Localization, Resonance, and Non-Hermitian Quantum Mechanics

Relativistic Non-Hermitian Quantum Mechanics

We develop relativistic wave equations in the framework of the new non-hermitian PT quantum mechanics. The familiar Hermitian Dirac equation emerges as an exact result of imposing the Dirac algebra, the criteria of PT -symmetric quantum mechanics, and relativistic invariance. However, relaxing the constraint that in particular the mass matrix be Hermitian also allows for models that have no cou...

Neutrino Oscillations and Non-Hermitian Quantum Mechanics

In this dissertation we firstly present a brief review of the Standard Model of particle physics, focussing on aspects of the model that prove most relevant in the context of explaining the observed oscillation of neutrinos. The phenomenology of neutrino oscillations is then introduced, and different possible extensions to the Standard Model that would allow for non-zero neutrino masses, thereb...

Pseudo-Hermitian Quantum Mechanics

A diagonalizable non-Hermitian Hamiltonian having a real spectrum may be used to define a unitary quantum system, if one modifies the inner product of the Hilbert space properly. We give a comprehensive and essentially self-contained review of the basic ideas and techniques responsible for the recent developments in this subject. We provide a critical assessment of the role of the geometry of t...

Localization in non-Hermitian quantum mechanics and flux-line pinning in superconductors ⋆

A recent development in studies of random non-Hermitian quantum systems is reviewed. Delocalization was found to occur under a sufficiently large constant imaginary vector potential even in one and two dimensions. The phenomenon has a physical realization as flux-line depinning in type-II superconductors. Relations between the delocalization transition and the complex energy spectrum of the non...

Minimal length in Quantum Mechanics and non-Hermitian Hamiltonian systems