Seminar

Parity-Time (PT)-symmetry, proposed by Bender and collaborators in the 1990s, is being actively studied as a fundamental property of quantum mechanics. It has also been applied to many other branches of physics. We prove that in finite dimensions PT-symmetric operators are necessarily pseudo-Hermitian, regardless of whether they are diagonalizable or not (arXiv:1801.01676). Pseudo-Hermitian operators, defined by Dirac and Pauli in 1940s, are equivalent to the G-Hamiltonian operators defined by Krein, Gelfand and collaborators in the 1950s. The confirmation of pseudo-Hermiticity for PT-symmetric operators enables the application of the Krein-collision theory to the study of spontaneous breaking of PT-symmetry. Specifically, we show that the physical mechanism of PT-symmetry breaking is the resonance between positive- and negative-action modes.