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Asymptotic theory of quasiperiodically driven quantum systems
David Cubero1, Ferruccio Renzoni2
1Departamento de Física Aplicada I, EUP, Universidad de Sevilla, Calle Virgen de África 7, 41011 Sevilla, Spain.
Physical Review. E
|July 18, 2018
Summary
We developed a new theory for quasiperiodically driven quantum systems, overcoming limitations of the Floquet theorem. Our findings reveal universal scaling in the long-time limit, validated by quantum ratchet simulations.
Area of Science:
- Quantum mechanics
- Non-equilibrium physics
- Theoretical physics
Background:
- The Floquet theorem, crucial for analyzing periodically driven quantum systems, is inapplicable to quasiperiodic driving.
- Understanding the long-time behavior of driven quantum systems is essential for exploring non-equilibrium phenomena.
- Classical quasiperiodic driving exhibits universal scaling, offering a potential parallel for quantum systems.
Purpose of the Study:
- To develop a theoretical framework for quasiperiodically driven quantum systems in the asymptotic long-time limit.
- To derive expressions for asymptotic scaling based on Floquet states of approximating periodic systems.
- To numerically validate the theoretical framework using a quantum ratchet model.
Main Methods:
- Consideration of a quantum system subjected to biharmonic driving.
- Examination of the asymptotic long-time limit where periodic and quasiperiodic driving behaviors diverge.
- Development of a theoretical framework utilizing Floquet states of approximating periodic systems.
- Numerical testing of derived expressions for asymptotic scaling.
Main Results:
- A theoretical framework for quasiperiodically driven quantum systems in the long-time limit was established.
- Expressions for asymptotic scaling of relevant quantities were derived, based on Floquet states.
- Numerical simulations of a quantum ratchet showed excellent agreement with the derived scaling expressions for finite-time average velocity.
Conclusions:
- The developed theoretical framework accurately describes the asymptotic long-time limit of quasiperiodically driven quantum systems.
- The study demonstrates universal scaling properties in the long-time limit, analogous to classical systems.
- The findings provide a method for analyzing complex driven quantum systems beyond the scope of the standard Floquet theorem.
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