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Chiral bound states in a staggered array of coupled resonators
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作者 金伍林 李静 +2 位作者 卢竞 龚志瑞 周兰 《Chinese Physics B》 SCIE EI CAS CSCD 2024年第2期124-130,共7页
We study the chiral bound states in a coupled-resonator array with staggered hopping strengths,which interacts with a two-level small atom through a single coupling point or two adjacent ones.In addition to the two ty... We study the chiral bound states in a coupled-resonator array with staggered hopping strengths,which interacts with a two-level small atom through a single coupling point or two adjacent ones.In addition to the two typical bound states found above and below the energy bands,this system presents an extraordinary chiral bound state located within the energy gap.We use the chirality to quantify the breaking of the mirror symmetry.We find that the chirality value undergoes continuous changes by tuning the coupling strengths.The preferred direction of the chirality is controlled not only by the competition between the intracell and the intercell hoppings in the coupled-resonator array,but also by the coherence between the two coupling points.In the case with one coupling point,the chirality values varies monotonously with difference between the intracell hopping and the intercell hoppings.While in the case with two coupling points,due to the coherence between the two coupling points the perfect chiral states can be obtained. 展开更多
关键词 bound states two-level small atom coupled-resonator array CHIRALITY
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Enhancing the Goos-Hänchen shift based on quasi-bound states in the continuum through material asymmetric dielectric compound gratings
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作者 江孝伟 方彬 占春连 《Chinese Physics B》 SCIE EI CAS CSCD 2024年第3期393-400,共8页
Quasi-bound state in the continuum(QBIC)resonance is gradually attracting attention and being applied in Goos-Hänchen(GH)shift enhancement due to its high quality(Q)factor and superior optical confinement.Current... Quasi-bound state in the continuum(QBIC)resonance is gradually attracting attention and being applied in Goos-Hänchen(GH)shift enhancement due to its high quality(Q)factor and superior optical confinement.Currently,symmetry-protected QBIC resonance is often achieved by breaking the geometric symmetry,but few cases are achieved by breaking the material symmetry.This paper proposes a dielectric compound grating to achieve a high Q factor and high-reflection symmetry-protectede QBIC resonance based on material asymmetry.Theoretical calculations show that the symmetry-protected QBIC resonance achieved by material asymmetry can significantly increase the GH shift up to-980 times the resonance wavelength,and the maximum GH shift is located at the reflection peak with unity reflectance.This paper provides a theoretical basis for designing and fabricating high-performance GH shift tunable metasurfaces/dielectric gratings in the future. 展开更多
关键词 bound state in the continuum Goos-Hänchen shift dielectric compound grating material asymmetry
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Interface state-based bound states in continuum and below-continuum-resonance modes with high-Q factors in the rotational periodic system
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作者 杨嘉玲 史奥芊 +2 位作者 彭宇宸 彭鹏 刘建军 《Chinese Physics B》 SCIE EI CAS CSCD 2024年第8期288-293,共6页
We have introduced a new approach to calculate the orbital angular momentum(OAM)of bound states in continuum(BICs)and below-continuum-resonance(BCR)modes in the rotational periodic system nested inside and outside by ... We have introduced a new approach to calculate the orbital angular momentum(OAM)of bound states in continuum(BICs)and below-continuum-resonance(BCR)modes in the rotational periodic system nested inside and outside by transforming the Bloch wave number from the translational periodic system.We extensively classify and study these BICs and BCR modes,which exhibit high-quality(high-Q)factors,in different regions relative to the interface of the system.These BICs and BCR modes with a high-Q factor have been studied in detail based on distinctive structural parameters and scattering theory.The outcomes of this research break the periodic limitation of interface state-based BICs,and realize more and higher symmetry interface state-based BICs and BCR modes.Moreover,we can control the region where light is captured by adjusting the frequency,and show that the Q factor of BICs is more closely related to the ordinal number of rings and the rotational symmetry number of the system. 展开更多
