A two-mode model for black hole evaporation and information flow

TL;DR

This paper presents a two-oscillator model simulating black hole evaporation, capturing energy exchange and entanglement dynamics, providing insights into information flow with a minimal yet effective framework.

Contribution

It introduces a novel two-mode harmonic oscillator model with analytical and numerical analysis to study black hole evaporation and information transfer.

Findings

Oscillators exchange quanta in an out-of-phase manner.

Energy exchange pattern is consistent with effective conservation.

Reduced entropy shows periodic growth indicating entanglement.

Abstract

We develop and analyze a two-oscillator model for black hole evaporation in which an effective geometric degree of freedom and a representative Hawking radiation mode are described by coupled harmonic oscillators with opposite signs in their free Hamiltonians. The normal-mode structure is obtained analytically and the corresponding modal amplitudes determine the pattern of energy exchange between the two sectors. To bridge the discrete and semiclassical pictures, we introduce smooth envelope functions that provide a continuous effective description along the geometric variable. Numerical simulations in a truncated Fock space show that the two oscillators exchange quanta in an approximately out-of-phase manner, consistent with an effective conservation of $\langle n_x\rangle - \langle n_y\rangle$. The reduced entropy $S_x(t)$ exhibits periodic growth, indicating entanglement generation. These results demonstrate that even a minimal two-mode framework can capture key qualitative features of energy transfer and information flow during evaporation.