Resonance Perturbation Theory Research Articles

Enhanced four-band absorption in a tunable graphene subwavelength grating structure for photodetection

This paper investigates a sub-wavelength multilayer dielectric grating structure based on a simple metasurface, achieving dynamically switchable four-band absorption enhancement. This enhancement spans the visible to near-infrared (NIR) range, with absorption exceeding 90%, representing nearly a 40-fold increase over the intrinsic absorption of a single graphene layer. The contributions of guided-mode resonance (GMR), optical Tamm state (OTS), and photonic crystal defect cavity resonance to the absorption spectra are analyzed separately, offering a method for independent multi-channel signal extraction. Additionally, we explore the impact of structural parameters on the absorption response and examine the broad-spectrum multiband detection mechanism. This mechanism, explained through the integration of resonant cavity perturbation theory and the dynamic tuning of absorption efficiency via graphene's Fermi energy levels, results in an independently tunable optical system for four key operating bands. These properties make the structure suitable for applications such as multiband biomedical photodetectors or components in optoelectronic devices with multiple operating bands.

Design of Microwave Electromagnetic Sensor for Liquid Characterization

The design, fabrication, and testing of a highly sensitive GHz sensor for real-time measurement of engine oil quality are presented in this paper. The proposed microwave sensor is constructed on symmetric square slots structures, to improve the performance of the sensor. By using the resonant perturbation theory, the change in the max E field of test samples, produce the frequency shift. The footprint of the designed sensor is (0.5523λeff × 0.0920λeff) where λeff is the effective wavelength value calculated at the operating frequency of 5.52GHz. The oil sample adulteration analysis is done by immersion of a dielectric probe up to a reference level of 20 mm. Thus, the dielectric behavior of the sensor is estimated with an average sensitivity of 1.7. The performance of the microwave sensor is evaluated by submerging it in different engine oil samples, thereby resulting in frequency shifts from 5.53 to lower values. The result obtained from it indicated that the sensor has a quality factor of 54.55 and a FoM of 19.17. Thus, the proposed GHz sensor due to its good sensitivity, FoM, and quality factor is the eminent solution for the automobile industry.

Experimental study of the dielectric properties of energy-containing materials at variable temperatures.

Due to the inherent material characteristics of fireworks and negligent safety management, safety accidents have occurred in recent years, resulting in significant personal and property losses. Therefore, the status inspection of fireworks and other energy-containing materials is a hot issue in the field of energy-containing materials production, storage, transportation, and application. The dielectric constant is a parameter used to characterize the interaction between materials and electromagnetic waves. The methods of obtaining this parameter in the microwave band are not only numerous but also fast and easy. Thus, the real-time status of energy-containing materials can be monitored by monitoring their dielectric properties. Usually, temperature variation has an important effect on the state of energy-containing materials, and the accumulation of temperature can directly cause energy-containing materials to burn or even explode. Based on the above background, this paper proposes a method for testing the dielectric properties of energy-containing materials under variable temperature conditions based on the resonant cavity perturbation theory, which provides important theoretical support for testing the state of energy-containing materials under variable temperatures. Based on the constructed test system, the law of the variation of the dielectric constant of black powder with temperature was obtained, and the theoretical analysis of the test results was carried out. Experimental results show that the temperature change will induce chemical changes in the black powder material, specifically in its dielectric properties, and the magnitude of the changes is large, which is very conducive to real-time monitoring of the black powder state. The system and method developed in this paper can be used to obtain the high-temperature evolution of the dielectric properties of other types of energy-containing materials and provide technical support for the safe production, storage, and application of various types of energy-containing materials.

