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Quantum Neimark-Sacker bifurcation
1Department of Applied Mathematics, Lobachevsky University, Nizhny Novgorod, Russia.
Scientific Reports
|December 1, 2019
Summary
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.
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.
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