Thermodynamics of analogue black holes in a non-Hermitian tight-binding model

TL;DR

This paper introduces a non-Hermitian lattice model that mimics black-hole physics, deriving thermodynamic properties and proposing an experimental setup to observe black-hole features in a quantum system.

Contribution

It presents a novel non-Hermitian tight-binding model that emulates black-hole phenomena and connects theoretical predictions with experimental realization.

Findings

Derived Hawking temperature and entropy for the analogue black hole.

Mapped the lattice system to an effective Schwarzschild metric.

Proposed an experimental setup for detecting black-hole features.

Abstract

We present a non-Hermitian model with gain/loss and non-reciprocal next-nearest-neighbor hopping that emulates black-hole physics. The model describes a one-dimensional lattice with a smooth connection between regions with distinct hopping parameters. By mapping the system to an effective Schwarzschild metric in the Painlev\'e-Gullstrand coordinates, we find that the interface is analogue to a black-hole event horizon. We obtain emission rates for particles and antiparticles, the Hawking temperature, the Bekenstein-Hawking entropy, and the mass of the analogue black hole as a function of the interface sharpness and the system parameters. An experimental realization of the theoretical model is proposed, thus opening the way to the detection of elusive black-hole features.