Metastability of breather modes of time-dependent potentials
dc.contributor.author | Miller, P. D. | en_US |
dc.contributor.author | Soffer, A. | en_US |
dc.contributor.author | Weinstein, Michael I. | en_US |
dc.date.accessioned | 2006-12-19T19:12:03Z | |
dc.date.available | 2006-12-19T19:12:03Z | |
dc.date.issued | 2000-05-01 | en_US |
dc.identifier.citation | Miller, P D; Soffer, A; Weinstein, M I (2000). "Metastability of breather modes of time-dependent potentials." Nonlinearity. 13(3): 507-568. <http://hdl.handle.net/2027.42/49071> | en_US |
dc.identifier.issn | 0951-7715 | en_US |
dc.identifier.uri | https://hdl.handle.net/2027.42/49071 | |
dc.description.abstract | We study the solutions of linear Schrödinger equations in which the potential energy is a periodic function of time and is sufficiently localized in space. We consider the potential to be close to one that is time periodic and yet explicitly solvable. A large family of such potentials has been constructed and the corresponding Schrödinger equation solved by Miller and Akhmediev. Exact bound states, or breather modes, exist in the unperturbed problem and are found to be generically metastable in the presence of small periodic perturbations. Thus, these states are long-lived but eventually decay. On a time scale of order -2 , where is a measure of the perturbation size, the decay is exponential, with a rate of decay given by an analogue of Fermi's golden rule. For times of order -1 the breather modes are frequency shifted. This behaviour is derived first by classical multiple-scale expansions, and then in certain circumstances we are able to apply the rigorous theory developed by Soffer and Weinstein and extended by Kirr and Weinstein to justify the expansions and also provide longer-time asymptotics that indicate eventual dispersive decay of the bound states with behaviour that is algebraic in time. As an application, we use our techniques to study the frequency dependence of the guidance properties of certain optical waveguides. We supplement our results with numerical experiments. | en_US |
dc.format.extent | 3118 bytes | |
dc.format.extent | 962286 bytes | |
dc.format.mimetype | text/plain | |
dc.format.mimetype | application/pdf | |
dc.language.iso | en_US | |
dc.publisher | IOP Publishing Ltd | en_US |
dc.title | Metastability of breather modes of time-dependent potentials | en_US |
dc.type | Article | en_US |
dc.subject.hlbsecondlevel | Mathematics | en_US |
dc.subject.hlbsecondlevel | Physics | en_US |
dc.subject.hlbtoplevel | Science | en_US |
dc.description.peerreviewed | Peer Reviewed | en_US |
dc.contributor.affiliationother | Department of Mathematics and Statistics, Monash University, Clayton, Victoria 3800, Australia and | en_US |
dc.contributor.affiliationother | Department of Mathematics, Hill Center, Rutgers University, 110 Frelinghuysen Road, Piscataway, NJ 08854-8019, USA | en_US |
dc.contributor.affiliationother | Mathematical Sciences Research, Bell Labs 2C-358, Lucent Technologies, 600 Mountain Avenue, Murray Hill, NJ 07974, USA and | en_US |
dc.description.bitstreamurl | http://deepblue.lib.umich.edu/bitstream/2027.42/49071/2/no0303.pdf | en_US |
dc.identifier.doi | http://dx.doi.org/10.1088/0951-7715/13/3/303 | en_US |
dc.identifier.source | Nonlinearity. | en_US |
dc.owningcollname | Interdisciplinary and Peer-Reviewed |
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