Population Dynamics of Schr\"odinger Cats

TL;DR

This paper introduces quantum population dynamics models that extend classical population theories by allowing superpositions of population states, revealing a new quantum phase transition with unique critical scaling.

Contribution

It develops a field theory framework combining Keldysh and third quantization techniques for quantum populations, and identifies a novel quantum phase transition in a Schr"odinger cat population model.

Findings

Existence of a phase transition between dark and active quantum populations.

Distinct critical scaling behavior from classical and standard quantum phase transitions.

Application of renormalization group methods to analyze the transition.

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 Schr\"odinger'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 ``Schr\"odigner 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 Schr\"odinger cat population distinct from that observed in both classical population dynamics and usual quantum phase transitions.