We investigate the sine model, a one-dimensional tight-binding Hamiltonian
featuring hoppings with a sinusoidal dependence on position, and demonstrate
the formation of synthetic horizons where electronic wave packets exhibit
exponential slowdown. Interestingly, employing the exact transformation between
this model and the Harper equation, which describes the eigenstates of a square
lattice tight-binding model subjected to a perpendicular magnetic field, we
find that analogous semi-classical horizons can emerge in a quantum Hall setup
at half-filling for specific values of the magnetic flux. Furthermore, by
applying sudden quenches to the sine model’s hopping profile, we observe the
emergence of thermal states characterized by an Unruh temperature. Our
numerical calculations of this temperature reveal a non-universal behavior,
suggesting the involvement of physical mechanisms beyond a simple low-energy
description.

Cet article explore les excursions dans le temps et leurs implications.

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