March 2024

The Eigenstate Thermalization Hypothesis (ETH) has played a key role in recent advances in the high energy and condensed matter communities. It explains how an isolated quantum system in a far-from-equilibrium initial state can evolve to a state that is indistinguishable from thermal equilibrium, with observables relaxing to almost time-independent results that can be described using traditional statistical mechanics ensembles. In this work we probe the limits of ETH, pushing it outside its prototypical applications in several directions. We design a qutrit lattice system with conserved quasilocal charge, in which we verify a form of generalized eigenstate thermalization. We also observe signatures of thermalization in states well outside microcanonical windows of both charge and energy, which we dub `generic ETH.’

An influential theorem by Satosi Wantabe convinced many that there can be no genuinely probabilistic theory with both non-trivial forward and backward transition probabilities. We show that this conclusion does not follow from the theorem. We point out the flaw in the argument, and we showcase examples of theories with well-defined backward and forward transition probabilities.

In general relativity as well as gauge theories, non-trivial symmetries can appear at boundaries. In the presence of radiation some of the symmetries are not Hamiltonian vector fields, hence the definition of charges for the symmetries becomes delicate. It can lead to the problem of field-dependent 2-cocycles in the charge algebra, as opposed to the central extensions allowed in standard classical mechanics. We show that if the Wald-Zoupas prescription is implemented, its covariance requirement guarantees that the algebra of Noether currents is free of field-dependent 2-cocycles, and its stationarity requirement further removes central extensions. Therefore the charge algebra admits at most a time-independent field-dependent 2-cocycle, whose existence depends on the boundary conditions. We report on new results for asymptotic symmetries at future null infinity that can be derived with this approach.

Quantum theory is in principle compatible with processes that violate causal inequalities, an analogue of Bell inequalities that constrain the correlations observed by a set of parties operating in a definite order. Since the introduction of causal inequalities, determining their maximum quantum violation, analogue to Tsirelson’s bound, has remained an open problem. Here we provide a general method for bounding the violation of causal inequalities by arbitrary quantum processes with indefinite causal order. We prove that the maximum violation is generally smaller than the algebraic maximum, and determine a Tsirelson-like bound for the paradigmatic example of the Oreshkov-Brukner-Costa causal inequality. Surprisingly, we find that the algebraic maximum of arbitrary causal inequalities can be achieved by a new type of processes that allow for information to flow in an indefinite direction within the parties’ laboratories. In the classification of the possible correlations, these processes play a similar role as the no-signalling processes in Bell scenarios.

Experimental proposals for testing quantum gravity-induced entanglement of masses (QGEM) typically involve two interacting masses which are each in a spatial superposition state. Here, we propose a QGEM experiment with two particles which are each in a superposition of rotational states, this amounts to a superposition of mass through mass-energy equivalence. Our proposal relies on the fact that rotational energy gravitates. This approach would test a feature unique to gravity since it amounts to sourcing a spacetime in superposition due to a superposition of ‘charge’. We propose and analyse a concrete experimental protocol and discuss challenges.

Null infinity (Scri) arises as a boundary of the Penrose conformal completion of an asymptotically flat physical space-time. We first note that Scri is a weakly isolated horizon (WIH), and then show that its familiar properties can be derived from the general WIH framework. This seems quite surprising because physics associated with black hole (and cosmological) WIHs is very different from that extracted at Scri. We show that these differences can be directly traced back to the fact that Scri is a WIH in the conformal completion rather than the physical space-time. In particular, the BMS group at Scri stems from the symmetry group of WIHs. We also introduce a unified procedure to arrive at fluxes and charges associated with the BMS symmetries at Scri and those associated with black hole (and cosmological) horizons. This procedure differs from those commonly used in the literature and its novel elements seem interesting in their own right. The fact that is there is a single mathematical framework underlying black hole (and cosmological) horizons and Scri paves the way to explore the relation between horizon dynamics in the strong field region and waveforms at infinity. It should also be useful in the analysis of black hole evaporation in quantum gravity.