关键词 bound states in the continuum below continuum resonance modes high-quality factors
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Hybrid bound states in the continuum in terahertz metasurfaces 被引量:6
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作者 Junxing Fan Zuolong Li +6 位作者 Zhanqiang Xue Hongyang Xing Dan Lu Guizhen Xu Jianqiang Gu Jiaguang Han Longqing Cong 《Opto-Electronic Science》 2023年第4期12-20,共9页
Bound states in the continuum(BICs)have exhibited extraordinary properties in photonics for enhanced light-matter interactions that enable appealing applications in nonlinear optics,biosensors,and ultrafast optical sw... Bound states in the continuum(BICs)have exhibited extraordinary properties in photonics for enhanced light-matter interactions that enable appealing applications in nonlinear optics,biosensors,and ultrafast optical switches.The most common strategy to apply BICs in a metasurface is by breaking symmetry of resonators in the uniform array that leaks the otherwise uncoupled mode to free space and exhibits an inverse quadratic relationship between quality factor(Q)and asymmetry.Here,we propose a scheme to further reduce scattering losses and improve the robustness of symmetry-protected BICs by decreasing the radiation density with a hybrid BIC lattice.We observe a significant increase of radiative Q in the hybrid lattice compared to the uniform lattice with a factor larger than 14.6.In the hybrid BIC lattice,modes are transferred toГpoint inherited from high symmetric X,Y,and M points in the Brillouin zone that reveal as multiple Fano resonances in the far field and would find applications in hyperspectral sensing.This work initiates a novel and generalized path toward reducing scattering losses and improving the robustness of BICs in terms of lattice engineering that would release the rigid requirements of fabrication accuracy and benefit applications of photonics and optoelectronic devices. 展开更多
关键词 bound states in the continuum metasurfaces terahertz photonics radiative losses Fano resonances
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Fundamentals and applications of photonic waveguides with bound states in the continuum
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作者 Zejie Yu He Gao +4 位作者 Yi Wang Yue Yu Hon Ki Tsang Xiankai Sun Daoxin Dai 《Journal of Semiconductors》 EI CAS CSCD 2023年第10期11-24,共14页
Photonic waveguides are the most fundamental element for photonic integrated circuits(PICs).Waveguide properties,such as propagation loss,modal areas,nonlinear coefficients,etc.,directly determine the functionalities ... Photonic waveguides are the most fundamental element for photonic integrated circuits(PICs).Waveguide properties,such as propagation loss,modal areas,nonlinear coefficients,etc.,directly determine the functionalities and performance of PICs.Recently,the emerging waveguides with bound states in the continuum(BICs)have opened new opportunities for PICs because of their special properties in resonance and radiation.Here,we review the recent progress of PICs composed of waveguides with BICs.First,fundamentals including background physics and design rules of a BIC-based waveguide will be introduced.Next,two types of BIC-based waveguide structures,including shallowly etched dielectric and hybrid waveguides,will be presented.Lastly,the challenges and opportunities of PICs with BICs will be discussed. 展开更多
关键词 photonic waveguide bound states in the continuum integrated photonics
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Resonantly enhanced second-and third-harmonic generation in dielectric nonlinear metasurfaces 被引量:1
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作者 Ji Tong Wang Pavel Tonkaev +5 位作者 Kirill Koshelev Fangxing Lai Sergey Kruk Qinghai Song Yuri Kivshar Nicolae C.Panoiu 《Opto-Electronic Advances》 SCIE EI CAS CSCD 2024年第5期5-19,共15页
Nonlinear dielectric metasurfaces provide a promising approach to control and manipulate frequency conversion optical processes at the nanoscale,thus facilitating both advances in fundamental research and the developm... Nonlinear dielectric metasurfaces provide a promising approach to control and manipulate frequency conversion optical processes at the nanoscale,thus facilitating both advances in fundamental research and the development of new practical applications in photonics,lasing,and sensing.Here,we employ symmetry-broken metasurfaces made of centrosymmetric amorphous silicon for resonantly enhanced second-and third-order nonlinear optical response.Exploiting the rich physics of optical