Quantum reaction-limited reaction–diffusion dynamics of noninteracting Bose gases

Abstract

We investigate quantum reaction–diffusion (RD) systems in one-dimension with bosonic particles that coherently hop in a lattice, and when brought in range react dissipatively. Such reactions involve binary annihilation ( $A + A \to \emptyset$ ) and coagulation ( $A + A \to A$ ) of particles at distance d . We consider the reaction-limited regime, where dissipative reactions take place at a rate that is small compared to that of coherent hopping. In classical RD systems, this regime is correctly captured by the mean-field approximation. In quantum RD systems, for noninteracting fermionic systems, the reaction-limited regime recently attracted considerable attention because it has been shown to give universal power law decay beyond mean field for the density of particles as a function of time. Here, we address the question whether such universal behavior is present also in the case of the noninteracting Bose gas. We show that beyond mean-field density decay for bosons is possible only for reactions that allow for destructive interference of different decay channels. Furthermore, we study an absorbing-state phase transition induced by the competition between branching $A\to A+A$ , decay $A\to \emptyset$ and coagulation $A+A\to A$ . We find a stationary phase-diagram, where a first and a second-order transition line meet at a bicritical point which is described by tricritical directed percolation. These results show that quantum statistics significantly impact on both the stationary and the dynamical universal behavior of quantum RD systems.

Keywords

• quantum reaction–diffusion systems
• dissipative many-body quantum systems
• quantum critical dynamics
• absorbings-state phase transitions
• Bose gas
• time-dependent generalized Gibbs ensemble