Population dynamics of Schrödinger cats
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-cla...
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| Language: | English |
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2025-02-01
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| Series: | SciPost Physics |
| Online Access: | https://scipost.org/SciPostPhys.18.2.046 |
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| author | Foster Thompson, Alex Kamenev |
| author_facet | Foster Thompson, Alex Kamenev |
| author_sort | Foster Thompson, Alex Kamenev |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-54bce9f76fb340309e84d1a340ce4159 |
| institution | Kabale University |
| issn | 2542-4653 |
| language | English |
| publishDate | 2025-02-01 |
| publisher | SciPost |
| record_format | Article |
| series | SciPost Physics |
| spelling | doaj-art-54bce9f76fb340309e84d1a340ce41592025-02-06T12:30:09ZengSciPostSciPost Physics2542-46532025-02-0118204610.21468/SciPostPhys.18.2.046Population dynamics of Schrödinger catsFoster Thompson, Alex KamenevWe 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.https://scipost.org/SciPostPhys.18.2.046 |
| spellingShingle | Foster Thompson, Alex Kamenev Population dynamics of Schrödinger cats SciPost Physics |
| title | Population dynamics of Schrödinger cats |
| title_full | Population dynamics of Schrödinger cats |
| title_fullStr | Population dynamics of Schrödinger cats |
| title_full_unstemmed | Population dynamics of Schrödinger cats |
| title_short | Population dynamics of Schrödinger cats |
| title_sort | population dynamics of schrodinger cats |
| url | https://scipost.org/SciPostPhys.18.2.046 |
| work_keys_str_mv | AT fosterthompsonalexkamenev populationdynamicsofschrodingercats |