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

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 Painlevé-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.

Figures (4)

• Figure 1: Sketch of the nH-TB model. The blue lines describe the hopping parameter $\tau$, the cyan (magenta) lines represent the gain(loss) potential $\gamma$ ($-\gamma$), and the green (orange) lines describe the non-reciprocal NNN hopping $-\kappa$ ($\kappa$).
• Figure 2: Behavior of the energy square (see color code) as a function of $\gamma$ and $k$ for different values of $\kappa$. For simplicity, $\tau=1$. Red lines indicate the exceptional points
• Figure 3: Sketch of the two coupled gain/loss nH-TB chains with non-reciprocal NNN hopping. The blue line represents the nearest neighbor hopping parameter $\tau$. The green (orange) line represents the NNN hopping parameter $\kappa_1$ ($\kappa_2$) for the first chain (second chain). The purple (gray) line represents the NNN hopping parameter ($\kappa_3$) between A (B) sites through the interface between the first and second chain, mimicking the horizon of the BH.
• Figure S1: Contour deformation of the function $\tilde{r}$. Green (red) line represents the particle (antiparticle) channel and $\varepsilon$ represents the radius of the curve.