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Reaction-diffusion models, where particles are allowed to react when they meet, display genuine non-equilibrium behaviour. In classical settings, it has been shown that universal properties arise, and that non-equilibrium steady-state phase transitions between fluctuating and absorbing phases can appear. Recent studies have shown that quantum dynamics can modify the properties of critical non-equilibrium systems, and that even the reaction-limited asymptotics cannot be properly described by a mean-field approximation. Starting from the quantum Master equation, we propose a field-theoretical approach to the study of quantum reaction-diffusion systems, building on the Keldysh formalism. We tackle the problem starting from the two-particle loss process A + A -> O. By means of a perturbative expansion, we exploit the Dyson equation in order to derive Boltzmann-like equations for the bosonic and fermionic particle densities. These are compared to the classical and quantum reaction-limited rate equations, and are solved both in the homogeneous and non-homogeneous case. We study the dynamics of a quench from a double- to a single-well confining potential, where a novel decay regime is reached.

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Federico Gerbino, Uni Tuebingen
Seminar Room 0.03, ETP
Contact: Sebastian Diehl