Population Dynamics of Schrödinger Cats

Abstract

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 {\em 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 ``Schrödigner 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.

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Cited by in corpus (4)

• Stabilizing Non-Abelian Topological Order against Heralded Noise via Local Lindbladian Dynamics
• Absorbing state phase transitions beyond directed percolation in dissipative quantum state preparation
• Non-perturbative switching rates in bistable open quantum systems: from driven Kerr oscillators to dissipative cat qubits
• Control-driven critical fluctuations across quantum trajectories