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Phase-space mixing in dynamically unstable, integrable few-mode quantum systems.

R Mathew1, E Tiesinga2

  • 1Joint Quantum Institute, University of Maryland and National Institute of Standards and Technology, College Park, Maryland 20742, USA.

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Summary
This summary is machine-generated.

Quantum systems quench and relax to steady states via phase-space mixing. This study reveals deviations from classical values scale with 1/ln N, with relaxation as damped oscillations.

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Area of Science:

  • Quantum physics
  • Many-body systems
  • Quantum dynamics

Background:

  • Isolated quantum systems and quenches are areas of active research.
  • Quantum few-mode systems integrable in the classical mean-field limit exhibit dynamic instability post-quench.

Purpose of the Study:

  • Investigate the dynamics of quantum few-mode systems after a parameter quench.
  • Analyze relaxation to steady states and deviations from classical behavior.

Main Methods:

  • Truncated Wigner Approximation (TWA) for time dynamics.
  • Action-angle formalism and pendulum analogy for analytical expressions.
  • Numerical TWA simulations for validation.

Main Results:

  • Systems relax to a steady state through phase-space mixing.
  • Deviation from classical values scales as O(1/ln N), where N is the number of atoms.
  • Relaxation occurs as Gaussian-damped oscillations with a time scale of O[(ln N)^2].

Conclusions:

  • The study provides analytical expressions for time evolution and steady-state limits.
  • Quantitative dependencies of steady-state values and damping times on system parameters are determined.
  • Results are validated through numerical simulations, confirming the theoretical findings.