This paper is devoted to considering the quasiperiodicity of complex differential polynomials,complex difference polynomials and complex delay-differential polynomials of certain types,and to studying the similarities...This paper is devoted to considering the quasiperiodicity of complex differential polynomials,complex difference polynomials and complex delay-differential polynomials of certain types,and to studying the similarities and differences of quasiperiodicity compared to the corresponding properties of periodicity.展开更多
One-way coupled optical bistability lattice (OCBL) system for open flow is investigated. By using numerical simulations spatiotemporal quasiperiodicity is found. A rough phase diagram indicating the main spatiotempora...One-way coupled optical bistability lattice (OCBL) system for open flow is investigated. By using numerical simulations spatiotemporal quasiperiodicity is found. A rough phase diagram indicating the main spatiotemporal dynamic behavior in weakly coupled lattice is given. The transitions between spatiotemporal quasiperiodicity and chaos are observed. This result is important for the understanding of turbulence.展开更多
This paper investigates optical transport in metamaterial waveguide arrays(MMWAs)exhibiting Bloch-like oscillations(BLOs).The MMWAs is fabricated by laterally combining metal and dielectric layers in a Fibonacci seque...This paper investigates optical transport in metamaterial waveguide arrays(MMWAs)exhibiting Bloch-like oscillations(BLOs).The MMWAs is fabricated by laterally combining metal and dielectric layers in a Fibonacci sequence.By mapping the field distribution of Gaussian wave packets in these arrays,we directly visualize the mechanical evolution in a classical wave environment.Three distinct oscillation modes are observed at different incident positions in the ninth-generation Fibonacci structure,without introducing thickness or refractive index gradient in any layer.Additionally,the propagation period of BLOs increases with a redshift of the incident wavelength for both ninth-and tenth-generation Fibonacci MMWAs.These findings provide a valuable method for manipulating BLOs and offer new insights into optical transport in metamaterials,with potential applications in optical device and wave control technologies.展开更多
Classification of quantum phases is one of the most important areas of research in condensed matter physics.In this work,we obtain the phase diagram of one-dimensional quasiperiodic models via unsupervised learning.Fi...Classification of quantum phases is one of the most important areas of research in condensed matter physics.In this work,we obtain the phase diagram of one-dimensional quasiperiodic models via unsupervised learning.Firstly,we choose two advanced unsupervised learning algorithms,namely,density-based spatial clustering of applications with noise(DBSCAN)and ordering points to identify the clustering structure(OPTICS),to explore the distinct phases of the Aubry–André–Harper model and the quasiperiodic p-wave model.The unsupervised learning results match well with those obtained through traditional numerical diagonalization.Finally,we assess similarity across different algorithms and find that the highest degree of similarity between the results of unsupervised learning algorithms and those of traditional algorithms exceeds 98%.Our work sheds light on applications of unsupervised learning for phase classification.展开更多
We construct a one-dimensional quasiperiodic quantum walk to investigate the localization–delocalization transition.The inverse participation ratio and Lyapunov exponent are employed as two indexes to determine the m...We construct a one-dimensional quasiperiodic quantum walk to investigate the localization–delocalization transition.The inverse participation ratio and Lyapunov exponent are employed as two indexes to determine the mobility edge, a critical energy to distinguish the energy regions of extended and localized states. The analytical solution of mobility edge is obtained by the Lyapunov exponents in global theory, and the consistency of the two indexes is confirmed. We further study the dynamic characteristics of the quantum walk and show that the probabilities are localized to some specific lattice sites with time evolution. This phenomenon is explained by the effective potential of the Hamiltonian which corresponds to the phase in the coin operator of the quantum walk.展开更多
