2009/09/07 by Sameer M. Ikhdair, R. Sever, Ramazan Sever
Physics and Astronomy · #Black Holes and Theoretical Physics #Quantum Electrodynamics and Casimir Effect #Quantum Mechanics and Non-Hermitian Physics #quant-ph
paper · pdf · doi:10.1002/andp.200910369
published as Ann. Phys. 18 (10-11) (2009) 747-758. · 18 pages
arxiv created 2009/09/07 · openalex publication_date 2009/09/16 · arxiv updated 2009/12/01 · openalex created_date 2019/06/27 · openalex updated_date 2026/08/01
We discuss the dynamics of two harmonic oscillators of which one has a negative kinetic term. This model mimics the Hamiltonian in quantum geometrodynamics, which possesses an indefinite kinetic term. We solve for the time evolution in both the uncoupled and coupled case. We use this setting as a toy model for studying some possible aspects of the final stage of black-hole evaporation. We assume that one oscillator mimics the black hole, while the other mimics Hawking radiation. In the uncoupled case, the negative term leads to a squeezing of the quantum state, while in the coupled case, which includes back reaction, we get a strong entangled state between the mimicked black hole and the radiation. We discuss the meaning of this state. We end by analyzing the limits of this model and its relation to more fundamental approaches.