From scattering theory to complex wave dynamics in non-hermitian PT-symmetric resonators
arXiv:1207.1454 · doi:10.1098/rsta.2012.0194
Abstract
I review how methods from mesoscopic physics can be applied to describe the multiple wave scattering and complex wave dynamics in non-hermitian PT-symmetric resonators, where an absorbing region is coupled symmetrically to an amplifying region. Scattering theory serves as a convenient tool to classify the symmetries beyond the single-channel case and leads to effective descriptions which can be formulated in the energy domain (via Hamiltonians) and in the time domain (via time evolution operators). These models can then be used to identify the mesoscopic time and energy scales which govern the spectral transition from real to complex eigenvalues. The possible presence of magneto-optical effects (a finite vector potential) in multichannel systems leads to a variant (termed PTT' symmetry) which imposes the same spectral constraints as PT symmetry. I also provide multichannel versions of generalized flux-conservation laws.
10 pages, 5 figures, minireview for a theme issue, Philosophical Transactions of the Royal Society A
References in corpus (31)
- Real Spectra in Non-Hermitian Hamiltonians Having PT Symmetry
- Making Sense of Non-Hermitian Hamiltonians
- Random-Matrix Theory of Quantum Transport
- Novel Symmetry Classes in Mesoscopic Normal-Superconducting Hybrid Structures
- Unidirectional Invisibility induced by PT-Symmetric Periodic Structures
- Coherent Perfect Absorbers: Time-reversed Lasers
- PT-symmetry breaking and laser-absorber modes in optical scattering systems
- PT-symmetric laser-absorber
- Pseudo-Hermitian Representation of Quantum Mechanics
- Unidirectional Nonlinear PT-symmetric Optical Structures
- Statistics of resonance poles, phase shifts and time delays in quantum chaotic scattering for systems with broken time reversal invariance
- Conservation relations and anisotropic transmission resonances in one-dimensional PT-symmetric photonic heterostructures
- Invisibility in PT-symmetric complex crystals
- Quantum noise and self-sustained radiation of PT-symmetric systems
- PT-Symmetric Wave Chaos
- Fractal Weyl laws for chaotic open systems
- Quantum-to-classical crossover of quasi-bound states in open quantum systems
- Induced superconductivity distinguishes chaotic from integrable billiards
- Scattering in PT-symmetric quantum mechanics
- Parity anomaly and Landau-level lasing in strained photonic honeycomb lattices
- Conceptual Problems in Scattering from Localized non-Hermitian Potentials
- Secular determinants of random unitary matrices
- Quantum noise and mode nonorthogonality in nonhermitian PT-symmetric optical resonators
- Random matrices beyond the Cartan classification
- Spectra of Random Contractions and Scattering Theory for Discrete-Time Systems
- Quantum-to-classical correspondence in open chaotic systems
- Quantum Andreev map: A paradigm of quantum chaos in superconductivity
- What is the Thouless Energy for Ballistic Systems?
- Universal routes to spontaneous PT-symmetry breaking in non-hermitian quantum systems
- Reflection of light from a disordered medium backed by a phase-conjugating mirror
- Random-matrix theory of amplifying and absorbing resonators with PT or PTT' symmetry
Cited by in corpus (28)
- Nonlinear switching and solitons in PT-symmetric photonic systems
- PT-symmetric scattering in flow duct acoustics
- Transfer matrix study of the Anderson transition in non-Hermitian systems
- Non-Hermitian Floquet Topological Matter -- A Review
- Transfer Matrices as Non-Unitary S-Matrices, Multimode Unidirectional Invisibility, and Perturbative Inverse Scattering
- Symmetry-Protected Scattering in Non-Hermitian Linear Systems
- Bulk and edge-state arcs in non-hermitian coupled-resonator arrays
- Gain/loss induced localization in one-dimensional PT-symmetric tight-binding models
- Localization, quantum resonances and ratchet acceleration in a periodically-kicked -symmetric quantum rotator
- Compatibility of transport effects in non-Hermitian nonreciprocal systems
- Scattering properties of PT-symmetric objects
- Nonlocal discrete continuity and invariant currents in locally symmetric effective Schrödinger arrays
- Localization of Chaotic Resonance States due to a Partial Transport Barrier
- PT-symmetric quantum oscillator in an optical cavity
- Universal intensity statistics of multifractal resonance states
- Unitary Scattering Protected by Pseudo-Hermiticity
- Uniform response theory of non-Hermitian systems: Non-Hermitian physics beyond the exceptional point
- Fundamental constraints on the observability of non-Hermitian effects in passive systems
- Spectral and transport properties of a -symmetric tight-binding chain with gain and loss
- Transport effects in non-Hermitian nonreciprocal systems: General approach
- Local random vector model for semiclassical fractal structure of chaotic resonance states
- Resonance spectra for quantum maps of kicked scattering systems by complex scaling
- Quantum dynamics of PT-symmetrically kicked particle confined in a 1D box
- Spectral singularity enhances transverse spin
- Fragmented exceptional points and their bulk and edge realizations in lattice models
- Non-Hermitian interaction of a discrete state with a continuum
- Exceptionally deficient topological square-root insulators
- Physical relevance of time-independent scattering calculations in non-Hermitian systems: The role of time-growing bound states