Non-Hermitian Hamiltonians with a Real Spectrum and Their Physical Applications

Abstract

We present an evaluation of some recent attempts at understanding the role of pseudo-Hermitian and PT-symmetric Hamiltonians in modeling unitary quantum systems and elaborate on a particular physical phenomenon whose discovery originated in the study of complex scattering potentials.

9 pages, contributed to Homi Bhabha Centenary Conference on Non-Hermitian Hamiltonians in Quantum Physics (8th International Workshop on Pseudo-Hermitian Hamiltonians in Quantum Physics), held in Mumbai, January 13-16, 2009

References in corpus (3)

• Making Sense of Non-Hermitian Hamiltonians
• Geometric Phase for Non-Hermitian Hamiltonians and Its Holonomy Interpretation
• Differential Realization of Pseudo-Hermiticity: A quantum mechanical analog of Einstein's field equation

Cited by in corpus (14)

• Nonlinear waves in $\mathcal{P}\mathcal{T}$-symmetric systems
• An update on PT-symmetric complexified Scarf II potential, spectral singularities and some remarks on the rationally-extended supersymmetric partners
• Wavepacket Self-imaging and Giant Recombinations via Stable Bloch-Zener Oscillations in Photonic Lattices with Local $\mathcal{P}\mathcal{T}$-Symmetry
• Perturbative Analysis of Spectral Singularities and Their Optical Realizations
• Fundamental length in quantum theories with PT-symmetric Hamiltonians II: The case of quantum graphs
• Non-Hermitian time-dependent perturbation theory: asymmetric transitions and transitionless interactions
• Bi-squeezed states arising from pseudo-bosons
• Conserved Correlation in PT -symmetric Systems: Scattering and Bound States
• Anomalous Faraday effect in a $\mathcal{P}\mathcal{T}$-symmetric dielectric slab
• Solitons in a Hamiltonian $PT$-symmetric coupler
• Non-Hermitian Model for Asymmetrical Tunneling
• Non-hermitian model for resonant cavities coupled by a chiral mirror
• Resolutions of Identity for Some Non-Hermitian Hamiltonians. I. Exceptional Point in Continuous Spectrum
• Time reversal of a discrete system coupled to a continuum based on non-Hermitian flip