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Quantum Neimark-Sacker bifurcation.

I I Yusipov1, M V Ivanchenko2

  • 1Department of Applied Mathematics, Lobachevsky University, Nizhny Novgorod, Russia.

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|December 1, 2019
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Summary
This summary is machine-generated.

Researchers discovered a quantum Neimark-Sacker bifurcation in open quantum systems, transitioning distributions from unimodal to bagel shapes. This quantum bifurcation is sensitive to particle number, offering new control parameters for quantum dynamics.

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Area of Science:

  • Quantum dynamics
  • Nonlinear quantum systems
  • Quantum chaos

Background:

  • Open quantum systems can exhibit classical-like bifurcations.
  • Previous studies showed pitchfork, saddle-node, and period-doubling bifurcations in quantum systems.
  • Understanding bifurcations is key to controlling quantum states.

Purpose of the Study:

  • To investigate a quantum Neimark-Sacker bifurcation in a periodically modulated open quantum dimer model.
  • To characterize the transition from unimodal to bagel-shaped distributions.
  • To explore the role of particle number as a control parameter.

Main Methods:

  • Utilized a periodically modulated open quantum dimer model.
  • Employed Quantum Monte-Carlo wave function (QMCWF) unraveling of the Lindblad master equation.
  • Analyzed spectral properties of the Floquet map and stroboscopic distributions (Husimi representation).

Main Results:

  • Observed a quantum Neimark-Sacker bifurcation, analogous to the classical birth of a torus.
  • Demonstrated a transition from unimodal to bagel-shaped stroboscopic distributions.
  • Identified spectral changes in the Floquet map (eigenvalues approaching the unit circle).
  • Quantified single trajectory dynamics on a "quantum torus" using rotation number.

Conclusions:

  • The quantum Neimark-Sacker bifurcation is a novel phenomenon in open quantum systems.
  • The particle number acts as a sensitive control parameter for this bifurcation.
  • This finding opens avenues for controlling quantum dynamics and exploring quantum chaos.