SciPost Phys. 18, 046 (2025) ·
published 6 February 2025
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We demonstrate an exact equivalence between classical population dynamics and Lindbladian evolution admitting a dark state and obeying a set of certain local symmetries. We then introduce quantum population dynamics as models in which this local symmetry condition is relaxed. This allows for non-classical processes in which animals behave like Schrödinger's cat and enter superpositions of live and dead states, thus resulting in coherent superpositions of different population numbers. We develop a field theory treatment of quantum population models as a synthesis of Keldysh and third quantization techniques and draw comparisons to the stochastic Doi-Peliti field theory description of classical population models. We apply this formalism to study a prototypical "Schrödinger cat" population model on a $d$-dimensional lattice, which exhibits a phase transition between a dark extinct phase and an active phase that supports a stable quantum population. Using a perturbative renormalization group approach, we find a critical scaling of the Schrödinger cat population distinct from that observed in both classical population dynamics and usual quantum phase transitions.