Localization phenomenon is an important research field in condensed matter physics.However,due to the complexity and subtlety of disordered systems,new localization phenomena always emerge unexpectedly.For example,it ...Localization phenomenon is an important research field in condensed matter physics.However,due to the complexity and subtlety of disordered systems,new localization phenomena always emerge unexpectedly.For example,it is generally believed that the phase of the hopping term does not affect the localization properties of the system,so the calculation of the phase is often ignored in the study of localization.Here,we introduce a quasiperiodic model and demonstrate that the phase change of the hopping term can significantly alter the localization properties of the system through detailed numerical simulations,such as the inverse participation ratio and multifractal analysis.This phase-induced localization transition provides valuable information for the study of localization physics.展开更多
Time-synchronous-averaging(TSA)is based on the idea of denoising by averaging,and it extracts the periodic components of a quasiperiodic signal and keeps the extracted waveform undistorted.This paper studies the mathe...Time-synchronous-averaging(TSA)is based on the idea of denoising by averaging,and it extracts the periodic components of a quasiperiodic signal and keeps the extracted waveform undistorted.This paper studies the mathematical properties of TSA,where three propositions are given to reveal the nature of TSA.This paper also proposes a TSA-spectrum based on super-resolution analysis and it decomposes a signal without using any base function.In contrast to discrete Fourier transform spectrum(DFT-spectrum),which is a spectrum in frequency domain,TSA-spectrum is a period-based spectrum,which can present more details of the cross effects between different periodic components of a quasiperiodic signal.Finally,a case study is carried out using bearing fault analysis to illustrate the performance of TSA-spectrum,where the rotation speed fluctuation of the shaft is estimated,which is about 0.12 ms difference.The extracted fault signals are presented and some insights are provided.We believe that this paper can provide new motivation for TSA-spectrum to be widely used in applications involving quasiperiodic signal processing(QSP).展开更多
Quantum physics is primarily concerned with real eigenvalues,stemming from the unitarity of time evolutions.With the introduction of PT symmetry,a widely accepted consensus is that,even if the Hamiltonian of the syste...Quantum physics is primarily concerned with real eigenvalues,stemming from the unitarity of time evolutions.With the introduction of PT symmetry,a widely accepted consensus is that,even if the Hamiltonian of the system is not Hermitian,the eigenvalues can still be purely real under specific symmetry.Hence,great enthusiasm has been devoted to exploring the eigenvalue problem of non-Hermitian systems.In this work,from a distinct perspective,we demonstrate that real eigenvalues can also emerge under the appropriate recursive condition of eigenstates.Consequently,our findings provide another path to extract the real energy spectrum of non-Hermitian systems,which guarantees the conservation of probability and stimulates future experimental observations.展开更多
In this paper, we report the dynamical behaviours of a four-dimenslonal autonomous continuous dissipative system analysed when the parameter is varied in the range we are interested in. The system changes its dynamica...In this paper, we report the dynamical behaviours of a four-dimenslonal autonomous continuous dissipative system analysed when the parameter is varied in the range we are interested in. The system changes its dynamical modes between periodic motion and quasiperiodic motion. Furthermore, the existence of two-torus is investigated numerically by means of Lyapunov exponents. By taking advantage of phase portraits and Poincaré sections, two types of the two-torus are observed and proved to have the structure of ring torus and horn torus, both of which are known to be the standard tori.展开更多
We investigate the dynamical behavior of a symmetric linear coupling of three quadratic maps with exponential terms, and identify various interesting features as a function of two control parameters. In particular, we...We investigate the dynamical behavior of a symmetric linear coupling of three quadratic maps with exponential terms, and identify various interesting features as a function of two control parameters. In particular, we investigate the emergence of quasiperiodic states arising from Naimark-Sacker bifurcations of stable period-l, period-2, and period-3 orbits. We also investigate the multistability in the same coupling. Lyapunov exponents, parameter planes, phase space portraits, and bifurcation diagrams are used to investigate transitions from periodic to quasiperiodic states, from quasiperiodic to mode-locked states and to chaotic states, and from chaotic to hyperchaotic states.展开更多
