Open quantum battery in three-dimensional rotating black hole spacetime

TL;DR

The paper studies how rotation in a three-dimensional BTZ black hole modifies the dissipative charging of a quantum battery coupled to a scalar field. Using a two-level battery and Lindblad dynamics derived from the Wightman function in rotating BTZ spacetime, it links local thermodynamic effects to spacetime rotation through the local temperature $T=T_H/\gamma$ and rotation-dependent rates. Key findings show that Dirichlet boundary conditions and the ratio $Δ/(A)$ determine whether rotation enhances or suppresses finite-time charging, while approaching extremality can cause dramatic, regime-dependent amplification or suppression; rotation generally reduces the battery's ability to extract energy from vacuum fluctuations. These results demonstrate a novel interface between quantum thermodynamics and relativistic gravitation, suggesting that quantum batteries could serve as probes of black hole rotation and extremal transitions.

Abstract

We investigate the charging performance of a quantum battery coupled to a scalar field in the background of a three-dimensional rotating black hole. We show that for Dirichlet boundary conditions, the black hole rotation enhances the charging performance at finite times when the quantum battery's energy level spacing is smaller than the charging amplitude, whereas it degrades the charging performance in other parameter regimes. Notably, as the black hole approaches extremal rotation, charging performance undergoes significant amplification or suppression, depending on the parameter regime. This indicates that the performance of quantum battery can probe critical properties of black holes. Additionally, regarding the energy flow in quantum battery, it is further demonstrated that the energy extraction from vacuum fluctuations via dissipation, and rotation suppresses the quantum battery's capacity to extract this energy. Our findings not only advance the relativistic dissipation dynamics of quantum battery but also propose a novel method to detect black hole rotation and extremal-state transitions.

Figures (6)

• Figure 1: The average energy $\langle E_{\mathrm{B}}(\infty) \rangle$ stored in the quantum battery, given by Eq. (\ref{['eq35']}), parameterized by the angular momentum $J/M\ell$. The gray surface indicates the maximum average energy $\langle E_{\mathrm{B}}(\tau) \rangle_{\mathrm{static}}$ stored by the closed quantum battery. The parameters are: $\ell = 1$, $M = 1$, $A \ell = 0.1$ and $R = 1.01$.
• Figure 2: Evolution of the average energy $\langle E_{\mathrm{B}}(\tau) \rangle$ stored in the quantum battery over time. In the first row take $\Delta \ell$ = 0.05, $A \ell$ = 0.1. In the second row take $\Delta \ell$ = 0.15 and $A \ell$= 0.1. Here we set the mass $M = 1$, the radial coordinates of quantum battery $R = 1.01$ and coupling strength $\lambda\sqrt{\ell} = 0.2$. The black dotted line indicates the maximum average energy of the quantum battery when the coupling strength $\lambda \sqrt{\ell} = 0$.
• Figure 3: Variation of the maximum average energy $\langle \, E_{\mathrm{B}} \rangle_{\text{max}}$ of the quantum battery as a function of angular momentum $J/M \ell$ when $\Delta \ell = 0.05$ and $A \ell = 0.1$. The other parameters are: $\ell = 1$, $M = 1$ and $R = 1.01$.
• Figure 4: The average charging power $P_\mathrm{B}(\tau)$ versus the charging time $\tau/\ell$ for different values of the angular momentum $J/M\ell$. (a)-(b): $\Delta \ell$ = 0.05, $A \ell$ = 0.1; (b)-(c) $\Delta \ell$ = 0.15, $A \ell$ = 0.1.The other parameters are: $\ell = 1$, $M = 1$, $R = 1.01$ and $\lambda\sqrt{\ell} = 0.2$.
• Figure 5: Variation of the maximum charging power $P_{\text{max}}$ with the angular momentum $J/M \ell$. The first row shows $\Delta \ell$ = 0.05, $A \ell$ = 0.1; the second row shows $\Delta \ell$ = 0.15, $A \ell$ = 0.1. The other parameters are: $\ell = 1$, $M = 1$, $R = 1.01$ and $\lambda\sqrt{\ell} = 0.2$.