Springer International Publishing, Switzerland, 2016. – 399 p. – ISBN: 978-3-319-31354-2This volume collects the selected contributions presented at or inspired by the 15th International Workshop on Pseuso-Hermitian Hamiltonians in Quantum Physics (PHHQP15), held in Palermo, Italy, from May 18 to 23, 2015. This workshop was the 15th in the series of international meetings that was started in 2003. These meetings were mainly attended by mathematicians and physicists interested in the study of non-Hermitian operators and Hamiltonians, and in their physical applications. About 80 mathematicians and physicists attended the 2015 Workshop in Palermo. Even though mathematicians have deeply studied several aspects of the spectral theory of operators since long time, the realization that non-Hermitian Hamiltonians with PT symmetry may have a real spectrum has produced a growing interest in theoretical physicists for this subject. From the mathematical side this renewed perspective concerning operators with real spectrum has put on the stage new methods aimed to find conditions for a non-self-adjoint operator to have a real spectrum or it has led to revisiting (and, often, generalizing) older concepts (similarity, affinity, metric operators, etc.) as tools for studying this problem. From a physical point of view the main outcome of this unconventional approach to quantum mechanics has been the exploration of several new and interesting models. Contents 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 D–Deformed and SUSY-Deformed Graphene: First Results Localised Nonlinear Modes in the PT-Symmetric Double-Delta Well Gross-Pitaevskii Equation Exactly Solvable Wadati Potentials in the PT-Symmetric Gross-Pitaevskii Equation The EMM and the Spectral Analysis of a Non Self-adjoint Hamiltonian on an Infinite Dimensional Hilbert Space Bessel Sequences, Riesz-Like Bases and Operators in Triplets of Hilbert Spaces Geometric Aspects of Space-Time Reflection Symmetry in Quantum Mechanics Mathematical and Physical Meaning of the Crossings of Energy Levels in PT-Symmetric Systems Non-unitary Evolution of Quantum Logics A Unifying E2-Quasi Exactly Solvable Model Sublattice Signatures of Transitions in a PT-Symmetric Dimer Lattice Physical Aspect of Exceptional Point in the Liouvillian Dynamics for a Quantum Lorentz Gas Some Features of Exceptional Points Spontaneous Breakdown of a PT-Symmetry in the Liouvillian Dynamics at a Non-Hermitian Degeneracy Point Pseudo-Hermitian b-Ensembles with Complex Eigenvalues Green’s Function of a General PT-Symmetric Non-Hermitian Non-central Potential Non-Hermitian Quantum Annealing and Superradiance The Relationship Between Complex Quantum Hamiltonian Dynamics and Krein Space Quantization Non-Hermitian PT -Symmetric Relativistic Quantum Theory in an Intensive Magnetic Field Quasi-Hermitian Lattices with Imaginary Zero-Range Interactions Quantization of Big Bang in Crypto-Hermitian Heisenberg Picture
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