quasi-bound states in the continuum and guided mode resonances,we comprehensively study through rigorous numerical calculations the relative contribution of surface and bulk effects to second-harmonic generation(SHG)and the bulk contribution to third-harmonic generation(THG) from the meta-atoms.Next,we experimentally achieve optical resonances with high quality factors,which greatly boosts light-matter interaction,resulting in about 550 times SHG enhancement and nearly 5000-fold increase of THG.A good agreement between theoretical predictions and experimental measurements is observed.To gain deeper insights into the physics of the investigated nonlinear optical processes,we further numerically study the relation between nonlinear emission and the structural asymmetry of the metasurface and reveal that the generated harmonic signals arising from linear sharp resonances are highly dependent on the asymmetry of the meta-atoms.Our work suggests a fruitful strategy to enhance the harmonic generation and effectively control different orders of harmonics in all-dielectric metasurfaces,enabling the development of efficient active photonic nanodevices. 展开更多
关键词 second-harmonic generation third-harmonic generation bound state in the continuum guided mode resonance all-dielectric metasurfaces nonlinear optics
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Nonlinear Seebeck and Peltier effects in a Majorana nanowire coupled to leads
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作者 迟锋 刘佳 +2 位作者 付振国 刘黎明 易子川 《Chinese Physics B》 SCIE EI CAS CSCD 2024年第7期547-552,共6页
We theoretically study nonlinear thermoelectric transport through a topological superconductor nanowire hosting Majorana bound states(MBSs) at its two ends, a system named as Majorana nanowire(MNW). We consider that t... We theoretically study nonlinear thermoelectric transport through a topological superconductor nanowire hosting Majorana bound states(MBSs) at its two ends, a system named as Majorana nanowire(MNW). We consider that the MNW is coupled to the left and right normal metallic leads subjected to either bias voltage or temperature gradient. We focus our attention on the sign change of nonlinear Seebeck and Peltier coefficients induced by mechanisms related to the MBSs, by which the possible existence of MBSs might be proved. Our results show that for a fixed temperature difference between the two leads, the sign of the nonlinear Seebeck coefficient(thermopower) can be reversed by changing the overlap amplitude between the MBSs or the system equilibrium temperature, which are similar to the cases in linear response regime. By optimizing the MBS–MBS interaction amplitude and system equilibrium temperature, we find that the temperature difference may also induce sign change of the nonlinear thermopower. For zero temperature difference and finite bias voltage, both the sign and magnitude of nonlinear Peltier coefficient can be adjusted by changing the bias voltage or overlap amplitude between the MBSs. In the presence of both bias voltage and temperature difference, we show that the electrical current at zero Fermi level and the states induced by overlap between the MBSs keep unchanged, regardless of the amplitude of temperature difference. We also find that the direction of the heat current driven by bias voltage may be changed by weak temperature difference. 展开更多
关键词 quantum dot nonlinear Seebeck coefficient Peltier coefficient Majorana bound states sign change
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Solution of the Nucleon Structure Problem from a Field Theory of Fermions and Bosons and the Origin of the Proton Stability
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作者 Hans-Peter Morsch 《Journal of High Energy Physics, Gravitation and Cosmology》 CAS 2024年第4期1655-1669,共15页
A bound state formalism derived from a fermion-boson symmetric Lagrangian has been used to calculate the nucleon masses, the charge neutrality of the neutron, the magnetic moments and the electromagnetic form factor r... A bound state formalism derived from a fermion-boson symmetric Lagrangian has been used to calculate the nucleon masses, the charge neutrality of the neutron, the magnetic moments and the electromagnetic form factor ratios μpGEp/GMpand μnGEn/GMn. A quantitative description is obtained, assuming a mixing of a scalar bound state of 3(f f¯)fstructure with its corresponding vector (f f¯)fstate (f indicating massless elementary fermions). Only a few parameters are needed, mainly fixed by energy and momentum conservation. The nucleon stability is explained by an extra binding in the confinement potential, negative for electric and positive for magnetic binding of the proton, and opposite for the neutron. The stronger electric extra binding of the proton allows a decay of the neutron to proton and electron. 展开更多
