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Quantum systems with classical chaos can lead to global quantum diffusion. A model system demonstrates this, showing diffusion in additional modes when coupled, especially with sufficient degrees of freedom.

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Area of Science:

  • Quantum mechanics
  • Chaos theory
  • Statistical physics

Background:

  • Classical chaos in bounded quantum systems can induce global quantum diffusion.
  • A model system is needed to study this phenomenon effectively.

Purpose of the Study:

  • To investigate global quantum diffusion in systems with classical chaos.
  • To propose and analyze an ideal model system for studying quantum diffusion.

Main Methods:

  • Utilizing a small quantum chaotic system with finite Hilbert space dimension (N).
  • Weakly coupling this system with M additional degrees of freedom approximated by linear systems.
  • Employing system twinning for numerical investigation of diffusion in additional modes.

Main Results:

  • Quantum diffusion occurs in additional modes as coupling strength increases, provided M is at least 3.
  • For a sufficiently large Hilbert space dimension (N), a distinct quantum transition to diffusion is observed.
  • This transition is characterized by critical subdiffusion with an anomalous diffusion exponent.

Conclusions:

  • Weakly coupled quantum chaotic systems can exhibit global quantum diffusion.
  • The proposed model system effectively simulates diffusion without explicit unbounded spaces.
  • System size (N) and number of additional degrees of freedom (M) are critical factors in observing quantum diffusion and transitions.