Related papers: Nash states versus eigenstates for many-body quant…
In this paper I propose a new way for counting the microstates of a system out of equilibrium. As, according to quantum mechanics, things happen as if a given particle can be found in more than one state at once, I extend this concept to…
In the context of large population symmetric games, approximate Nash equilibria are introduced through equilibrium solutions of the corresponding mean field game in the sense that the individual gain from optimal unilateral deviation under…
Foundation models are highly versatile neural-network architectures capable of processing different data types, such as text and images, and generalizing across various tasks like classification and generation. Inspired by this success, we…
We discuss the the notion of a partial dynamical symmetry (PDS), for which a prescribed symmetry is obeyed by only a subset of solvable eigenstates, while other eigenstates are strongly mixed. We present an explicit construction of…
We consider isolated quantum systems with all of their many-body eigenstates localized. We define a sense in which such systems are integrable, and discuss a method for finding their localized conserved quantum numbers ("constants of…
We introduce an approximate description of an $N$-qubit state, which contains sufficient information to estimate the expectation value of any observable with precision independent of $N$. We show, in fact, that the error in the estimation…
We construct exact eigenstates of quantum many-body systems with Hamiltonians that are not frustration-free in matrix product form, based on a local error cancellation ansatz motivated by the Derrida-Evans-Hakim-Pasquier method for finding…
The aim of the paper is to study the question whether or not equilibrium states exist in open quantum systems that are embedded in at least two environments and are described by a non-Hermitian Hamilton operator $\cal H$. The eigenfunctions…
During the recent developments of quantum theory it has been clarified that the observable quantities (like energy or position) may be represented by operators (with real spectra) which are manifestly non-Hermitian. The mathematical…
Most work in game theory assumes that players are perfect reasoners and have common knowledge of all significant aspects of the game. In earlier work, we proposed a framework for representing and analyzing games with possibly unaware…
Under unitary time evolution, expectation values of physically reasonable observables often evolve towards the predictions of equilibrium statistical mechanics. The eigenstate thermalization hypothesis (ETH) states that this is also true…
Solving ground states of quantum many-body systems has been a long-standing problem in condensed matter physics. Here, we propose a new unsupervised machine learning algorithm to find the ground state of a general quantum many-body system…
The unavoidable interaction of quantum systems with their environment usually results in the loss of desired quantum resources. Suitably chosen system Hamiltonians, however, can, to some extent, counteract such detrimental decay, giving…
This work introduces a novel approach to quantum simulation by leveraging continuous-variable systems within a photonic hardware-inspired framework. The primary focus is on simulating static properties of the ground state of Hamiltonians…
We consider the problem of learning Nash equilibrial policies for two-player risk-sensitive collision-avoiding interactions. Solving the Hamilton-Jacobi-Isaacs equations of such general-sum differential games in real time is an open…
Measurement correlations in quantum systems can exhibit non-local behavior, a fundamental aspect of quantum mechanics with applications such as device-independent quantum information processing. However, the explicit construction of local…
We investigate whether a generic multipartite pure state can be the unique asymptotic steady state of locality-constrained purely dissipative Markovian dynamics. In the simplest tripartite setting, we show that the problem is equivalent to…
Explaining quantum many-body dynamics is a long-held goal of physics. A rigorous operator algebraic theory of dynamics in locally interacting systems in any dimension is provided here in terms of time-dependent equilibrium (Gibbs)…
In a recent paper, Eisert et al. presented a quantum mechanical generalization of Prisoner's Dilemma. They asserted that the maximally entangled game exhibits a unique Nash equilibrium which yields a pay-off equivalent to cooperative…
We study a sequence of symmetric $n$-player stochastic differential games driven by both idiosyncratic and common sources of noise, in which players interact with each other through their empirical distribution. The unique Nash equilibrium…