The half-filled Hubbard chains with the Fibonacci and Harper modulating site potentials are studied in a selfconsistent mean-field approximation. A new order parameter is introduced to describe a charge density order....The half-filled Hubbard chains with the Fibonacci and Harper modulating site potentials are studied in a selfconsistent mean-field approximation. A new order parameter is introduced to describe a charge density order. We also calculate the von Neumann entropy of the ground state. The results show that the von Neumann entropy can identify a CDW/SDW （charge density wave/spin density wave） transition for quasiperiodic models.展开更多
Superperiodicity,chaos and coexisting orbits of ion-acoustic waves(IAWs)are studied in a multi-component plasma consisting of fluid ions,q-nonextensive cold and hot electrons and Maxwellian hot positrons.The significa...Superperiodicity,chaos and coexisting orbits of ion-acoustic waves(IAWs)are studied in a multi-component plasma consisting of fluid ions,q-nonextensive cold and hot electrons and Maxwellian hot positrons.The significant impacts of the system parameters on superperiodic and nonlinear periodic IAWs are presented.Considering an external periodic perturbation various types of quasiperiodic and chaotic features for IAWs are studied in different parametric ranges through time series’plots,phase spaces and Lyapunov exponents.It has been observed that there exist some coexisting orbits for IAWs.Coexisting orbits for IAWs in a classical electron-positron-ion plasma system are reported.展开更多
A simulation model and the dynamics of the forced modulation doped heterostructure, which operates in the state far from thermodynamic equilibrium, are discussed. The numerical simulations clearly reveal that the sys...A simulation model and the dynamics of the forced modulation doped heterostructure, which operates in the state far from thermodynamic equilibrium, are discussed. The numerical simulations clearly reveal that the system under an appropriate bias including DC and AC voltages exhibits expected complex dynamical behaviors. The amplitude and frequency of the externally applied microwave field are taken as the control parameters in the system. Because many nonlinear dynamical systems may have more than one possible time asympotic final state depending on the different initial conditions, the basins of attractions of both ordinary attractor and chaotic attractor are also studied respecively. Finally, as a possible application a method based on pulse driving to control chaos in semiconductor is proposed.展开更多
Porous silicon is a nanostructured material and exhibits efficient photo- and electro-luminescence in the visible range at room temperature, as well as a tunable refractive index determined by its porosity. Porous sil...Porous silicon is a nanostructured material and exhibits efficient photo- and electro-luminescence in the visible range at room temperature, as well as a tunable refractive index determined by its porosity. Porous silicon samples can be obtained by etching a crystalline silicon wafer in a solution of hydrofluoric acid. In this work, we report the fabrication of porous silicon multilayers alternating layers with high and low porosities, which correspondingly produce low and high refractive indices. The free-standing multilayers were formed following three different sequences: periodic, Fibonacci and ThueMorse. These structures were verified by scanning electron microscopy and their infrared transmission spectra were measured by means of Fourier-transform infrared spectroscopy. On the other hand, we calculate the light transmittance of porous silicon multilayers by using the transfer matrix method for all directions of incidence and a wide range of wavelengths. The experimental measurements are compared with theoretical results and a good agreement is observed. In addition, an analysis of infrared absorption peaks due to the molecular vibrations at pore surfaces reveals the presence of hydrogen and oxygen atoms.展开更多
The mobility edges and reentrant localization transitions are studied in one-dimensional dimerized lattice with non-Hermitian either uniform or staggered quasiperiodic potentials.We find that the non-Hermitian uniform...The mobility edges and reentrant localization transitions are studied in one-dimensional dimerized lattice with non-Hermitian either uniform or staggered quasiperiodic potentials.We find that the non-Hermitian uniform quasiperiodic disorder can induce an intermediate phase where the extended states coexist with the localized ones,which implies that the system has mobility edges.The localization transition is accompanied by the PT symmetry breaking transition.While if the non-Hermitian quasiperiodic disorder is staggered,we demonstrate the existence of multiple intermediate phases and multiple reentrant localization transitions based on the finite size scaling analysis.Interestingly,some already localized states will become extended states and can also be localized again for certain non-Hermitian parameters.The reentrant localization transitions are associated with the intermediate phases hosting mobility edges.Besides,we also find that the non-Hermiticity can break the reentrant localization transition where only one intermediate phase survives.More detailed information about the mobility edges and reentrant localization transitions are presented by analyzing the eigenenergy spectrum,inverse participation ratio,and normalized participation ratio.展开更多
