Microscopic Unitarity and the Quantization of Black Hole Evaporation Time
This work presents an effective microscopic, time-dependent Hamiltonian framework for investigating information dynamics during black hole evaporation. While current approaches often rely on gravitational path integrals or statistical ensembles to recover the Page curve, our model provides an explicit, unitary quantum-mechanical evolution of the radiation. We utilize the Independent Unitary Pairing assumption, where the total Hilbert space is decomposed into N_{total} mutually independent bipartite subsystems. Each subsystem consists of a single interior qubit interacting unitarily with a single radiation qubit, ensuring strict global microscopic unitarity (Von Neumann entropy =0) throughout the process. To reconcile this with macroscopic thermodynamics, we introduce a methodology called "Fermion-like Occupancy Bound", which can be considered as a Holographic Binary Capacity Constraint, where each radiation channel is modeled as a two-level system representing the fundamental unit of information. This truncation, justified by the holographic principle at the Planck scale, enforces a maximum entropy bound of ln2 per channel, which naturally yields the entropy turnaround and final state purification. The central result of this framework is the derivation of a Quantum Condition for Unitarity , which couples microscopic phase evolution with macroscopic observables.