We present a generalization of the ETH conjecture. Using this generalization we are able to derive the fact that an arbitrary eigenstate of a general many body system may be used to represent microcanonical ensemble in any many body experiment that involves only local operators and projectors onto eigenstates of the system Hamiltonian. In particular we extend the ETH to include some non-local operators. We present a derivation of this conjecture in the case of a many body model whose Hamiltonian is composed of two parts: an integrable Hamiltonian and a small but finite Gaussian perturbation.
n this series of papers we substantially extend investigations of Israel and Kandrup on nonequilibrium statistical mechanics in the framework of special relativity. This is the first one devoted to the general mathematical structure. Basing on the action-at-a-distance formalism we obtain a single-time Liouville equation. This equation describes the manifestly covariant evolution of the distribution function of full classical many-body systems. For such global evolution the Bogoliubov functional assumption is justified. In particular, using the Balescu-Wallenborn projection operator approach we find that the distribution function of full many-body systems is completely determined by the reduced one-body distribution function. A manifestly covariant closed nonlinear equation satisfied by the reduced one-body distribution function is rigorously derived. We also discuss extensively the generalization to the general relativity especially an application to self-gravitating systems.
Many-body cages have very recently emerged as a general route for nonergodic behaviour in quantum matter. Here, we show that new types of many-body cages can be engineered in Floquet circuits with the potential to realize novel nonequilibrium quantum states. For that purpose, we first identify an explicit, general construction of Floquet circuits capable of hosting many-body cages. We then present a generic strategy to engineer and structure Floquet many-body cages. We demonstrate the developed scheme for the quantum hard disk model as a generic constrained model system, realizable for instance in Rydberg atom arrays. We construct Floquet circuits yielding Floquet many-body cages with topological properties and
π-quasienergy modes, implying `time crystalline' spatiotemporal order. Our results can be directly extended to general quantum circuits, thus providing a new tool to engineer nonequilibrium behaviour in driven systems.