标题： 纳什态与多体量子系统的本征态 显示英文标题

标题： Nash states versus eigenstates for many-body quantum systems

摘要： 可观测量（如哈密顿量）的本征态在量子力学中起着核心作用。 受经典博弈论中纯纳什均衡的启发，我们提出多个可观测量的“纳什态”，作为单个可观测量本征态的推广。 这种推广对于具有内在张量积结构的多体量子系统来说在数学上是自然的。 每个可观测量集合都会产生我们称之为“纳什流形”的纳什态向量代数流形。 我们提供了关于纳什态存在性和纳什流形几何性的分析和数值结果。 我们将这些思想与早期关于少体量子博弈纳什均衡的开创性工作联系起来，并讨论与局部哈密顿量变分最小化的关系。 显示英文摘要

摘要： 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.