In this paper, we consider the electromagnetic scattering by a periodic chiral structure. The media is homogeneous and the structure is periodic in one direction and invariant in another direction. The electromagnetic...In this paper, we consider the electromagnetic scattering by a periodic chiral structure. The media is homogeneous and the structure is periodic in one direction and invariant in another direction. The electromagnetic fields inside the chiral medium are governed by Maxwell equations together with the Drude-BornFedorov equations. We simplify the problem to a two-dimensional scattering problem and discuss the existence and the uniqueness of solutions by an integral equation approach. We show that for all but possibly a discrete set of wave numbers, the integral equation has a unique solution.展开更多
We analytically and numerically study a 1 D tight-binding model with tunable incommensurate potentials.We utilize the self-dual relation to obtain the critical energy,namely,the mobility edge.Interestingly,we analytic...We analytically and numerically study a 1 D tight-binding model with tunable incommensurate potentials.We utilize the self-dual relation to obtain the critical energy,namely,the mobility edge.Interestingly,we analytically demonstrate that this critical energy is a constant independent of strength of potentials.Then we numerically verify the analytical results by analyzing the spatial distributions of wave functions,the inverse participation rate and the multifractal theory.All numerical results are in excellent agreement with the analytical results.Finally,we give a brief discussion on the possible experimental observation of the invariable mobility edge in the system of ultracold atoms in optical lattices.展开更多
This paper studies quantum diffusion in semi-infinite one-dimensional periodic lattice and quasiperiodic Fibonacci lattice. It finds that the quantum diffusion in the semi-infinite periodic lattice shows the same prop...This paper studies quantum diffusion in semi-infinite one-dimensional periodic lattice and quasiperiodic Fibonacci lattice. It finds that the quantum diffusion in the semi-infinite periodic lattice shows the same properties as that for the infinite periodic lattice. Different behaviour is found for the semi-infinite Fibonacci lattice. In this case, there are still C（t） - t^-δ and d（t） - t^β. However, it finds that 0 〈δ 〈 1 for smaller time, and δ = 0 for larger time due to the influence of surface localized states. Moreover, β for the semi-infinite Fibonacci lattice is much smaller than that for the infinite Fibonacci lattice. Effects of disorder on the quantum diffusion are also discussed.展开更多
By means of a Monte Carlo simulation,we study the three-state Potts model on a two-dimensional quasiperiodic structure based on a dodecagonal cluster covering pattern.The critical temperature and exponents are obtaine...By means of a Monte Carlo simulation,we study the three-state Potts model on a two-dimensional quasiperiodic structure based on a dodecagonal cluster covering pattern.The critical temperature and exponents are obtained from finite-size scaling analysis.It is shown that the Potts model on the quasiperiodic lattice belongs to the same universal class as those on periodic ones.展开更多
A new class of 1D quasiperiodic lattices,for which the substitution rules are B→BA,and A→BAB,has been studied in several aspects.The high-dimensional projection method for obtaining the quasilattice is presented.A m...A new class of 1D quasiperiodic lattices,for which the substitution rules are B→BA,and A→BAB,has been studied in several aspects.The high-dimensional projection method for obtaining the quasilattice is presented.A multifractral spectral behavior and gap fabeling properties have been found,which display the perfect quasiperiodicity of the studied model.展开更多
基金partially supported by the NSFC(12061042)the NSF of Jiangxi(20202BAB201003)+3 种基金the support of the National Science Center(Poland)via grant 2017/25/B/ST1/00931partially supported by the Project PID2021-124472NB-I00funded by MCIN/AEI/10.13039/501100011033by"EFDF A way of making Europe"。
文摘This paper is devoted to considering the quasiperiodicity of complex differential polynomials,complex difference polynomials and complex delay-differential polynomials of certain types,and to studying the similarities and differences of quasiperiodicity compared to the corresponding properties of periodicity.
