A class of non-equilibrium states and the black hole interior

TL;DR

This paper introduces a class of non-equilibrium pure states in quantum systems with holographic duals, interpreting them as black holes with transient behind-horizon excitations, and explores their properties and potential for traversable wormhole protocols.

Contribution

It characterizes a new class of non-equilibrium states in holographic systems and discusses their interpretation as black holes with behind-horizon excitations, including their potential for information extraction.

Findings

States can be interpreted as black holes with transient interior excitations

Cancellations in correlators reveal non-equilibrium nature of states

Potential for implementing traversable wormhole protocols

Abstract

We consider a class of non-equilibrium pure states, which are generally present in an isolated quantum statistical system. These are states of the form $|\Psi\rangle=e^{-{\beta H \over 2}} U e^{{\beta H \over 2}} |\Psi_0\rangle$, where $U$ is a unitary made out of simple operators and $|\Psi_0\rangle$ is a typical equilibrium pure state with sharply peaked energy. We argue that in a system with a holographic dual these states have a natural interpretation as an AdS black hole with transient excitations behind the horizon. We explore the interpretation of these states as pure states undergoing a time-dependent spontaneous fluctuation out of equilibrium. While these states are atypical and the microscopic phases of the wavefunction are correlated with the matrix elements of simple operators, the states are partly disguised as equilibrium states due to cancellations between contributions from different coarse-grained energy bins. These cancellations are guaranteed by the KMS condition of the underlying equilibrium state $|\Psi_0\rangle$. However, in correlators which include the Hamiltonian $H$ these cancellations are spoiled and the non-equilibrium nature of the state $|\Psi\rangle$ can be detected. We discuss connections with the proposal that local observables behind the horizon are realized as state-dependent operators. The states studied in this paper may be useful for implementing an analogue of the "traversable wormhole" protocol for a 1-sided black hole, which could potentially allow us to extract the excitation from behind the horizon. We include some pedagogical background material.