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. Particle hopping is coherent while reactions, such as pair annihilation or pair coalescence, are dissipative. These are quantum open generalizations of the A+A→⌀ and A+A→A classical RD models. We characterize 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 nonequilibrium 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→⌀ and A+A→A systems, behaves asymptotically as t-b with 1/2<b<1.

Keldysh Field Theory for Driven Open Quantum Systems

“…( 73) the rates can be tuned fully independently from the Hamiltonian parameters -they have completely different physical origins. Finally, we note that, while an explicit violation of the sym-metry is present on the microscopic scales on which the quantum master equation ( 16) or the corresponding Keldysh action (27) provide a suitable description of the system, in several cases it has been found that driven-dissipative systems appear as approximately thermal at low frequencies [25,33,54,110,112,122,191,213,214]. In driven-dissipative condensates in three spatial dimensions, this thermalization at low frequencies is particularly sharply reflected via the emergence of the thermal symmetry in the RG flow in this regime [26,181], cf.…”

Quantum dynamical field theory for nonequilibrium phase transitions in driven open systems

“…In addition to these relevant examples, drivendissipative quantum many body systems, i.e. manyparticle systems where quantum coherent dynamics and dissipative effects occur on the same footing, can constitute a promising platform [55][56][57][58][59][60][61][62] to initiate a systematic classification of quantum dynamical criticality [63][64][65][66][67][68][69][70][71] .…”

Keldysh field theory for driven open quantum systems

“…(73) the rates can be tuned fully independently from the Hamiltonian parameters -they have completely different physical origins. Finally, we note that, while an explicit violation of the symmetry is present on the microscopic scales on which the quantum master equation (16) or the corresponding Keldysh action (27) provide a suitable description of the system, in several cases it has been found that driven-dissipative systems appear as approximately thermal at low frequencies [25,33,54,110,112,122,191,213,214]. In driven-dissipative condensates in three spatial dimensions, this thermalization at low frequencies is particularly sharply reflected via the emergence of the thermal symmetry in the RG flow in this regime [26,181], cf.…”

“…This rules out conventional theoretical equilibrium concepts and techniques to be used, and calls for the development of new theoretical tools. The physical framework sparks broader theoretical questions on the existence of new phases of bosonic [18,19] and fermionic [20][21][22] matter, the nature of phase transitions in such driven systems [10,[23][24][25][26], and the observable consequences of quantum mechanics at the largest scales [27,28]. Beyond stationary states [29], a fundamental challenge is set by the time evolution of interacting quantum systems, which is currently explored theoretically [30][31][32][33][34][35][36] and experimentally in cold atomic [37][38][39][40][41] and photonic systems [42].…”