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[Springer Tracts in Modern Physics] Parity-time Symmetry and Its Applications Volume 280 || PT-Symmetry and Non-Hermitian Wave Transport in Microwaves and RF Circuits
摘要： Many novel concepts in PT -symmetric wave transport were initially explored and demonstrated in the conceptually simpler and experimentally more accessible framework of active electronic circuits. These include eigenmode analysis and spatio-temporal dynamics of the stored energy in static and in periodically driven (Floquet) PT -symmetric circuits, and PT -symmetric scattering in both the linear and nonlinear regime. We review several of these advances – often stretching the borders of investigation to the most general area of non-Hermitian wave transport where concepts like coherent perfect absorbers, gain-induced lasing shut-down, and asymmetric transport are naturally emerging.
关键词： coherent perfect absorbers,RF circuits,asymmetric transport,microwaves,PT-symmetry,non-Hermitian wave transport,gain-induced lasing shut-down
更新于2025-09-10 09:29:36
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[Springer Tracts in Modern Physics] Parity-time Symmetry and Its Applications Volume 280 || Krein Signature in Hamiltonian and P T $$\mathbb {PT}$$ -Symmetric Systems
摘要： We explain the concept of Krein signature in Hamiltonian and PT -symmetric systems on the case study of the one-dimensional Gross–Pitaevskii equation with a real harmonic potential and an imaginary linear potential. These potentials correspond to the magnetic trap, and a linear gain/loss in the mean-?eld model of cigar-shaped Bose–Einstein condensates. For the linearized Gross–Pitaevskii equation, we introduce the real-valued Krein quantity, which is nonzero if the eigenvalue is neutrally stable and simple and zero if the eigenvalue is unstable. If the neutrally stable eigenvalue is simple, it persists with respect to perturbations. However, if it is multiple, it may split into unstable eigenvalues under perturbations. A necessary condition for the onset of instability past the bifurcation point requires existence of two simple neutrally stable eigenvalues of opposite Krein signatures before the bifurcation point. This property is useful in the parameter continuations of neutrally stable eigenvalues of the linearized Gross–Pitaevskii equation.
关键词： Hamiltonian systems,Instability bifurcations,PT -symmetry,Gross–Pitaevskii equation,Krein signature
更新于2025-09-10 09:29:36
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[Springer Tracts in Modern Physics] Parity-time Symmetry and Its Applications Volume 280 || PT-Symmetry on-a-Chip: Harnessing Optical Loss for Novel Integrated Photonic Functionality
摘要： The development of non-Hermitian parity-time (PT) symmetric quantum mechanics has offered a powerful platform to engineer novel device functionality for integrated photonics. In this chapter, we review the chip-scale applications of PT-symmetry in photonic devices, including the implementation of the unidirectional reflectionless PT metamaterial, coherent asymmetric light-light switching, and orbital angular momentum (OAM) laser on-chip. We study the optical analogy of non-Hermitian PT systems, manipulate the complex refractive index properties such as gain/loss modulation, and investigate the unique wave transport characteristics near the exceptional point (EP) to achieve these intriguing on-chip functionalities.
关键词： light-light switching,orbital angular momentum laser,optical loss,non-Hermitian quantum mechanics,integrated photonics,PT-symmetry,unidirectional reflectionless,exceptional point
更新于2025-09-10 09:29:36
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[Springer Tracts in Modern Physics] Parity-time Symmetry and Its Applications Volume 280 || Parity-Time Symmetry in Scattering Problems
摘要： The realization that non-Hermitian parity-time (PT) symmetric Hamiltonians can exhibit entirely real spectra has raised considerable interest in the physics and engineering communities. In the context of optics and photonics, in particular, mathematical analogies with quantum mechanical problem have enabled several breakthrough in terms of observing and utilizing PT-symmetry in closed guided-wave systems. On the other hand, less attention has been paid to the scattering behavior of open PT-symmetric systems. In this chapter, we consider canonical PT-symmetric open systems and explore some of the scattering characteristics of coupled waveguide cavity arrangements. In this regard, we show how an open PT-symmetric configuration can be compared to a closed system, and how the scattering properties are related to the spectral properties of the PT-symmetric system and the associated phase transitions. Afterwards, different scattering geometries are explored in one, two and three dimensions. In addition, we review recent investigations on this topic and highlight opportunities for future research.
关键词： Non-Hermitian Hamiltonians,Parity-Time Symmetry,Optics,Photonics,Scattering Problems
更新于2025-09-10 09:29:36
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[Springer Tracts in Modern Physics] Parity-time Symmetry and Its Applications Volume 280 || Scattering Theory and P T $$\mathbb {P}\mathbb {T}$$ -Symmetry
摘要： We outline a global approach to scattering theory in one dimension that allows for the description of a large class of scattering systems and their P-, T -, and PT -symmetries. In particular, we review various relevant concepts such as Jost solutions, transfer and scattering matrices, reciprocity principle, unidirectional re?ection and invisibility, and spectral singularities. We discuss in some detail the mathematical conditions that imply or forbid reciprocal transmission, reciprocal re?ection, and the presence of spectral singularities and their time-reversal. We also derive generalized unitarity relations for time-reversal-invariant and PT -symmetric scattering systems, and explore the consequences of breaking them. The results reported here apply to the scattering systems de?ned by a real or complex local potential as well as those determined by energy-dependent potentials, nonlocal potentials, and general point interactions.
