Colóquios do NAT

27/05 - Observables and spectral functions in pseudo-hermitian theories

Dr. Rui Aquino (IFT-Unesp)

Non-hermitian systems are emerging as feasible platforms to describe new phenomena on different scales. In Non-Hermitian topological photonics, the topology ensures the robustness of propagation of electromagnetic waves, while the non-Hermiticity allows for more methods of wave manipulation. In open quantum systems, where the dynamics of density matrices are described by a Lindblad master equation, the effective Hamiltonian of the quantum system is non-hermitian, which describes the dissipation of energy of the original system with the bath. These intriguing hamiltonians can possess unexpected properties, as for instance the lack of conservation of probability during time evolution and complex eigenvalues. In this talk, I will present a class of nonhermitian theories, the so called pseudo-hermitian theories. I will discuss explicitly how such hamiltonians lead to perfectly sound physical theories with real spectra and unitary time evolution, in spite of their non-hermiticity. We also analyze two-point correlation functions and their associated Källen-Lehmann representation. In particular, we discuss the intimate relation between positivity violation of the spectral functions and the non-observability of operators in a given correlation function.