基金Project supported by the Natural Science Foundation of Hebei Province
文摘One-way coupled optical bistability lattice (OCBL) system for open flow is investigated. By using numerical simulations spatiotemporal quasiperiodicity is found. A rough phase diagram indicating the main spatiotemporal dynamic behavior in weakly coupled lattice is given. The transitions between spatiotemporal quasiperiodicity and chaos are observed. This result is important for the understanding of turbulence.
文摘This paper investigates optical transport in metamaterial waveguide arrays(MMWAs)exhibiting Bloch-like oscillations(BLOs).The MMWAs is fabricated by laterally combining metal and dielectric layers in a Fibonacci sequence.By mapping the field distribution of Gaussian wave packets in these arrays,we directly visualize the mechanical evolution in a classical wave environment.Three distinct oscillation modes are observed at different incident positions in the ninth-generation Fibonacci structure,without introducing thickness or refractive index gradient in any layer.Additionally,the propagation period of BLOs increases with a redshift of the incident wavelength for both ninth-and tenth-generation Fibonacci MMWAs.These findings provide a valuable method for manipulating BLOs and offer new insights into optical transport in metamaterials,with potential applications in optical device and wave control technologies.
基金Project supported by the Natural Science Foundation of Nanjing University of Posts and Telecommunications(Grant Nos.NY223109,NY220119,and NY221055)China Postdoctoral Science Foundation(Grant No.2022M721693)the National Natural Science Foundation of China(Grant No.12404365)。
文摘Classification of quantum phases is one of the most important areas of research in condensed matter physics.In this work,we obtain the phase diagram of one-dimensional quasiperiodic models via unsupervised learning.Firstly,we choose two advanced unsupervised learning algorithms,namely,density-based spatial clustering of applications with noise(DBSCAN)and ordering points to identify the clustering structure(OPTICS),to explore the distinct phases of the Aubry–André–Harper model and the quasiperiodic p-wave model.The unsupervised learning results match well with those obtained through traditional numerical diagonalization.Finally,we assess similarity across different algorithms and find that the highest degree of similarity between the results of unsupervised learning algorithms and those of traditional algorithms exceeds 98%.Our work sheds light on applications of unsupervised learning for phase classification.
文摘We construct a one-dimensional quasiperiodic quantum walk to investigate the localization–delocalization transition.The inverse participation ratio and Lyapunov exponent are employed as two indexes to determine the mobility edge, a critical energy to distinguish the energy regions of extended and localized states. The analytical solution of mobility edge is obtained by the Lyapunov exponents in global theory, and the consistency of the two indexes is confirmed. We further study the dynamic characteristics of the quantum walk and show that the probabilities are localized to some specific lattice sites with time evolution. This phenomenon is explained by the effective potential of the Hamiltonian which corresponds to the phase in the coin operator of the quantum walk.
基金supported by the National Natural Science Foundation of China(Grant No.62071248)the Zhejiang Provincial Natural Science Foundation of China(Grant No.LQ24A040004)+1 种基金Natural Science Foundation of Nanjing University of Posts and Telecommunications(Grant No.NY223109)China Postdoctoral Science Foundation(Grant No.2022M721693).
