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/26605
dc.subject	resonance states	en
dc.subject	time asymmetry	en
dc.subject	nonexponential decay	en
dc.subject.classification	Chemistry, Physical	en
dc.subject.classification	Mathematics, Interdisciplinary Applications	en
dc.subject.classification	Physics, Atomic, Molecular & Chemical	en
dc.subject.other	TRIPLY EXCITED RESONANCES	en
dc.subject.other	NON-EXPONENTIAL DECAY	en
dc.subject.other	AUTOIONIZING STATES	en
dc.subject.other	QUANTUM-MECHANICS	en
dc.subject.other	SYSTEMS	en
dc.subject.other	HE	en
dc.subject.other	ENERGIES	en
dc.subject.other	DEPENDENCE	en
dc.subject.other	THRESHOLD	en
dc.subject.other	PHYSICS	en
dc.title	Time asymmetry, nonexponential decay,and complex eigenvalues in the theory and computation of resonance states	en
heal.type	journalArticle	en
heal.language	English	en
heal.publicationDate	2002	en
heal.abstract	Stationary-state quantum mechanics presents no difficulties in defining and computing discrete excited states because they obey the rules established in the properties of Hilbert space. However, when this idealization has to be abandoned to formulate a theory of excited states dissipating into a continuous spectrum, the problem acquires additional interest in many fields of physics. In this article, the theory of resonances in the continuous spectrum is formulated as a problem of decaying states, whose treatment can entail time-dependent as well as energy-dependent theories. The author focuses on certain formal and computational issues and discusses their application to polyelectronic atomic states. It is argued that crucial to the theory is the understanding and computation of a multiparticle localized wavepacket, Psi(0), at t = 0, having a real energy E-0. Assuming this as the origin, without memory of the excitation process, the author discusses aspects of time-dependent dynamics, for t approximate to 0 as well as for t --> infinity, and the possible significance of nonexponential decay in the understanding of time asymmetry. Also discussed is the origin of the complex eigenvalue Schrodinger equation (CESE) satisfied by resonance states and the state-specific methodology for its solution. The complex eigenvalue drives the decay exponentially, with a rate Gamma, to a good approximation. It is connected to E-0 via analytic continuation of the complex self-energy function, A(z), (z is complex), into the second Riemann sheet, or, via the imposition of outgoing wave boundary conditions on the stationary state Schrodinger equation satisfied by the Fano standing wave superposition in the vicinity of E-0. If the nondecay amplitude, G(t), is evaluated by inserting the unit operator I = integraldE \E><E\ G(t) = < Psi(0) \e(-iHt)\ Psi(0) >, then the resulting spectral function is real, g(E) = \<Psi(0)\E>\(2), and does not differentiate between positive and negative times. The introduction of time asymmetry, which is associated with irreversibility, is achieved by starting from <Psi(0)\theta(t)e(-iHt)\Psi(0)>, where theta(t) is the step function at the discontinuity point t = 0. In this case, the spectral function is complex. Within the range of validity of exponential decay, the complex spectral function is the same as the coefficient of Psi(0) in the theory of the CESE. A calculation of G(t) using the simple pole approximation and the constraints that t > 0 and E > 0 results in a nonexponential decay (NED) correction for t much greater than 1/Gamma that is different than when a real g(E) is used, representing the contribution of both "in" and "out" states. Earlier formal and computational work has shown that resonance states close to threshold are good candidates for NED to acquire nonnegligible magnitude. In this context, a pump-probe laser experiment in atomic physics is proposed, using as a paradigm the He- 1s2p(2) P-4 shape resonance. (C) 2002 Wiley Periodicals, Inc.	en
heal.publisher	JOHN WILEY & SONS INC	en
heal.journalName	INTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY	en
dc.identifier.isi	ISI:000176681600003	en
dc.identifier.volume	89	en
dc.identifier.issue	2	en
dc.identifier.spage	94	en
dc.identifier.epage	105	en