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Analytic approaches to periodically driven closed quantum systems: methods and applications.

Arnab Sen1, Diptiman Sen2, K Sengupta1

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This study overviews analytic perturbative techniques for computing the Floquet Hamiltonian in quantum many-body systems. These methods offer insights into phenomena like the Floquet-Magnus expansion and rotating wave approximation.

Keywords:
Floquet Hamiltonianmany-body theorynon-equilibrium dynamicsperiodically driven systems

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Area of Science:

  • Quantum Many-Body Physics
  • Theoretical Physics

Background:

  • Periodically driven quantum systems exhibit unique behaviors.
  • Calculating the Floquet Hamiltonian is crucial for understanding these systems.

Purpose of the Study:

  • To provide a pedagogical overview of analytic perturbative techniques.
  • To discuss phenomena illuminated by these computational methods.

Main Methods:

  • Floquet-Magnus (FM) expansion
  • Adiabatic-impulse approximation
  • Floquet perturbation theory
  • Rotating wave approximation
  • Hamiltonian flow method

Main Results:

  • Detailed explanations of key technical aspects of each method.
  • Demonstration of the utility of these techniques in explaining physical phenomena.

Conclusions:

  • These methods provide valuable tools for analyzing Floquet quantum systems.
  • Open problems remain that can be addressed with these techniques.