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Area of Science:

  • Quantum physics
  • Statistical mechanics
  • Condensed matter theory

Background:

  • Classical reaction-diffusion (RD) models describe particle dynamics with hopping and reactions.
  • Open quantum systems involve interactions with an environment, leading to dissipation.
  • Understanding quantum generalizations of classical RD is crucial for quantum many-body physics.

Purpose of the Study:

  • To extend classical stochastic reaction-diffusion dynamics to open quantum systems.
  • To analyze quantum open generalizations of A+A→⌀ and A+A→A models.
  • To characterize relaxation dynamics and stationary states in these quantum systems.

Main Methods:

  • Utilizing a quantum master operator to generate system dynamics.
  • Decomposing the system's Hilbert space into transient and recurrent subspaces.
  • Analyzing spectral properties and dark states of the quantum master operator.

Main Results:

  • Developed quantum open reaction-diffusion models with coherent hopping and dissipative reactions.
  • Classified the structure of recurrent subspaces and nonequilibrium steady states using dark states.
  • Demonstrated slower-than-mean-field relaxation in one dimension due to quantum fluctuation effects.

Conclusions:

  • Quantum fluctuations significantly impact relaxation dynamics in one-dimensional open quantum RD systems.
  • The asymptotic decay of particle density follows a power law t⁻ᵇ with 1/2 < b < 1.
  • These findings offer insights into the behavior of open quantum many-body systems with dissipative interactions.