TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhys.18.2.046
TI  - Population dynamics of Schrödinger cats
PY  - 2025/02/06
UR  - https://www.scipost.org/SciPostPhys.18.2.046
JF  - SciPost Physics
JA  - SciPost Phys.
VL  - 18
IS  - 2
SP  - 046
A1  - Thompson, Foster
AU  - Kamenev, Alex
AB  - 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.
ER  -

@Article{10.21468/SciPostPhys.18.2.046,
	title={{Population dynamics of Schrödinger cats}},
	author={Foster Thompson and Alex Kamenev},
	journal={SciPost Phys.},
	volume={18},
	pages={046},
	year={2025},
	publisher={SciPost},
	doi={10.21468/SciPostPhys.18.2.046},
	url={https://scipost.org/10.21468/SciPostPhys.18.2.046},
}