关键词 Proton and Neutron Properties Described in a New Bound State Formalism by a Mixing of Two Related Bound states Quantitative Agreement with Their Masses RADII Magnetic Moments and Electromagnetic Form Factor Ratios High Stability Due to Extra Binding in the Confinement Potential
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Structure of Massive “Standard Model” Particles
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作者 Hans-Peter Morsch 《Journal of High Energy Physics, Gravitation and Cosmology》 CAS 2024年第4期1670-1674,共5页
The massive vector bosons Z o, W ± and the scalar Higgs-boson H o assumed in weak interaction theory, but also the six quarks required in strong interactions are well understood in an alternative quantum field th... The massive vector bosons Z o, W ± and the scalar Higgs-boson H o assumed in weak interaction theory, but also the six quarks required in strong interactions are well understood in an alternative quantum field theory of fermions and bosons: Z o and W ± as well as all quark-antiquark states (here only the tt¯state is discussed) are described by bound states with scalar coupling between their massless constituents and have a structure similar to leptons. However, the scalar Higgs-boson H o corresponds to a state with vector coupling between the elementary constituents. Similar scalar states are expected also in the mass region of the mesons ω (0.782 GeV) - Υ ( 9.46 GeV). The underlying calculations can be run on line using the Web-address https://h2909473.stratoserver.net. 展开更多
关键词 Quantum Field Theory of Fermion and Bosons Z o and W ± Boson as Well as the Quark-Antiquark State Are Well Described as Bound states of Massless Fermions and Bosons with Scalar Coupling between the Elementary Constituents The Scalar H o-Boson Involves Vector Coupling between Them
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High-Q resonances governed by the quasi-bound states in the continuum in all-dielectric metasurfaces 被引量:12
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作者 Cizhe Fang Qiyu Yang +6 位作者 Qingchen Yuan Xuetao Gan Jianlin Zhao Yao Shao Yan Liu Genquan Han Yue Hao 《Opto-Electronic Advances》 SCIE 2021年第6期1-10,共10页
The realization of high-Q resonances in a silicon metasurface with various broken-symmetry blocks is reported. Theoretical analysis reveals that the sharp resonances in the metasurfaces originate from symmetry-protect... The realization of high-Q resonances in a silicon metasurface with various broken-symmetry blocks is reported. Theoretical analysis reveals that the sharp resonances in the metasurfaces originate from symmetry-protected bound in the continuum(BIC) and the magnetic dipole dominates these peculiar states. A smaller size of the defect in the broken-symmetry block gives rise to the resonance with a larger Q factor. Importantly, this relationship can be tuned by changing the structural parameter, resulting from the modulation of the topological configuration of BICs. Consequently, a Q factor of more than 3,000 can be easily achieved by optimizing dimensions of the nanostructure. At this sharp resonance, the intensity of the third harmonic generation signal in the patterned structure can be 368 times larger than that of the flat silicon film. The proposed strategy and underlying theory can open up new avenues to realize ultrasharp resonances, which may promote the development of the potential meta-devices for nonlinearity, lasing action, and sensing. 展开更多
关键词 all-dielectric metasurface bound states in the continuum optical nonlinearity topological configuration
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BOUND STATES FOR A STATIONARY NONLINEAR SCHRDINGER-POISSON SYSTEM WITH SIGN-CHANGING POTENTIAL IN R^3 被引量:2
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作者 蒋永生 周焕松 《Acta Mathematica Scientia》 SCIE CSCD 2009年第4期1095-1104,共10页
We study the following Schrodinger-Poisson system where (Pλ){-△u+ V(x)u+λФ(x)u^p=x∈R^3,-△Ф=u^2,lim│x│→∞Ф(x) =0,u〉0,where λ≥0 is a parameter,1 〈 p 〈 +∞, V(x) and Q(x)=1 ,D.Ruiz[19] prov... We study the following Schrodinger-Poisson system where (Pλ){-△u+ V(x)u+λФ(x)u^p=x∈R^3,-△Ф=u^2,lim│x│→∞Ф(x) =0,u〉0,where λ≥0 is a parameter,1 〈 p 〈 +∞, V(x) and Q(x)=1 ,D.Ruiz[19] proved that(Pλ)with p∈ (2, 5) has always a positive radial solution, but (Pλ) with p E (1, 2] has solution only if λ 〉 0 small enough and no any nontrivial solution if λ≥1/4.By using sub-supersolution method,we prove that there exists λ0〉0 such that(Pλ)with p ∈(1+∞)has alaways a bound state(H^1(R^3)solution for λ∈[0,λ0)and certain functions V(x)and Q(x)in L^∞(R^3).Moreover,for every λ∈[0,λ0),the solutions uλ of (Pλ)converges,along a subsequence,to a solution of (P0)in H^1 as λ→0 展开更多
