Symplectic Eigenvalues and the Black Hole Information Paradox
A talk in the Seminar Zufallsmatrizen series by
Mario Kieburg
| Abstract: | The information paradox in quantum information exists since Hawking's proposal of black hole radiation. The fundamental question is: how is it possible to have a thermal radiation while the time evolution in a Hilbert space must be unitary? This physical question actually offers an interesting playground for random matrix theorists when studying the problem from a statistical mechanics' point of view. Already the very simple model by Page, who considered a uniformly distributed pure quantum state, gave rise for the fixed trace ensemble. Considering Hawking's description of black hole radiation via bosons one obtains a random matrix model involving the non-compact symplectic group. The relevant spectral quantities are not the eigenvalues but the symplectic eigenvalues of the corresponding covariance matrix. I will introduce the rather exotic concept of this kind of spectral statistics and report on the random matrix model we have studied. Within the CRC this talk is associated to the project(s): C6 |