This book presents the Proceedings of the 15th International Conference on Non-Hermitian Hamiltonians in Quantum Physics, held in Palermo, Italy, from 18 to 23 May 2015. Non-Hermitian operators, and non-Hermitian Hamiltonians in particular, have recently received considerable attention from both the mathematics and physics communities. There has been a growing interest in non-Hermitian Hamiltonians in quantum physics since the discovery that PT-symmetric Hamiltonians can have a real spectrum and thus a physical relevance. The main subjects considered in this book include: PT-symmetry in quantum physics, PT-optics, Spectral singularities and spectral techniques, Indefinite-metric theories, Open quantum systems, Krein space methods, and Biorthogonal systems and applications. The book also provides a summary of recent advances in pseudo-Hermitian Hamiltonians and PT-symmetric Hamiltonians, as well as their applications in quantum physics and in the theory of open quantum systems.

Real Discrete Spectrum of Complex PT-Symmetric Scattering Potentials.- Geometrical and Asymptotical Properties of Non-Selfadjoint Induction Equation with the Jump of the Velocity Field. Time Evolution and Spatial Structure of the Magnetic Field.- PT Symmetric Classical and Quantum Cosmology.- Operator (Quasi-)Similarity, Quasi-Hermitian Operators and All that.- Generalized Jaynes-Cummings Model with a Pseudo-Hermitian: A Path Integral Approach.- Exceptional Points in a Non-Hermitian Extension of the Jaynes-Cummings Hamiltonian.