Asymptotic theory of quasiperiodically driven quantum systems

Physical Review. E
David Cubero, F Renzoni

Abstract

The theoretical treatment of quasiperiodically driven quantum systems is complicated by the inapplicability of the Floquet theorem, which requires strict periodicity. In this work we consider a quantum system driven by a biharmonic driving and examine its asymptotic long-time limit, the limit in which features distinguishing systems with periodic and quasiperiodic driving occur. Also, in the classical case this limit is known to exhibit universal scaling, independent of the system details, with the system's reponse under quasiperiodic driving being described in terms of nearby periodically driven system results. We introduce a theoretical framework appropriate for the treatment of the quasiperiodically driven quantum system in the long-time limit and derive an expression, based on Floquet states for a periodically driven system approximating the different steps of the time evolution, for the asymptotic scaling of relevant quantities for the system at hand. These expressions are tested numerically, finding excellent agreement for the finite-time average velocity in a prototypical quantum ratchet consisting of a space-symmetric potential and a time-asymmetric oscillating force.

References

Dec 8, 2009·Science·Tobias SalgerMartin Weitz
May 24, 2011·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Philipp Bader, Sergio Blanes
Apr 16, 2013·Physical Review Letters·Tobias SalgerMartin Weitz
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
Feb 9, 2016·Nature Communications·Christopher GrossertMartin Weitz

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Citations

Dec 6, 2018·Physical Review Letters·David CuberoFerruccio Renzoni
Mar 31, 2021·Physical Review Letters·David M LongAnushya Chandran

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