A toy quantum black hole (video)
Alexei Kitaev, Ronald and Maxine Linde Professor of Theoretical Physics and Mathematics, Caltech
More than forty years ago Hawking showed that black holes do not only absorb matter and energy but also radiate as black bodies with a certain temperature. However, Hawking's semiclassical theory is at odds with unitarity, which implies that information contained in infalling objects should eventually come out. We currently have a partial solution to this puzzle, and sharpening it might help to construct a fully quantum theory of gravity. The basic picture of interaction between incoming and outgoing particles and the resulting information exchange involves out-of-time-order correlators (OTOCs) of quantum observables. Such correlators can also be defined for more conventional systems, e.g. a chunk of metal, but the black hole OTOCs are special in certain ways. I will describe a quantum Hamiltonian, known as the Sachdev-Ye-Kitaev model, that has very similar OTOCs. Furthermore, this 0+1-dimensional model has a collective mode that is equivalent to dilaton gravity in 1+1 space-time dimensions.