RT Journal Article
T1 General approach for dealing with dynamical systems with spatiotemporal periodicities
A1 Casado Pascual, Jesús
A1 Cuesta, José A.
A1 Rodríguez Quintero, Niurka
A1 Álvarez Nodarse, Renato
AB Dynamical systems often contain oscillatory forces or depend on periodic potentials. Time or space periodicity is reflected in the properties of these systems through a dependence on the parameters of their periodic terms. In this paper we provide a general theoretical framework for dealing with these kinds of systems, regardless of whether they are classical or quantum, stochastic or deterministic, dissipative or nondissipative, linear or nonlinear, etc. In particular, we are able to show that simple symmetry considerations determine, to a large extent, how their properties depend functionally on some of the parameters of the periodic terms. For the sake of illustration, we apply this formalism to find the functional dependence of the expectation value of the momentum of a Bose-Einstein condensate, described by the Gross-Pitaewskii equation, when it is exposed to a sawtooth potential whose amplitude is periodically modulated in time. We show that, by using this formalism, a small set of measurements is enough to obtain the functional form for a wide range of parameters. This can be very helpful when characterizing experimentally the response of systems for which performing measurements is costly or difficult.
PB American Physical Society
SN 1539-3755
YR 2015
FD 2015-02-09
LK https://hdl.handle.net/10016/21452
UL https://hdl.handle.net/10016/21452
LA eng
NO This work has been supported by through Grants No. MTM2012-36732-C03-03 (R.A.N.), No. FIS2011-24540 (N.R.Q.), and PRODIEVO (J.A.C.), from the Ministerio de Economía y Competitividad (Spain), Grants No. FQM262 (R.A.N.), No. FQM207 (N.R.Q.), and Nos. FQM-7276 and P09-FQM-4643 (N.R.Q., R.A.N.), from the Ministerio de Ciencia e Innovación of Spain, Grant No. FIS2008-02873 (J.C.-P.), from Junta de Andalucía (Spain), and from the Alexander von Humboldt-Stiftung, Germany, through Research Fellowship for Experienced Researchers SPA, Grant No. 1146358 STP (N.R.Q.).
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RD 1 sept. 2024