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Quantum Lyapunov exponents beyond continuous measurements.

I I Yusipov1, O S Vershinina1, S Denisov2

  • 1Department of Applied Mathematics, Lobachevsky University, Nizhny Novgorod 603950, Russia.

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Researchers developed a new method to quantify dissipative quantum chaos using quantum trajectories. This approach reveals a period-doubling route to quantum chaos in open quantum systems, mirroring classical chaos.

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Area of Science:

  • Quantum physics
  • Nonlinear dynamics
  • Quantum information theory

Background:

  • Quantum systems interacting with environments can enter nonequilibrium states resembling classical chaotic attractors.
  • Quantifying dissipative quantum chaos is challenging due to limited tools, especially for quantum analogs of Lyapunov exponents.
  • Existing quantum Lyapunov exponents typically require continuous measurements, limiting their applicability.

Purpose of the Study:

  • To propose and validate an alternative method for quantifying dissipative quantum chaos.
  • To establish a connection between quantum chaos and classical chaos routes.
  • To explore quantum analogs of chaotic attractors in open quantum systems.

Main Methods:

  • Unraveling the quantum master equation into an ensemble of quantum trajectories.
  • Utilizing the Monte Carlo wave-function method for trajectory generation.
  • Analyzing a periodically modulated open quantum dimer as a model system.

Main Results:

  • The proposed method successfully quantifies dissipative quantum chaos.
  • The transition to quantum chaos in the model system was observed.
  • The observed transition followed a period-doubling route, consistent with classical systems.

Conclusions:

  • The quantum trajectory approach provides a viable alternative for quantifying dissipative quantum chaos.
  • The study demonstrates a shared period-doubling route to chaos in both classical and open quantum systems.
  • This work offers new insights into the nature of quantum chaos and its relation to classical chaos.