The information horizon entropy for quantum dot and a symmetrical bath

TL;DR

This paper investigates the entropy and information horizon of a quantum dot coupled to a symmetrical conformal field theory bath in AdS3, deriving the generalized entropy and Page curve, with potential for higher-dimensional generalizations.

Contribution

It provides an exact method to locate the information horizon and compute the generalized entropy for a quantum dot in a holographic setting, extending previous models.

Findings

Exact location of the information horizon for the quantum dot.

Derivation of the generalized entropy including the horizon contribution.

Reproduction of the Page curve for the radiation in this setup.

Abstract

We study the entropy of quantum-dot system in contact with a symmetrical CFT bath living on the boundary of pure AdS3 black hole. The q-dot is localized at the centre of bath system of finite size. We first determine the exact location of the `information horizon' for q-dot and then obtain corresponding generalised entropy of q-dot plus bath system. It is done by finding codim-2 time extremal curve whose end point uniquely determines the information horizon of localised q-dot system. By including the (bulk) entropy contribution of the information horizon the Page curve for the radiation follows. These results can be easily generalized to higher dimensional cases as well.