General approach for dealing with dynamical systems with spatiotemporal periodicities

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
Jesús Casado-PascualRenato Alvarez-Nodarse

Abstract

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.

References

Jul 22, 1991·Physical Review Letters·F GrossmannP Hänggi
May 15, 1995·Physical Review Letters·J C RobinsonB Sundaram
Apr 5, 2003·Chaos·Jan A FreundPeter Hänggi
Dec 20, 2003·Physical Review Letters·Jesús Casado-PascualPeter Hänggi
Jun 1, 2004·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·J Casado-Pascual, J P Baltanás
Feb 9, 2005·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Jesús Casado-PascualPeter Hänggi
Jul 23, 2005·Chaos·Jesús Casado-PascualManuel Morillo
Aug 16, 2006·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·David CuberoJesús Casado-Pascual
Dec 13, 2006·Physical Review Letters·Igor GoychukPeter Hänggi
Apr 28, 2009·Physical Review Letters·Dario PolettiBaowen Li
Aug 8, 2009·Physical Review Letters·A V PonomarevP Hänggi
Dec 12, 2012·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·David Cubero, Ferruccio Renzoni
Feb 4, 2014·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Jesús Casado-PascualFerruccio Renzoni
May 20, 2014·Physical Review Letters·David CuberoFerruccio Renzoni

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Citations

Jan 23, 2016·Physical Review Letters·David Cubero, Ferruccio Renzoni
May 14, 2016·Physical Review. E·Niurka R QuinteroA R Bishop
Aug 31, 2016·Physical Review. E·Bernardo Sánchez-ReyNiurka R Quintero
Jun 4, 2019·Chaos·Jesús Casado-PascualNiurka R Quintero

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