文摘Localization phenomenon is an important research field in condensed matter physics.However,due to the complexity and subtlety of disordered systems,new localization phenomena always emerge unexpectedly.For example,it is generally believed that the phase of the hopping term does not affect the localization properties of the system,so the calculation of the phase is often ignored in the study of localization.Here,we introduce a quasiperiodic model and demonstrate that the phase change of the hopping term can significantly alter the localization properties of the system through detailed numerical simulations,such as the inverse participation ratio and multifractal analysis.This phase-induced localization transition provides valuable information for the study of localization physics.
基金supported by the National Natural Science Foundation of China(Nos.52008198,51425804,U20A20283,and U1813222)the Shenzhen International Cooperation Research Program(No.GJHZ20200731095009029)+2 种基金the Shenzhen Science and Technology Program(Nos.RCBS20210609103823048 and KJZD20230923114916032)the Foundation of the Department of Science and Technology of Guangdong Province(No.2019TQ05Z654)the Guangdong Provincial Key Laboratory of Construction Robotics and Intelligent Construction(No.2022KSYS013),China.
文摘Time-synchronous-averaging(TSA)is based on the idea of denoising by averaging,and it extracts the periodic components of a quasiperiodic signal and keeps the extracted waveform undistorted.This paper studies the mathematical properties of TSA,where three propositions are given to reveal the nature of TSA.This paper also proposes a TSA-spectrum based on super-resolution analysis and it decomposes a signal without using any base function.In contrast to discrete Fourier transform spectrum(DFT-spectrum),which is a spectrum in frequency domain,TSA-spectrum is a period-based spectrum,which can present more details of the cross effects between different periodic components of a quasiperiodic signal.Finally,a case study is carried out using bearing fault analysis to illustrate the performance of TSA-spectrum,where the rotation speed fluctuation of the shaft is estimated,which is about 0.12 ms difference.The extracted fault signals are presented and some insights are provided.We believe that this paper can provide new motivation for TSA-spectrum to be widely used in applications involving quasiperiodic signal processing(QSP).
基金This work was supported by the National Natural Science Foundation of China(Grant No.62071248)the Natural Science Foundation of Nanjing University of Posts and Telecommunications(Grant No.NY223109)China Postdoctoral Science Foundation(Grant No.2022M721693).
文摘Quantum physics is primarily concerned with real eigenvalues,stemming from the unitarity of time evolutions.With the introduction of PT symmetry,a widely accepted consensus is that,even if the Hamiltonian of the system is not Hermitian,the eigenvalues can still be purely real under specific symmetry.Hence,great enthusiasm has been devoted to exploring the eigenvalue problem of non-Hermitian systems.In this work,from a distinct perspective,we demonstrate that real eigenvalues can also emerge under the appropriate recursive condition of eigenstates.Consequently,our findings provide another path to extract the real energy spectrum of non-Hermitian systems,which guarantees the conservation of probability and stimulates future experimental observations.
基金Project supported by the National Natural Science Foundation of China (Grant Nos 60774088 and 60574036)the Specialized Research Fund for the Doctoral Program of China (Grant No 20050055013)+1 种基金the Program for New Century Excellent Talents in University of China (NCET)the Science and Technology Research Key Project of Education Ministry of China (Grant No 107024)
文摘In this paper, we report the dynamical behaviours of a four-dimenslonal autonomous continuous dissipative system analysed when the parameter is varied in the range we are interested in. The system changes its dynamical modes between periodic motion and quasiperiodic motion. Furthermore, the existence of two-torus is investigated numerically by means of Lyapunov exponents. By taking advantage of phase portraits and Poincaré sections, two types of the two-torus are observed and proved to have the structure of ring torus and horn torus, both of which are known to be the standard tori.
基金supported by Conselho Nacional de Desenvolvimento Científico e Tecnológico-CNPq,Brazil
文摘We investigate the dynamical behavior of a symmetric linear coupling of three quadratic maps with exponential terms, and identify various interesting features as a function of two control parameters. In particular, we investigate the emergence of quasiperiodic states arising from Naimark-Sacker bifurcations of stable period-l, period-2, and period-3 orbits. We also investigate the multistability in the same coupling. Lyapunov exponents, parameter planes, phase space portraits, and bifurcation diagrams are used to investigate transitions from periodic to quasiperiodic states, from quasiperiodic to mode-locked states and to chaotic states, and from chaotic to hyperchaotic states.
