Nash states versus eigenstates for many-body quantum systems

Nash states versus eigenstates for many-body quantum systems

Eigenstates of observables such as the Hamiltonian play a central role in quantum mechanics. Inspired by the pure Nash equilibria that arise in classical game theory, we propose ''Nash states'' of multiple observables as a generalization of eigenstates of single observables. This...

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Veröffentlicht in:arXiv.org 2024-05
Hauptverfasser: Lin, Chuqiao, Bulchandani, Vir B, Sondhi, Shivaji L
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Eigenvectors
Game theory
Hamiltonian functions
Quantum mechanics
State vectors
Tensors
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description Eigenstates of observables such as the Hamiltonian play a central role in quantum mechanics. Inspired by the pure Nash equilibria that arise in classical game theory, we propose ''Nash states'' of multiple observables as a generalization of eigenstates of single observables. This generalization is mathematically natural for many-body quantum systems, which possess an intrinsic tensor product structure. Every set of observables gives rise to algebraic varieties of Nash state vectors that we call ''Nash varieties''. We present analytical and numerical results on the existence of Nash states and on the geometry of Nash varieties. We relate these ideas to earlier, pioneering work on the Nash equilibria of few-body quantum games and discuss connections to the variational minimization of local Hamiltonians.
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subjects Eigenvectors
Game theory
Hamiltonian functions
Quantum mechanics
State vectors
Tensors
title Nash states versus eigenstates for many-body quantum systems
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