关键词 Schrodinger-Poisson system sub-supersolutions supercritical Sobolev expo-nent sign-changing potential bound state
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Quantum information entropies of the eigenstates for the Pschl-Teller-like potential 被引量:2
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作者 Guo-Hua Sun M. Avila Aoki Shi-Hai Dong 《Chinese Physics B》 SCIE EI CAS CSCD 2013年第5期113-117,共5页
Shannon entropy for lower position and momentum eigenstates of Ptschl-Teller-like potential is evaluated. Based on the entropy densities demonstrated graphically, we note that the wave through of the position informat... Shannon entropy for lower position and momentum eigenstates of Ptschl-Teller-like potential is evaluated. Based on the entropy densities demonstrated graphically, we note that the wave through of the position information entropy density p (x) moves right when the potential parameter V1 increases and its amplitude decreases. However, its wave through moves left with the increase in the potential parameter 丨V2丨. Concerning the momentum information entropy density p(p), we observe that its amplitude increases with increasing potential parameter V1, but its amplitude decreases with increasing丨V2丨. The Bialynicki-Birula-Mycielski (BBM) inequality has also been tested for a number of states. Moreover, there exist eigenstates that exhibit squeezing in the momentum information entropy. Finally, we note that position information entropy increases with V1, but decreases with 丨V2丨, However, the variation of momentum information entropy is contrary to that of the position information entropy. 展开更多
关键词 bound states quantum information entropy Poschl-Teller-like potential
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Dual bound states in the continuum enhanced second harmonic generation with transition metal dichalcogenides monolayer 被引量:2
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作者 Peilong Hong Lei Xu Mohsen Rahmani 《Opto-Electronic Advances》 SCIE EI CAS 2022年第7期16-23,共8页
The emergence of two dimensional(2D)materials has opened new possibilities for exhibiting second harmonic genera-tion(SHG)at the nanoscale,due to their remarkable optical response related to stable excitons at room te... The emergence of two dimensional(2D)materials has opened new possibilities for exhibiting second harmonic genera-tion(SHG)at the nanoscale,due to their remarkable optical response related to stable excitons at room temperature.However,the ultimate atomic-scale interaction length with light makes the SHG of Transition Metal Dichalcogenides(TM-Ds)monolayers naturally weak.Here,we propose coupling a monolayer of TMDs with a photonic grating slab that works with doubly resonant bound states in the continuum(BIC).The BIC slabs are designed to exhibit a pair of BICs,reson-ant with both the fundamental wave(FW)and the second harmonic wave(SHW).Firstly,the spatial mode matching can be fulfilled by tilting FW's incident angle.We theoretically demonstrate that this strategy leads to more than four orders of magnitude enhancement of SHG efficiency than a sole monolayer of TMDs,under a pump light intensity of 0.1 GW/cm^(2).Moreover,we demonstrate that patterning the TMDs monolayer can further enhance the spatial overlap coefficient,which leads to an extra three orders of magnitude enhancement of SHG efficiency.These results demonstrate remarkable pos-sibilities for enhancing SHG with nonlinear 2D materials,opening many opportunities for chip-based light sources,nano-lasers,imaging,and biochemical sensing. 展开更多
关键词 second harmonic generation transition metal dichalcogenides bound state in the continuum photonic grating slab
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NODAL BOUND STATES WITH CLUSTERED SPIKES FOR NONLINEAR SCHRDINGER EQUATIONS 被引量:1
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作者 代晋军 何其涵 李必文 《Acta Mathematica Scientia》 SCIE CSCD 2014年第6期1892-1906,共15页
We consider the following nonlinear Schroodinger equations -ε^2△u + u = Q(x)|u|^p-2u in R^N, u ∈ H^1(R^N),where ε is a small positive parameter, N ≥ 2, 2 〈 p 〈 ∞ for N = 2 and 2 〈 p 〈2N/N-2 for N ≥ 3... We consider the following nonlinear Schroodinger equations -ε^2△u + u = Q(x)|u|^p-2u in R^N, u ∈ H^1(R^N),where ε is a small positive parameter, N ≥ 2, 2 〈 p 〈 ∞ for N = 2 and 2 〈 p 〈2N/N-2 for N ≥ 3. We prove that this problem has sign-changing(nodal) semi-classical bound states with clustered spikes for sufficiently small ε under some additional conditions on Q(x).Moreover, the number of this type of solutions will go to infinity as ε→ 0^+. 展开更多
