Non-Hermiticity and conservation of orthogonal relation in dielectric microcavity
arXiv:1802.06569 · doi:10.1088/2399-6528/aacfda
Abstract
Non-Hermitian properties of open quantum systems and their applications have attracted much attention in recent years. While most of the studies focus on the characteristic nature of non-Hermitian systems, here we focus on the following issue: A non-Hermitian system can be a subsystem of a Hermitian system as one can clearly see in Feshbach projective operator (FPO) formalism. In this case, the orthogonality of the eigenvectors of the total (Hermitian) system must be sustained, despite the eigenvectors of the subsystem (non-Hermitian) satisfy the bi-orthogonal condition. Therefore, one can predict that there must exist some remarkable processes that relate the non-Hermitian subsystem and the rest part, and ultimately preserve the Hermiticity of the total system. In this paper, we study such processes in open elliptical microcavities. The inner part of the cavity is a non-Hermitian system, and the outer part is the coupled bath in FPO formalism. We investigate the correlation between the inner- and the outer-part behaviors associated with the avoided resonance crossings (ARCs), and analyze the results in terms of a trade-off between the relative difference of self-energies and collective Lamb shifts. These results come from the conservation of the orthogonality in the total Hermitian quantum system.
arXiv comment11 pages, 5 figures
References in corpus (22)
- Real Spectra in Non-Hermitian Hamiltonians Having PT Symmetry
- Dynamically encircling exceptional points in a waveguide: asymmetric mode switching from the breakdown of adiabaticity
- Biorthogonal Quantum Mechanics
- Boundary element method for resonances in dielectric microcavities
- Formation of long-lived, scarlike modes near avoided resonance crossings in optical microcavities
- Unidirectional light emission from high-Q modes in optical microcavities
- Observation of resonance trapping in an open microwave cavity
- Asymmetric scattering and non-orthogonal mode patterns in optical micro-spirals
- Superradiance Transition in Transport Through Nanosystems
- Giant Lamb Shift in Photonic Crystals
- Quantum state discrimination: a geometric approach
- Coupled non-identical microdisks: avoided crossing of energy levels and unidirectional far-field emission
- Observation of emission from chaotic lasing modes in deformed microspheres: displacement by the stable orbit modes
- Spontaneous PT symmetry breaking in non-Hermitian coupled cavities array
- Spectroscopic studies in open quantum systems
- Correlated behavior of conductance and phase rigidity in the transition from the weak-coupling to the strong-coupling regime
- Width bifurcation and dynamical phase transitions in open quantum systems
- Dynamical stabilization and time in open quantum systems
- Correlations in quantum systems and branch points in the complex plane
- Regular Spectra and Universal Directionality of Emitted Radiation from a Quadrupolar Deformed Microcavity
- Non-Hermitian Hamiltonian and Lamb shift in circular dielectric microcavity
- Behavior of three modes of decay channels and their self-energies of elliptic dielectric microcavity