基金supported by the National Natural Science Foundation of China (Grant Nos 90203009, 10175035 and 10674072)the Specialized Research Fund for the Doctoral Programme (SRFDP) of Higher Education of China (Grant No 20060319007)the Foundation for outstanding Young Teacher of Ministry of Education of China
文摘The half-filled Hubbard chains with the Fibonacci and Harper modulating site potentials are studied in a selfconsistent mean-field approximation. A new order parameter is introduced to describe a charge density order. We also calculate the von Neumann entropy of the ground state. The results show that the von Neumann entropy can identify a CDW/SDW （charge density wave/spin density wave） transition for quasiperiodic models.
基金SMIT and SMU for research support(6100/SMIT/R&D/Project/05/2018)。
文摘Superperiodicity,chaos and coexisting orbits of ion-acoustic waves(IAWs)are studied in a multi-component plasma consisting of fluid ions,q-nonextensive cold and hot electrons and Maxwellian hot positrons.The significant impacts of the system parameters on superperiodic and nonlinear periodic IAWs are presented.Considering an external periodic perturbation various types of quasiperiodic and chaotic features for IAWs are studied in different parametric ranges through time series’plots,phase spaces and Lyapunov exponents.It has been observed that there exist some coexisting orbits for IAWs.Coexisting orbits for IAWs in a classical electron-positron-ion plasma system are reported.
文摘A simulation model and the dynamics of the forced modulation doped heterostructure, which operates in the state far from thermodynamic equilibrium, are discussed. The numerical simulations clearly reveal that the system under an appropriate bias including DC and AC voltages exhibits expected complex dynamical behaviors. The amplitude and frequency of the externally applied microwave field are taken as the control parameters in the system. Because many nonlinear dynamical systems may have more than one possible time asympotic final state depending on the different initial conditions, the basins of attractions of both ordinary attractor and chaotic attractor are also studied respecively. Finally, as a possible application a method based on pulse driving to control chaos in semiconductor is proposed.
文摘Porous silicon is a nanostructured material and exhibits efficient photo- and electro-luminescence in the visible range at room temperature, as well as a tunable refractive index determined by its porosity. Porous silicon samples can be obtained by etching a crystalline silicon wafer in a solution of hydrofluoric acid. In this work, we report the fabrication of porous silicon multilayers alternating layers with high and low porosities, which correspondingly produce low and high refractive indices. The free-standing multilayers were formed following three different sequences: periodic, Fibonacci and ThueMorse. These structures were verified by scanning electron microscopy and their infrared transmission spectra were measured by means of Fourier-transform infrared spectroscopy. On the other hand, we calculate the light transmittance of porous silicon multilayers by using the transfer matrix method for all directions of incidence and a wide range of wavelengths. The experimental measurements are compared with theoretical results and a good agreement is observed. In addition, an analysis of infrared absorption peaks due to the molecular vibrations at pore surfaces reveals the presence of hydrogen and oxygen atoms.
基金Project supported by the National Key Research and Development Program of China(Grant Nos.2016YFA0300600 and 2016YFA0302104)the National Natural Science Foundation of China(Grant Nos.12074410,12047502,11934015,11947301,and 11774397)+1 种基金the Strategic Priority Research Program of Chinese Academy of Sciences(Grant No.XDB33000000)the Fellowship of China Postdoctoral Science Foundation(Grant No.2020M680724).