Perturbation theory of optical resonances of deformed dielectric spheres

We analyze the optical resonances of a dielectric sphere whose surface has been slightly deformed in an arbitrary way. Setting up a perturbation series up to second order, we derive both the frequency shifts and modified linewidths. Our theory is applicable, for example, to freely levitated liquid drops or solid spheres, which are deformed by thermal surface vibrations, centrifugal forces or arbitrary surface waves. A dielectric sphere is effectively an open system whose description requires the introduction of non-Hermitian operators characterized by complex eigenvalues and not normalizable eigenfunctions. We avoid these difficulties using the Kapur-Peierls formalism which enables us to extend the popular Rayleigh-Schr\"{o}dinger perturbation theory to the case of electromagnetic Debye's potentials describing the light fields inside and outside the near-spherical dielectric object. We find analytical formulas, valid within certain limits, for the deformation-induced first- and second-order corrections to the central frequency and bandwidth of a resonance. As an application of our method, we compare our results with preexisting ones finding full agreement.

Rapid Characterization of Powder Mixtures through High Q Dielectric Resonator

In this research work a high quality factor cylindrical dielectric resonator is used to determine the dielectric properties of powder mixtures. The setup is based on resonant perturbation theory and it has a potential to quickly and accurately characterize samples in quantities as small as a tens of milligrams. The loaded quality factor of the proposed dielectric resonator is 19,217, which is operated in TM01δ mode at 10.57 GHz. The measured results are compared with the calculated values obtained from different mixing models. The worst case measured dielectric constant error of 9.4% and 9.95% has been observed for mixtures of boric acid – titanium dioxide and baking soda – titanium dioxide respectively with variable concentrations of weight. The proposed technique is suitable to be deployed in industries in order to rapidly assess the mixture concentration before subjected to the detail investigation.

Perturbation theory of quantum resonances

We propose a contribution to the theory of quantum resonances that combines complex absorbing potentials (CAP) with standard perturbation theory. We start from resolvents that depend on two variables, the complex energy z and a perturbation parameter $$\lambda$$ . The wave functions and the energies of the resonances are expanded in powers of $$\lambda$$ . It is shown that the zero-order terms correspond to the standard CAP method and that higher-order corrections are significant. The introduction of a convergence operator allows to control the convergence of the perturbation series. Due to the discretization of the continuum, the series are generally asymptotic. Finally, we relate the perturbation series to numerically convenient Taylor series. The theory is illustrated on two model examples.

Lissajous and Halo Orbits in the Restricted Three-Body Problem

We study the dynamics near the collinear Lagrangian points of the spatial, circular, restricted three-body problem. Following a standard procedure, we reduce the system to the center manifold and we analyze the Lissajous orbits as well as the halo orbits, the latter ones arising from bifurcations of the planar Lyapunov family of periodic orbits. To obtain the Lissajous orbits, we perform a classical perturbation theory and we provide a formal approximate solution under suitable non-degeneracy and non-resonance conditions. As for the halo orbits, we construct a normal form adapted to the synchronous resonance: introducing a detuning, measuring the displacement from the resonance, and expanding the energy in series of the detuning, we are able to evaluate the energy level at which the bifurcation takes place. Except for a particular case, the analytical values obtained after a second order resonant perturbation theory are in very good agreement (in some cases up to the fourth decimal digit) with the numerical values found in the literature.

Application of resonance perturbation theory to dynamics of magnetization in spin systems interacting with local and collective bosonic reservoirs

We apply our recently developed resonance perturbation theory to describe the dynamics of magnetization in paramagnetic spin systems interacting simultaneously with local and collective bosonic environments. We derive explicit expressions for the evolution of the reduced density matrix elements. This allows us to calculate explicitly the dynamics of the macroscopic magnetization, including characteristic relaxation and dephasing timescales. We demonstrate that collective effects (i) do not influence the character of the relaxation processes but merely renormalize the relaxation times and (ii) significantly modify the dephasing times, leading in some cases to a complicated (time inhomogeneous) dynamics of the transverse magnetization, governed by an effective time-dependent magnetic field.