关键词： invisibility,transfer matrices,spectral singularities,PT-symmetry,Jost solutions,scattering theory,unidirectional re?ection,scattering matrices,reciprocity principle
更新于2025-09-10 09:29:36
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[Springer Tracts in Modern Physics] Parity-time Symmetry and Its Applications Volume 280 || Exact Results for a Special PT-Symmetric Optical Potential
摘要： We present exact analytical results for the sinusoidal optical potentials υ(x) ∝ cos Kx + iλ sin Kx, particularly for the special case λ = 1. This is at the borderline between broken and unbroken P T symmetry, and propagation through such an optical lattice exhibits many remarkable properties. There are two main con?gurations for light largely propagating in the longitudinal (z) direction: (a) where the modulation of the refractive index is in the transverse (x) direction and (b) where the modulation is in the longitudinal direction. In the ?rst case one encounters such properties as non-reciprocity, power oscillations, beam splitting and phase dislocations, while the second case is characterized by unidirectional invisibility, that is, almost total transparency and zero re?ection from one side, but with a large, highly peaked, re?ection from the other side. The latter property can be exploited in lasing cavities.
关键词： lasing cavities,PT-symmetry,optical potential,unidirectional invisibility
更新于2025-09-10 09:29:36
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Ship Detection From PolSAR Imagery Using the Complete Polarimetric Covariance Difference Matrix
摘要： In this paper, we proposed a complete polarimetric covariance difference matrix [C P]-based algorithm for ship detection in polarimetric synthetic aperture radar (PolSAR) imagery. To calculate [C P], we first developed a scheme to reflect the polarimetric scattering differences between ship pixel (SP) and its neighboring pixels (ISPs) and, then, dividedly accumulated the amplitude and phase differences between SP and ISPs. Compared to the polarimetric covariance difference matrix [ P] developed in our earlier work, [C P] effectively overcomes the drawback of the lack of the phase information in [ P]. To demonstrate the effectiveness of the proposed algorithm, we applied the [C P]-based ship detection algorithm to four PolSAR data sets, including one UAVSAR L-band data set with 21 ships, two AIRSAR L-band data sets with 11 and 22 ships, respectively, and one Radarsat-2 C-band data set with 8 ships. Experimental results show that: 1) the proposed algorithm can effectively detect ships with high target-to-clutter ratio (TCR) values and 2) [C P] has a better performance than the traditional polarimetric covariance matrix [C] and [ P] on ship detection. To be more specific, the average TCR value of the proposed algorithm (23.86 dB) is 6.07 and 7.47 dB higher than PNFC (i.e., the geometrical perturbation-polarimetric notch filter) and RSC (i.e., the reflection symmetry method), respectively.
关键词： reflection symmetry (RS),target-to-clutter ratio (TCR),Complete polarimetric covariance difference matrix [C P],scattering differences,ship detection,polarimetric synthetic aperture radar (PolSAR) imagery,polarimetric notch filter (PNF)
更新于2025-09-10 09:29:36
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SU(3) topological insulators in the honeycomb lattice
摘要： We investigate realizations of topological insulators with spin-1 bosons loaded in a honeycomb optical lattice and subjected to a SU(3) spin-orbit coupling—a situation which can be realized experimentally using cold atomic gases. In this paper, we focus on the topological properties of the single-particle band structure, namely, Chern numbers (lattice with periodic boundary conditions) and edge states (lattice with strip geometry) and their connection to time-reversal symmetry and the sublattice symmetry. While SU(2) spin-orbit couplings always lead to time-reversal symmetric tight-binding models, and thereby to topologically trivial band structures, suitable SU(3) spin-orbit couplings can break time-reversal symmetry and lead to topologically nontrivial bulk band structures and to edge states in the strip geometry. In addition, we show that one can trigger a series of topological transitions (i.e., integer changes of the Chern numbers) that are speci?c to the geometry of the honeycomb lattice by varying a single parameter in the Hamiltonian.
关键词： sublattice symmetry,SU(3) spin-orbit coupling,honeycomb optical lattice,spin-1 bosons,time-reversal symmetry,edge states,topological insulators,Chern numbers
更新于2025-09-09 09:28:46
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The effect of the geometrical optical phase on the propagation of Hermite-Gaussian beams through transversal and parallel dielectric blocks
摘要： When an optical beam propagates through dielectric blocks, its optical phase is responsible for the path of the beam. In particular, the first order Taylor expansion of the geometrical part reproduces the path predicted by the Snell and reflection laws whereas the first order expansion of the Fresnel phase leads to the Goos-H?nchen shift. In this paper, we analyze the effects of the second order Taylor expansion of the geometrical phase on the shape of the optical beam and show how it affects the transversal symmetry of Hermite-Gaussian beams. From the analytical expression of the transmitted beam, it is possible to determine in which transversal and parallel dielectric blocks configuration the transversal symmetry breaking is maximized or when the symmetry is recovered. We also discuss the axial spreading delay.
关键词： spreading delay,Hermite-Gaussian beams,Optical phase,transversal symmetry breaking
更新于2025-09-09 09:28:46
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True Random Number Generator Realized by Extracting Entropy from a Negative-Inductance Superconducting Quantum Interference Device
摘要： A new type of superconductive true random number generator (TRNG) based on a negative-inductance superconducting quantum interference device (nSQUID) is proposed. The entropy harnessed to generate random numbers comes from the phenomenon of symmetry breaking in the nSQUID. The experimental circuit is fabricated by the Nb-based lift-off process. Low-temperature tests of the circuit verify the basic function of the proposed TRNG. The frequency characteristics of the TRNG have been analyzed by simulation. The generation rate of random numbers is expected to achieve hundreds of megahertz to tens of gigahertz.
关键词： true random number generator,negative-inductance superconducting quantum interference device,Nb-based lift-off process,frequency characteristics,symmetry breaking
更新于2025-09-09 09:28:46