Open quantum reaction-diffusion dynamics: absorbing states and relaxation

Abstract

We consider an extension of classical stochastic reaction-diffusion (RD) dynamics to open quantum systems. We study a class of models of hard core particles on a one-dimensional lattice whose dynamics is generated by a quantum master operator and where particle hopping is coherent while reactions, such as pair annihilation or pair coalescence, are dissipative. These are quantum open generalisations of the $A+A\to \varnothing$ and $A+A\to A$ classical RD models. We characterise the relaxation of the state towards the stationary regime via a decomposition of the system Hilbert space into transient and recurrent subspaces. We provide a complete classification of the structure of the recurrent subspace (and the non-equilibrium steady states) in terms of the dark states associated to the quantum master operator and its general spectral properties. We also show that, in one dimension, relaxation towards these absorbing dark states is slower than that predicted by a mean-field analysis due to fluctuation effects, in analogy with what occurs in classical RD systems. Numerical simulations of small systems suggest that the decay of the density in one dimension, in both the open quantum $A+A\to \varnothing$ and $A+A\to A$ cases, may go asymptotically as $t^{-b}$ with $1/2<b<1$.

14 pages, 10 figures

References in corpus (20)

• Nonequilibrium Critical Phenomena and Phase Transitions into Absorbing States
• The Quantum Jump Approach to Dissipative Dynamics in Quantum Optics
• Quantum States and Phases in Driven Open Quantum Systems with Cold Atoms
• Preparation of Entangled States by Quantum Markov Processes
• Symmetries and conserved quantities in Lindblad master equations
• Dynamical Phase Transitions and Instabilities in Open Atomic Many-Body Systems
• Applications of Field-Theoretic Renormalization Group Methods to Reaction-Diffusion Problems
• Keldysh approach for non-equilibrium phase transitions in quantum optics: beyond the Dicke model in optical cavities
• Collective quantum jumps of Rydberg atoms
• Probability currents as principal characteristics in the statistical mechanics of non-equilibrium steady states
• Non-equilibrium dynamics of bosonic atoms in optical lattices: Decoherence of many-body states due to spontaneous emission
• Analysis of quantum semigroups with GKS--Lindblad generators II. General
• Statistical mechanics of the coagulation-diffusion process with a stochastic reset
• Complete parameterization, and invariance, of diffusive quantum trajectories for Markovian open systems
• Quantum System Identification
• Non-equilibrium dynamics of Ising models with decoherence: an exact solution
• Thermalization of a strongly interacting closed spin system: From coherent many-body dynamics to a Fokker-Planck equation
• Measurement of a reaction-diffusion crossover in exciton-exciton recombination inside carbon nanotubes using femtosecond optical absorption
• Many-body out-of-equilibrium dynamics of hard-core lattice bosons with non-local loss
• Identifiability of Open Quantum Systems

Cited by in corpus (14)

• Keldysh Field Theory for Driven Open Quantum Systems
• Universality in driven open quantum matter
• Quantum dynamical field theory for non-equilibrium phase transitions in driven open systems
• Reaction-limited quantum reaction-diffusion dynamics
• Lindblad dynamics of a quantum spherical spin
• Large-scale universality in quantum reaction-diffusion from Keldysh field theory
• Quantum reaction-limited reaction-diffusion dynamics of annihilation processes
• Signatures of a quantum stabilized fluctuating phase and critical dynamics in a kinetically-constrained open many-body system with two absorbing states
• Quantum reaction-limited reaction-diffusion dynamics of noninteracting Bose gases
• Field theories and quantum methods for stochastic reaction-diffusion systems
• Dissipative quantum many-body dynamics in (1+1)D quantum cellular automata and quantum neural networks
• Reaction-diffusion dynamics of the weakly dissipative Fermi gas
• Kinetics of Quantum Reaction-Diffusion systems
• Absorbing state phase transitions beyond directed percolation in dissipative quantum state preparation