Open quantum reaction-diffusion dynamics: Absorbing states and relaxation

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.