  We study non-equilibrium processes in (1+1)-dimensional conformal field
theory (CFT) after quantum quenches starting from the thermal equilibrium
(Gibbs) state. Our quench protocol uses spatially inhomogeneous Hamiltonians,
the Mobius and sine-square-deformed (SSD) Hamiltonians. After a quench by the
Mobius Hamiltonian, physical quantities such as von Neumann entropy for
subsystems exhibit periodic oscillations (quantum revival). On the other hand,
there is no quantum revival after a quench using the SSD Hamiltonian. Instead,
almost all the degrees of freedom of the system are asymptotically gathered at
a single point, the fixed point of the SSD Hamiltonian. This results in a
point-like excitation that carries as much information as the total thermal
entropy -- like a black hole. We call this excitation a black-hole-like
excitation. In contrast, parts of the system other than the fixed point
approach the low-entropy (low-temperature) state at late times, and the reduced
density matrix is given effectively by that of the ground state. When the CFT
admits a holographic dual description, these quenches induce inhomogeneous
deformations of the black hole in the bulk. In particular, after the quench by
the SSD Hamiltonian, at late enough times, the horizon of the bulk black hole
asymptotically "touches" the boundary. We also propose and demonstrate that our
quench setups can be used to simulate the formation and evaporation processes
of black holes, and create low-temperature states.
