Nash states versus eigenstates for many-body quantum systems
Fuente:
arXiv
Guardado en:
| Autores principales: | , , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2024
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866909214061887488 |
|---|---|
| author | Lin, Chuqiao Bulchandani, Vir B. Sondhi, Shivaji L. |
| author_facet | Lin, Chuqiao Bulchandani, Vir B. Sondhi, Shivaji L. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_21011 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Nash states versus eigenstates for many-body quantum systems Lin, Chuqiao Bulchandani, Vir B. Sondhi, Shivaji L. Quantum Physics Statistical Mechanics High Energy Physics - Theory 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. |
| title | Nash states versus eigenstates for many-body quantum systems |
| topic | Quantum Physics Statistical Mechanics High Energy Physics - Theory |
| url | https://arxiv.org/abs/2405.21011 |