关键词 nodal bound states Lyapunov-Schmidt reduction Schrdinger equations
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Structure of Essential Spectrum and Discrete Spectra of the Energy Operator of Five-Electron Systems in the Hubbard Model. Third and Fourth Doublet States 被引量:1
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作者 S. M. Tashpulatov 《Journal of Applied Mathematics and Physics》 2020年第12期2886-2918,共33页
We consider a five-electron system in the Hubbard model with a coupling between nearest-neighbors. The structure of essential spectrum and discrete spectrum of the systems in the third and fourth doublet states in a &... We consider a five-electron system in the Hubbard model with a coupling between nearest-neighbors. The structure of essential spectrum and discrete spectrum of the systems in the third and fourth doublet states in a <em>v</em>-dimensional lattice is investigated. We prove that the essential spectrum of the system in a third doublet state consists is the union of at most four segments, and discrete spectrum of the system is empty. We show that the essential spectrum of the system in a fourth doublet state consists of the union of at most seven segments, and discrete spectrum of the system consists of no more than one point. 展开更多
关键词 Essential Spectrum Discrete Spectrum Five-Electron System Bound State Anti-Bound State Hubbard Model Doublet State Sextet State Quartet State
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Exact Quantized Momentum Eigenvalues and Eigenstates of a General Potential Model 被引量:1
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作者 Mahmoud Farout Ahmed Bassalat Sameer M. Ikhdair 《Journal of Applied Mathematics and Physics》 2020年第7期1434-1447,共14页
We obtain the quantized momentum eigenvalues, <i><i><span style="font-family:Verdana;">P</span></i><span style="font-family:Verdana;"></span></i><... We obtain the quantized momentum eigenvalues, <i><i><span style="font-family:Verdana;">P</span></i><span style="font-family:Verdana;"></span></i><i><i><sub><span style="font-family:Verdana;">n</span></sub></i><span style="font-family:Verdana;"></span></i>, and the momentum eigenstates for the space-like Schr<span style="white-space:nowrap;">&ouml;</span>dinger equation, the Feinberg-Horodecki equation, with the general potential which is constructed by the temporal counterpart of the spatial form of these potentials. The present work is illustrated with two special cases of the general form: time-dependent Wei-Hua Oscillator and time-dependent Manning-Rosen potential. We also plot the variations of the general molecular potential with its two special cases and their momentum states for few quantized states against the screening parameter. 展开更多
关键词 Bound states Feinberg-Horodecki Equation The Time-Dependent General Potential Time-Dependent Wei-Hua Oscillator TIME-DEPENDENT Manning-Rosen Potential
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Computing Quantum Bound States on Triply Punctured Two-Sphere Surface
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作者 K.T.Chan H.Zainuddin +1 位作者 K.A.M.Atan A.A.Siddig 《Chinese Physics Letters》 SCIE CAS CSCD 2016年第9期1-4,共4页
We are interested in a quantum mechanical system on a triply punctured two-sphere surface with hyperbolic metric. The bound states on this system are described by the Maass cusp forms (MCFs) which are smooth square ... We are interested in a quantum mechanical system on a triply punctured two-sphere surface with hyperbolic metric. The bound states on this system are described by the Maass cusp forms (MCFs) which are smooth square integrable eigenfunctions of the hyperbolic Laplacian. Their discrete eigenvalues and the MCF are not known analytically. We solve numerically using a modified Hejhal and Then algorithm, which is suitable to compute eigenvalues for a surface with more than one cusp. We report on the computational results of some lower-lying eigenvalues for the triply punctured surface as well as providing plots of the MCF using GridMathematica. 展开更多
关键词 of in for Computing Quantum Bound states on Triply Punctured Two-Sphere Surface is on MCF
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Fano Resonances Can Provide Two Criteria to Distinguish Majorana Bound States from Other Candidates in Experiments
