Quasinormal Modes and the Hawking-Unruh Effect in Quantum Hall Systems: Lessons from Black Hole Phenomena

Abstract

In this work, we propose the quantum Hall system as a platform for exploring black hole phenomena. By exhibiting deep rooted commonalities between lowest Landau level and spacetime symmetries, we show that features of both quantum Hall and gravitational systems can be elegantly captured by a simple quantum mechanical model, the inverted harmonic oscillator. Through this correspondence, we argue that radiation phenomena in gravitational situations, such as presented by W. G. Unruh and S. Hawking, bears a parallel with saddle-potential scattering of quantum Hall quasiparticles. We also find that scattering by the quantum Hall saddle potential can mimic the signature quasinormal modes in black holes, such as theoretically demonstrated through Gaussian scattering off a Schwarzschild black hole by C. V. Vishveshwara. We propose a realistic quantum Hall point contact setup for probing these temporally decaying modes in quasiparticle tunneling, offering a new mesoscopic parallel for black hole ringdown.

Complexity from the reduced density matrix: a new diagnostic for chaos

“…It is well known that, classically, the inverted oscillator has an unstable fixed point in phase space at (x = 0, p = 0) (and, hence, not chaotic in the strict sense). Nonetheless, in the context of studying quantum chaos in various quantum field theories [48][49][50][51][52][53][54][55], it has served as a powerful toy model mostly because it is an exactly solvable system. We begin by revisiting the complexity of the doubly-evolved circuit state, namely a state obtained by first evolving the system forward in time with a Hamiltonian H, and then evolving it backwards in time with a Hamiltonian H + δH.…”

Artificial event horizons in Weyl semimetal heterostructures and their non-equilibrium signatures

“…which correspond to quasi-bound states [23]. Classically, an incoming w 1 or w 2 particle is completely reflected at the turning point and the classical contribution to the transmission is a step function Θ(∓ω).…”

Towards the web of quantum chaos diagnostics

“…Classically, the inverted harmonic oscillator has an unstable fixed point and is not a chaotic system in the strict sense. Nonetheless, it has been used as a powerful toy model for studying quantum chaos in various quantum field theories [73][74][75][76][77], mostly because it is an exactly solvable system. The oscillator can be tuned to the regular and chaotic regime by changing the value of λ, i.e., for λ < m 2 the oscillator is simple, while for λ > m 2 the oscillator is inverted and chaotic.…”