Holographic open quantum systems: Toy models and analytic properties of thermal correlators

TL;DR

This paper develops a unified holographic framework for open quantum systems interacting with thermal environments, using gravitational techniques to analyze real-time correlators and their analytic structures, applicable to both Markovian and non-Markovian regimes.

Contribution

It introduces a comprehensive holographic approach to open quantum systems, including the computation of thermal correlators via the grSK geometry and the reduction of complex diagrams to single exterior black hole integrals.

Findings

Derived the structure of thermal n-point functions in holographic CFTs.

Showed that all relevant diagrams reduce to integrals on a single black hole exterior.

Presented a toy model capturing key features of open holographic quantum field theories.

Abstract

We present a unified picture of open quantum systems, the theory of a system probing a noisy thermal environment, distilling lessons learnt from previous holographic analyses. Our treatment is applicable both when the system is coupled to short-lived (Markovian), and long-lived (non-Markovian) environmental degrees of freedom. The thermal environment is modeled using an asymptotically AdS black hole, and the systems of interest are simple probe field theories. The effective stochastic dynamics of the system is governed by real-time thermal correlators, which we compute using the gravitational Schwinger-Keldysh (grSK) geometry. We describe the structure of arbitrary tree-level contact and exchange Witten diagrams in the grSK geometry. In particular, we argue, that all such diagrams reduce to integrals supported on a single copy of the exterior of the black hole. The integrand is obtained as a multiple discontinuity of a function comprising ingoing boundary-bulk propagators, monodromy functions which appear as radial Boltzmann weights, and vertex factors. These results allow us to deduce the analytic structure of real-time thermal n-point functions in holographic CFTs. We illustrate the general statements by a two-dimensional toy model, dual to fields in the BTZ background, which we argue captures many of the essential features of generic open holographic QFTs.