We investigate the quantum reaction-diffusion dynamics of fermionic particles which coherently hop in a one-dimensional lattice and undergo annihilation reactions. The latter are modelled as dissipative processes which involve losses of pairs 2A→∅, triplets 3A→∅, and quadruplets 4A→∅ of neighboring particles. When considering classical particles, the corresponding decay of their density in time follows an asymptotic power-law behavior. The associated exponent in one dimension is different from the mean-field prediction whenever diffusive mixing is not too strong and spatial correlations are relevant. This specifically applies to 2A→∅, while the mean-field power-law prediction just acquires a logarithmic correction for 3A→∅ and is exact for 4A→∅. A mean-field approach is also valid, for all the three processes, when the diffusive mixing is strong, i.e., in the so-called reaction-limited regime. Here we show that the picture is different for quantum systems. We consider the quantum reaction-limited regime and we show that for all the three processes power-law behavior beyond mean field is present as a consequence of quantum coherences, which are not related to space dimensionality. The decay in 3A→∅ is further, highly intricate, since the power-law behavior therein only appears within an intermediate time window, while at long times the density decay is not power law. Our results show that emergent critical behavior in quantum dynamics has a markedly different origin, based on quantum coherences, to that applying to classical critical phenomena, which is, instead, solely determined by the relevance of spatial correlations.

arXiv:2305.06944Physical review. EDec 4, 202313 citations

Reaction-diffusion processes and their connection with integrable quantum spin chains

Malte Henkel

This is a pedagogical account on reaction-diffusion systems and their relationship with integrable quantum spin chains.Reaction-diffusion systems are paradigmatic examples of non-equilibrium systems.Their long-time behaviour is strongly influenced through fluctuation effects in low dimensions which renders the habitual mean-field kinetic equations inapplicable.Starting from the master equation rewritten as a Schrödinger equation with imaginary time, the associated quantum Hamiltonian of certain one-dimensional reaction-diffusion models is closely related to integrable magnetic chains.The relationship with the Hecke algebra and its quotients allows to identify integrable reaction-diffusion models and, through the Baxterization procedure, relate them to the solutions of Yang-Baxter equations which can be solved via the Bethe ansatz.Methods such as spectral and partial integrability, free fermions, similarity transformations or diffusion algebras are reviewed, with several concrete examples treated explicitly.An outlook on how the recently-introduced concept of local scale invariance might become useful in the description of nonequilibrium ageing phenomena is presented, with particular emphasis on the kinetic Ising model with Glauber dynamics.

Institute of Physics eBooksNov 26, 20040 citations