文摘The mobility edges and reentrant localization transitions are studied in one-dimensional dimerized lattice with non-Hermitian either uniform or staggered quasiperiodic potentials.We find that the non-Hermitian uniform quasiperiodic disorder can induce an intermediate phase where the extended states coexist with the localized ones,which implies that the system has mobility edges.The localization transition is accompanied by the PT symmetry breaking transition.While if the non-Hermitian quasiperiodic disorder is staggered,we demonstrate the existence of multiple intermediate phases and multiple reentrant localization transitions based on the finite size scaling analysis.Interestingly,some already localized states will become extended states and can also be localized again for certain non-Hermitian parameters.The reentrant localization transitions are associated with the intermediate phases hosting mobility edges.Besides,we also find that the non-Hermiticity can break the reentrant localization transition where only one intermediate phase survives.More detailed information about the mobility edges and reentrant localization transitions are presented by analyzing the eigenenergy spectrum,inverse participation ratio,and normalized participation ratio.
基金The Special Funds for Major State Basic Research Projects (G1999032802) in China and the NNSF (10076006) of China.
文摘In this paper, we consider the electromagnetic scattering by a periodic chiral structure. The media is homogeneous and the structure is periodic in one direction and invariant in another direction. The electromagnetic fields inside the chiral medium are governed by Maxwell equations together with the Drude-BornFedorov equations. We simplify the problem to a two-dimensional scattering problem and discuss the existence and the uniqueness of solutions by an integral equation approach. We show that for all but possibly a discrete set of wave numbers, the integral equation has a unique solution.
基金supported by the Natural Science Foundation of Jiangsu Province,China(Grant No.BK20200737)NUPTSF(Grants Nos.NY220090 and NY220208)+2 种基金the National Natural Science Foundation of China(Grant No.12074064)the Innovation Research Project of Jiangsu Province,China(Grant No.JSSCBS20210521)NJUPT-STITP(Grant No.XYB2021294)。
文摘We analytically and numerically study a 1 D tight-binding model with tunable incommensurate potentials.We utilize the self-dual relation to obtain the critical energy,namely,the mobility edge.Interestingly,we analytically demonstrate that this critical energy is a constant independent of strength of potentials.Then we numerically verify the analytical results by analyzing the spatial distributions of wave functions,the inverse participation rate and the multifractal theory.All numerical results are in excellent agreement with the analytical results.Finally,we give a brief discussion on the possible experimental observation of the invariable mobility edge in the system of ultracold atoms in optical lattices.
基金Project supported by the National Natural Science Foundation of China(Grant No19674046)the Cheung Kong Scholars Programme of Chinathe Construct Program of the Key Discipline in Hunan Province,China
文摘This paper studies quantum diffusion in semi-infinite one-dimensional periodic lattice and quasiperiodic Fibonacci lattice. It finds that the quantum diffusion in the semi-infinite periodic lattice shows the same properties as that for the infinite periodic lattice. Different behaviour is found for the semi-infinite Fibonacci lattice. In this case, there are still C（t） - t^-δ and d（t） - t^β. However, it finds that 0 〈δ 〈 1 for smaller time, and δ = 0 for larger time due to the influence of surface localized states. Moreover, β for the semi-infinite Fibonacci lattice is much smaller than that for the infinite Fibonacci lattice. Effects of disorder on the quantum diffusion are also discussed.
基金Supported by the National Natural Science Foundation of China under Grant No 10474021.
文摘By means of a Monte Carlo simulation,we study the three-state Potts model on a two-dimensional quasiperiodic structure based on a dodecagonal cluster covering pattern.The critical temperature and exponents are obtained from finite-size scaling analysis.It is shown that the Potts model on the quasiperiodic lattice belongs to the same universal class as those on periodic ones.
基金Supported by the National Natural Science Foundation of China。
文摘A new class of 1D quasiperiodic lattices,for which the substitution rules are B→BA,and A→BAB,has been studied in several aspects.The high-dimensional projection method for obtaining the quasilattice is presented.A multifractral spectral behavior and gap fabeling properties have been found,which display the perfect quasiperiodicity of the studied model.
