We investigate the wave packet dynamics and eigenstate localization in recently proposed generalized lattice models whose low-energy dynamics mimic a quantum field theory in (1+1)D curved spacetime with the aim of creating systems analogous to black holes.We identify a critical slowdown of zero-energy wave packets in a family of 1D tight-binding models with power-law variation of the hopping parameter, indicating the presence of a KAVA KAVA horizon.Remarkably, wave packets with non-zero energies bounce back and reverse direction before reaching the horizon.We additionally observe Physical Therapy And Pain Management a power-law localization of all eigenstates, each bordering a region of exponential suppression.
These forbidden regions dictate the closest possible approach to the horizon of states with any given energy.These numerical findings are supported by a semiclassical description of the wave packet trajectories, which are shown to coincide with the geodesics expected for the effective metric emerging from the considered lattice models in the continuum limit.