Special features of galactic dynamics: Disc dynamics

This is a tutorial presentation of special features of galactic disc dynamics, which completes our introduction to galactic dynamics initially presented in [30]. The emphasis is on topics where galactic dynamics and celestial mechanics share common starting points and/or methods of approach. We start by giving some definitions and general notions on the link between observations and dynamical modeling of discs. Then we focus on the application of resonant Hamiltonian perturbation theory in disc resonances. By examining in detail the case of the Inner Lindblad resonance, we demonstrate how resonant perturbation theory leads to an orbital theory of spiral structure in normal galaxies. Passing to barred galaxies, the phase space structure and the role of chaos in the corotation region are analyzed. This is accomplished by a summary of the modern theory of invariant manifolds of unstable periodic orbits in the vicinity of L1 or L2, which can interpret the generation of spiral patterns by chaotic orbits beyond corotation. Some additional topics, potentially important for disc dynamics, are briefly commented.

Resonant Perturbation Theory of Decoherence and Relaxation of Quantum Bits

We describe our recent results on the resonant perturbation theory of decoherence and relaxation for quantum systems with many qubits. The approach represents a rigorous analysis of the phenomenon of decoherence and relaxation for general N‐level systems coupled to reservoirs of bosonic fields. We derive a representation of the reduced dynamics valid for all times t ≥ 0 and for small but fixed interaction strength. Our approach does not involve master equation approximations and applies to a wide variety of systems which are not explicitly solvable.

FASTERD: A Monte Carlo event generator for the study of final state radiation in the process [formula omitted] at DAΦNE

FASTERD is a Monte Carlo event generator to study the final state radiation both in the e + e − → π + π − γ and e + e − → π 0 π 0 γ processes in the energy region of the ϕ-factory DAΦNE. Differential spectra that include both initial and final state radiation and the interference between them are produced. Three different mechanisms for the ππγ final state are considered: Bremsstrahlung process (both in the framework of sQED and Resonance Perturbation Theory), the ϕ direct decay ( e + e − → ϕ → ( f 0 ; f 0 + σ ) γ → π π γ ) and the double resonance mechanism (as e + e − → ϕ → ρ ± π ∓ → π + π − γ and e + e − → ρ → ω π 0 → π 0 π 0 γ ). Additional models can be incorporated as well. Program summary Program title: FASTERD Catalogue identifier: AEDC_v1_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AEDC_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 4505 No. of bytes in distributed program, including test data, etc.: 155 490 Distribution format: tar.gz Programming language: FORTRAN77 Computer: any computer with FORTRAN77 compiler Operating system: UNIX, LINUX, MAC OSX Classification: 11.1 External routines: MATHLIB, PACKLIB from CERN library ( http://cernlib.web.cern.ch/cernlib/) Nature of problem: General parameterization of the γ ∗ → π π γ process; test models describing Bremsstrahlung process, the Φ direct decay, double vector resonance mechanism. Solution method: Numerical integration of analytical formulae. Restrictions: Only one photon emission is considered. Running time: 28 sec with standard input card (1e6 events generated) on an Intel Core 2 Duo 2 GHz with 1 GB RAM.

Final-state radiation and the possibility to test a pion-photon interaction model near the two-pion threshold

Final-state radiation in the process e + e − → π+π− is considered for the cuts used in the analysis of KLOE data at large angles. By means of the Monte Carlo event generator FEVA, effects of nonpointlike behavior of pions are estimated in the framework of resonance perturbation theory. An additional complication related to the ϕ-meson intermediate state is taken into account and the corresponding contributions (the direct decay ϕ → π+π−γ and the double resonance decay ϕ → ρ±π∓ → π+π−γ) are added to FEVA. A method is proposed to test effects of nonpointlike behavior of pions in a model-independent way.

Tests of the final-state radiation model at DAFNE near π + π - threshold

Effects due to the non-pointlike behaviour of pions in the process e+e− → π+ π− γ can arise for hard photons in the final state. By means of a Monte Carlo event generator, which also includes the contribution of the direct decay φ → π+ π− γ, we estimate these effects in the framework of the resonance perturbation theory. We consider angular cuts used in the KLOE analysis of the pion form factor at threshold. A method to reveal the effects of the non-pointlike behaviour of pions in a model-independent way is proposed.

