LIV-Decoherence on Gravitational Cat States

TL;DR

This work derives a Lindblad master equation from a stochastic, Lorentz-violating dispersion relation to study decoherence in gravitationally induced entanglement (gravcats). It introduces a Lindblad term with the operator $\hat{K}^{n/2}$, defines $\sigma_n$ and $A_n$ via the stochastic MDR, and obtains a decoherence timescale $\tau_{D,n}$. The gravcat system is analyzed in both mesoscopic parameter regimes and broader Lindblad generalizations, showing that systematic and stochastic LIV damp entanglement via off-diagonal suppression while the entanglement timescale $\tau_E=\hbar/\sqrt{\Omega^2+\epsilon^2}$ sets the oscillatory behavior. For realistic parameters, LIV decoherence is extremely slow compared with environmental decoherence, though the formalism connects to related MDR-based models (e.g., PI model) and motivates relativistic extensions for stronger effects.

Abstract

Inspired by approaches based on the stochastic generalized uncertainty principle, we propose a Lindblad equation derived from the quantization of a stochastic modified dispersion relation in a Lorentz Invariance Violation (LIV) scenario. This framework enables us to investigate decoherence effects in a system of particles exhibiting gravitationally induced entanglement. We analyze the impact of LIV on entanglement (quantified by concurrence) considering systematic and stochastic effects.

Figures (2)

• Figure 1: Representation of the gravcat states. The two particles are located in an even double-well potential with minima separated by distance $L$. The interparticle distance is $d$ or $d'$ when the particles occupy the same or different potential minima, respectively.
• Figure 2: Figs.(a)-(c) describe the concurrence for an initially unentangled state ($\theta=0$) for the cases without LIV ($A_n=0$), with systematic LIV ($t_{QG}=0$), and with stochastic LIV ($t_{QG}=1$), respectively. Fig.(d) describes the population with stochastic LIV ($t_{QG}=1$). We set $\hbar=c=1$.