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

Abstract

We investigate quantum reaction-diffusion 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 ($A+A\to \varnothing$) 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 reaction-diffusion systems, this regime is correctly captured by the mean-field approximation. In quantum reaction-diffusion systems, for non-interacting 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 non-interacting 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 $A\to \varnothing$ 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 reaction-diffusion systems.

22 pages: 15 pages main text, 6 figures, 5 pages appendices, 3 pages references

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• Instability of the engineered dark state in two-band fermions under number-conserving dissipative dynamics
• Dissipation-Induced Steady States in Topological Superconductors: Mechanisms and Design Principles
• Kinetics of Quantum Reaction-Diffusion systems