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Effective time-independent analysis for quantum kicked systems.

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Summary
This summary is machine-generated.

We mapped chaotic quantum systems to simpler, integrable ones. This effective Hamiltonian accurately models the original system

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Area of Science:

  • Quantum mechanics
  • Statistical physics
  • Nonlinear dynamics

Background:

  • Time-dependent quantum systems can exhibit chaotic behavior.
  • Analyzing these systems is computationally challenging.
  • Traditional methods like Baker-Campbell-Hausdorff can lead to divergences.

Purpose of the Study:

  • To develop an approximate mapping of chaotic time-dependent quantum systems to integrable time-independent systems.
  • To introduce an effective Hamiltonian that avoids spurious divergences.
  • To validate the effective Hamiltonian against the original system's behavior.

Main Methods:

  • Factorizing time evolution into discrete kicks and time-independent Hamiltonian evolution.
  • Applying the method to the kicked top model.
  • Comparing quasienergy spectra and density of states.

Main Results:

  • An effective time-independent Hamiltonian was derived for chaotic quantum systems.
  • The quasienergy spectrum of the Floquet operator matched the effective Hamiltonian's energy levels.
  • Density of states revealed quantum criticality.
  • Classical dynamics of the effective Hamiltonian agreed with the nonchaotic regime of the original system.

Conclusions:

  • The effective Hamiltonian provides an accurate approximation for chaotic quantum systems in the nonchaotic regime.
  • This method simplifies the analysis of complex quantum dynamics.
  • The approach is valid at both quantum and classical levels.