Test of FSR in the process e+e−→π+π−γ at DAΦNE and extraction of the pion form factor at threshold

Effects due to non-pointlike behavior of pions in the process e + e − → π + π − γ can arise for hard photons in the final state. By means of a Monte Carlo event generator, which also includes the contribution of the direct decay ϕ → π + π − γ , we estimate these effects in the framework of resonance perturbation theory. We consider angular cuts used in the KLOE analysis of the pion form factor at threshold. A method to reveal the effects of non-pointlike behavior of pions in a model-independent way is proposed.

Fano-Interference of Decaying States With Continuum in Nanostructures

A new scenario of quantum interference in open systems when a decaying (quasi-bound) state can interfere with the continuum is investigated. The resonant perturbation theory and numerical methods are applied to treat a scattering problem in an electron waveguide. Specifically, we use the Kapura and Peierls (KP) approach to extract resonances. In the waveguide with two antidots, we observe an interesting phenomenon: the interference between a quasi-bound state of one channel and background states of the other channel. Our results show that the zero of Fano resonance, arising from the interference between the quasi-bound states and the continuum, is generally placed in the complex plane.

Manipulating of Resonances in Conductance of an Electron Waveguide with Anti-Dots

A new scenario of quantum interference in open systems when a decaying (quasi-bound) state can interfere with the continuum is investigated. The resonant perturbation theory and numerical methods are applied to treat a scattering problem in an electron waveguide. Specifically, we use the Kapura and Peierls (KP) approach to extract resonances. In the waveguide with two and three anti-dots, we observe an interesting phenomenon: the interference between one subband of the quasi-bound states and background second subband, and the interference of resonant group states of different subbands. Our results show that the zero of Fano resonance, arising from the interference between the quasi-bound states and the continuum, is generally placed in the complex plane.

Analytical Proper Elements for the Hilda Asteroids I: Construction of a Formal Solution

In this paper, we present the mathematical basis for the calculation of proper elements for asteroids in 3:2 mean-motion resonance with Jupiter from their osculating Keplerian elements. The method is based on a new resonant Lie-series perturbation theory (Ferraz-Mello, 1997, 2002), which allows the construction of formal solutions in cases where resonant and long-period angles appear simultaneously. For the disturbing function, we used the Beauge’s expansion (Beauge, 1996), adapted to include short period terms. In this paper, the theory is restricted to the planar case and only the perturbations due to Jupiter are considered.

Scattering poles for asymptotically hyperbolic manifolds

For a class of manifolds X that includes quotients of real hyperbolic (n + 1)-dimensional space by a convex co-compact discrete group, we show that the resonances of the meromorphically continued resolvent kernel for the Laplacian on X coincide, with multiplicities, with the poles of the meromorphically continued scattering operator for X. In order to carry out the proof, we use Shmuel Agmon's perturbation theory of resonances to show that both resolvent resonances and scattering poles are simple for generic potential perturbations.

Dynamical stability of an ion in a linear trap as a solid-state problem of electron localization

When an ion confined in a linear ion trap interacts with a coherent laser field, the internal degrees of freedom, related to the electron transitions, couple to the vibrational degree of freedom of the ion. As a result of this interaction, the quantum dynamics of the vibrational degree of freedom becomes complicated, and in some ranges of parameters even chaotic. We analyze the vibrational ion dynamics using a formal analogy with the solid-state problem of electron localization. In particular, we show how the resonant approximation used in analysis of the ion dynamics, leads to a transition from a two-dimensional (2D) to a one-dimensional problem (1D) of electron localization. The localization length in the solid-state problem is estimated in cases of weak and strong interaction between the sites of the 2D cell by using the methods of resonance perturbation theory, common in analysis of 1D time-dependent dynamical systems. We show that the localization length can be used as an indicator of the effective temperature of the trapped ion, which can be experimentally measured.

Induced transitions between Wannier ladders

We study the transitions between the ground and excited Wannier states induced by a weak ac field. Because the upper Wannier states are several orders of magnitude less stable than the ground states, these transitions decrease the global stability of the system characterized by the rate of probability leakage or decay rate. Using non-Hermitian resonant perturbation theory we obtain an analytical expression for this induced decay rate. The analytical results are compared with exact numerical calculations of the system decay rate.