Non-Equilibrating a Black Hole with Inhomogeneous Quantum Quench

We study quantum quench processes in (1+1)-dimensional conformal field theory (CFT) in which the initial thermal equilibrium (Gibbs) state is time-evolved by spatially inhomogeneous Hamiltonians, the so-called M\"obius and sine-square-deformed (SSD) Hamiltonians. We found that, when the quench is induced by the SSD Hamiltonian, almost all the degrees of freedom are asymptotically gathered at a single point, resulting in a point-like excitation. This excitation, which we dub black hole-like excitation, carries as much information as the total thermal entropy. In contrast, other parts of the system approach the low-entropy (low-temperature) state at late times. For the quench by the M\"obius Hamiltonian, we instead found an eternal periodic oscillation of physical quantities such as von Neumann entropy for subsystems. When the CFT admits a holographic dual description, the SSD quench induces a time-dependent, inhomogeneous deformation of the bulk black hole horizon, which, at late enough times, ``touches'' the boundary. Our quench setups can be used as a way to create low-temperature states, and, also, simulate the formation and evaporation processes of black holes.