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作者 熊烨 《Chinese Physics Letters》 SCIE CAS CSCD 2016年第5期104-107,共4页
There are still debates on whether the observed zero energy peak in the experiment by Stevan et al. [Science 346 (2014) 602] reveals the existence of the long pursued Ala.jorana bound states (MBSs). We propose tha... There are still debates on whether the observed zero energy peak in the experiment by Stevan et al. [Science 346 (2014) 602] reveals the existence of the long pursued Ala.jorana bound states (MBSs). We propose that, by mounting two scanning tunneling microscopic tips on top of the topological superconducting chain and measuring the transmission spectrum between these two metallic tips, there are two kinds of characteristics on the spectrum that are caused by A.IBSs uniquely: One is symmetric peaks with respect to zero energy and the other is 4~r period caused by a nearby dosephson junction. The former refers to the fact that MBSs are eomposited by Alajorana fermions which distributed in the particle and hole subspaees equally. The latter is based on the well known 4w period of Josephson effect in topological superconductor. We think that such two characteristics can be used as criteria to distinguish MBSs from other candidates, such as impurities, Kondo effect and traditional Andreev bound states. 展开更多
关键词 in of from Fano Resonances Can Provide Two Criteria to Distinguish Majorana Bound states from Other Candidates in Experiments that is on
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Quantum Mechanics of Moving Bound States 被引量:1
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作者 Y. S. Kim 《Journal of Modern Physics》 2022年第2期138-165,共28页
The quantum mechanics of bound states with discrete energy levels is well understood. The quantum mechanics of scattering processes is also well understood. However, the quantum mechanics of moving bound states is sti... The quantum mechanics of bound states with discrete energy levels is well understood. The quantum mechanics of scattering processes is also well understood. However, the quantum mechanics of moving bound states is still debatable. When it is at rest, the space-like separation between the constituent particles is the primary variable. When the bound state moves, this space-like separation picks up the time-like separation. The time-separation is not a measurable variable in the present form of quantum mechanics. The only way to deal with this un-observable variable is to treat it statistically. This leads to rise of the statistical variables such entropy and temperature. Paul A. M. Dirac made efforts to construct bound-state wave functions in Einstein’s Lorentz-covariant world. In 1927, he noted that the c-number time-energy relation should be incorporated in the relativistic world. In 1945, he constructed four-dimensional oscillator wave functions with one time coordinate in addition to the three-dimensional space. In 1949, Dirac introduced the light-cone coordinate system for Lorentz transformations. It is then possible to integrate these contributions made by Dirac to construct the Lorentz-covariant harmonic oscillator wave functions. This oscillator system can explain the proton as a bound state of the quarks when it is at rest, and explain the Feynman’s parton picture when it moves with a speed close to that of light. While the un-measurable time-like separation becomes equal to the space-like separation at this speed, the statistical variables become prominent. The entropy and the temperature of this covariant harmonic oscillator are calculated. It is shown that they rise rapidly as the proton speed approaches that of light. 展开更多
关键词 Bound states in Einstein’s World Bohr and Einstein on the Hydrogen Atom Quark-Parton Puzzle Lorentz Group
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BOUND STATES FOR A CLASS OF QUASILINEAR SCALAR FIELD EQUATIONS WITH POTENTIALS VANISHING AT INFINITY
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作者 Athanasios N.Lyberopoulos 《Acta Mathematica Scientia》 SCIE CSCD 2012年第1期197-208,共12页
We study the existence and non-existence of bound states (i.e., solutions in W1,P(RN)) for a class of quasilinear scalar field equations of the for -△pu+V(x)|u|p-2u=a(x)|u|q-2u,x∈RN,1〈P〈N,mwhen the po... We study the existence and non-existence of bound states (i.e., solutions in W1,P(RN)) for a class of quasilinear scalar field equations of the for -△pu+V(x)|u|p-2u=a(x)|u|q-2u,x∈RN,1〈P〈N,mwhen the potentials V(.)≥ 0 and a(.) decay to zero at infinity. 展开更多
关键词 P-LAPLACIAN bound states decaying potentials Hardy potential weightedSobolev spaces
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