Universal asymptotic behavior in nonlinear systems driven by a two-frequency forcing

Casado‐Pascual, Jesús; Cubero, David; Renzoni, Ferruccio

doi:10.1103/physreve.88.062919

Cited by 9 publications

(15 citation statements)

References 20 publications

(21 reference statements)

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“…Using equation (8), it can easily be seen that the stationary value Q st t (Ω 0 , ϕ) is a T -periodic function of time. A further interesting fact is that the infinite-time average Q ∞ (Ω 0 , ϕ) displays a higher symmetry in ϕ than the obvious ϕ 1 → ϕ 1 + 2π and ϕ 2 → ϕ 2 + 2π [14]. To see that this is so, note that in the present case the condition k • Ω 0 = 0 becomes equivalent to k 1 q + k 2 p = 0.…”

Section: Commensurable Frequencies and Periodicity In ϕmentioning

confidence: 68%

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Generic shape of multichromatic resonance peaks

Olivera,

Casado-Pascual,

Kohler

2019

Preprint

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We investigate dissipative dynamical systems under the influence of an external driving with two or more frequencies. Our main quantities of interest are long-time averages of expectation values which turn out to exhibit universal features. In particular, resonance peaks in the vicinity of commensurable frequencies possess a generic enveloping function whose width is inversely proportional to the averaging time. While the universal features can be derived analytically, the transition from the specific short-time behavior to the long-time limit is illustrated for the examples of a classical random walk and a dissipative two-level system both with biharmonic driving. In these models, the dependence of the time-averaged response on the relative phase between the two driving frequencies changes with increasing integration time. For short times, it exhibits the 2π periodicity of the dynamic equations, while in the long-time limit, the period becomes a fraction of this value.

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Section: Commensurable Frequencies and Periodicity In ϕmentioning

confidence: 68%

“…The common physics behind these phenomena is an interplay of non-linearities and non-equilibrium. Driven systems have been studied in the Hamiltonian limit [11][12][13], as well as in the steady state of dissipative classical [8,9,14,15] and quantum mechanical models [16][17][18].…”

Section: Introductionmentioning

confidence: 99%

Generic shape of multichromatic resonance peaks

Olivera,

Casado-Pascual,

Kohler

2019

Preprint

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“…It was in particular shown that for the kicked rotor system quantum interference leads to a sub-Fourier response [1][2][3]. Sub-Fourier behaviour was also observed in bi-harmonically driven classical systems [4]. In both cases, the underlying mechanism relies on the system's extreme sensitivity to the nature of the driving, with periodic and quasiperiodic drivings leading to a completely different response.…”

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confidence: 95%

Avoided Crossing and sub-Fourier-sensitivity in Driven Quantum Systems

2018

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The response of a linear system to an external perturbation is governed by the Fourier limit, with the inverse of the interaction time constituting a lower limit for the system bandwidth. This does not hold for nonlinear systems, which can thus exhibit sub-Fourier behavior. The present work identifies a mechanism for sub-Fourier sensitivity in driven quantum systems, which relies on avoided crossing between Floquet states. Features up to three orders of magnitude finer than the Fourier limit are presented.

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“…In Sec. III we revisit the * dcubero@us.es † f.renzoni@ucl.ac.uk asymptotic theory for classical systems [9,10] which will be useful as an introduction to the quantum case, fully discussed in Sec. IV.…”

Section: Introductionmentioning

confidence: 99%

Asymptotic theory of quasiperiodically driven quantum systems

Cubero

Renzoni

2018

Phys. Rev. E

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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.

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Universal asymptotic behavior in nonlinear systems driven by a two-frequency forcing

Cited by 9 publications

References 20 publications

Generic shape of multichromatic resonance peaks

Generic shape of multichromatic resonance peaks

Avoided Crossing and sub-Fourier-sensitivity in Driven Quantum Systems

Asymptotic theory of quasiperiodically driven quantum systems

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