We present a numerical study of a model of quantum walk in a periodic potential on a line. We take the simple view that different potentials have different affects on the way in which the coin state of the walker is c...We present a numerical study of a model of quantum walk in a periodic potential on a line. We take the simple view that different potentials have different affects on the way in which the coin state of the walker is changed. For simplicity and definiteness, we assume that the walker's coin state is unaffected at sites without the potential, and rotated in an unbiased way according to the Hadamard matrix at sites with the potential. This is the simplest and most natural model of a quantum walk in a periodic potential with two coins. Six generic cases of such quantum walks are studied numerically. It is found that, of the six cases, four cases display significant localization effect where the walker is confined in the neighborhood of the origin for a sufficiently long time. Associated with such a localization effect is the recurrence of the probability of the walker returning to the neighborhood of the origin.展开更多
We investigate the ground states of spin-1 Bose–Einstein condensates (BECs) with spin–orbit coupling in a radiallyperiodic potential by numerically solving the coupled Gross–Pitaevskii equations. In the radially pe...We investigate the ground states of spin-1 Bose–Einstein condensates (BECs) with spin–orbit coupling in a radiallyperiodic potential by numerically solving the coupled Gross–Pitaevskii equations. In the radially periodic potential, wefirst demonstrate that spin–orbit-coupled antiferromagnetic BECs support a multiring petal phase. Polar–core vortex canbe observed from phase profiles, which is manifested as circularly symmetric distribution. We further show that spin–orbitcoupling can induce multiring soliton structure in ferromagnetic BECs. It is confirmed especially that the wave-functionphase of the ring corresponding to uniform distribution satisfies the rotational symmetry, and the wave-function phase ofthe ring corresponding to partial splitting breaks the rotational symmetry. Adjusting the spin–orbit coupling strength cancontrol the number of petal in antiferromagnetic BECs and the winding numbers of wave-function in ferromagnetic BECs.Finally, we discuss effects of spin-independent and spin-dependent interactions on the ground states.展开更多
We numerically investigate the gap solitons in Bose–Einstein condensates(BECs)with spin–orbit coupling(SOC)in the parity–time(PT)-symmetric periodic potential.We find that the depths and periods of the imaginary la...We numerically investigate the gap solitons in Bose–Einstein condensates(BECs)with spin–orbit coupling(SOC)in the parity–time(PT)-symmetric periodic potential.We find that the depths and periods of the imaginary lattice have an important influence on the shape and stability of these single-peak gap solitons and double-peak gap solitons in the first band gap.The dynamics of these gap solitons are checked by the split-time-step Crank–Nicolson method.It is proved that the depths of the imaginary part of the PT-symmetric periodic potential gradually increase,and the gap solitons become unstable.But the different periods of imaginary part hardly affect the stability of the gap solitons in the corresponding parameter interval.展开更多
Motivated by developing a simple model to calculate the diffusion coefficient in moderate friction region, a simplified model is proposed to deal with the diffusion of Brownian particles in a periodic potential. Where...Motivated by developing a simple model to calculate the diffusion coefficient in moderate friction region, a simplified model is proposed to deal with the diffusion of Brownian particles in a periodic potential. Where the internal noise is a Gaussian white noise, and the basic cell of the periodic potential is composed of a parabolic potential linked with a harmonic potential. When the particles cross the joint point of the potential, a time coarse-graining scheme is used to obtain a simple analytical expression of the probability distribution. The particles drift and diffuse from the first barrier to the second barrier, the passing probability over the second barrier corresponding to the escape rate becomes decrease serves as the long-jump probability. The theoretical result is confirmed by numerical simulation results. The approach can be extended to color noise case.展开更多
We investigate the topological properties of an antiferromagnetic(AFM)chain with an on-site periodic potential,considering the intrinsic spin–orbit coupling and an external Zeeman field along with the nanowire.Our re...We investigate the topological properties of an antiferromagnetic(AFM)chain with an on-site periodic potential,considering the intrinsic spin–orbit coupling and an external Zeeman field along with the nanowire.Our results indicate that Majorana zero modes(MZMs)can be observed by adjusting the strength of the periodic potential.We have calculated the energy spectrum,the wave-function and transport properties,and all these results support the existence of MZMs in the AFM chain.Additionally,multiple topological phase transitions occur as the strength of the periodic potential changes,and several regions support MZMs.展开更多
We present a formula approximating the mean escape time(MST)of a particle from a tilted multi-periodic potential well.The potential function consists of a weighted sum of a finite number of component functions,each of...We present a formula approximating the mean escape time(MST)of a particle from a tilted multi-periodic potential well.The potential function consists of a weighted sum of a finite number of component functions,each of which is periodic.For this particular case,the least period of the potential function is a common period amongst all of its component functions.An approximation of the MST for the potential function is derived,and this approximation takes the form of a product of the MSTs for each of the individual periodic component functions.Our first example illustrates the computational advantages of using the approximation for model validation and parameter tuning in the context of the biological application of DNA transcription.We also use this formula to approximate the MST for an arbitrary tilted periodic potential by the product of MSTs of a finite number of its Fourier modes.Two examples using truncated Fourier series are presented and analyzed.展开更多
Numerical solutions of a non-Fickian diffusion equation belonging to a hyperbolic type are presented in one space dimension.The Brownian particle modelled by this diffusion equation is subjected to a symmetric periodi...Numerical solutions of a non-Fickian diffusion equation belonging to a hyperbolic type are presented in one space dimension.The Brownian particle modelled by this diffusion equation is subjected to a symmetric periodic potential whose spatial shape can be varied by a single parameter.We consider a numerical method which consists of applying Laplace transform in time;we then obtain an elliptic diffusion equation which is discretized using a finite difference method.We analyze some aspects of the convergence of the method.Numerical results for particle density,flux and mean-square-displacement(covering both inertial and diffusive regimes)are presented.展开更多
Recently there has been a considerable amount of work on the existence of Tperiodic solutions for Hamiltonian systems with singular potentials, (see [1]—[7],[10], [11], [13], [14]). In this paper we will study the ex...Recently there has been a considerable amount of work on the existence of Tperiodic solutions for Hamiltonian systems with singular potentials, (see [1]—[7],[10], [11], [13], [14]). In this paper we will study the existence of T-periodic solutions for nonconservative second-order dynamical systems展开更多
The effect of MnO4- and silver content on electrochemical behaviour of five commercial Pb-Ag alloy anodes was studied in acid zinc sulphate electrolyte with and without MnO4- ions at 38 °C during potential decay ...The effect of MnO4- and silver content on electrochemical behaviour of five commercial Pb-Ag alloy anodes was studied in acid zinc sulphate electrolyte with and without MnO4- ions at 38 °C during potential decay periods. When the anodes were immersed into acid zinc sulphate electrolyte without MnO4- ions, the Pb-0.72%Ag anode entered complete passivation state in the shortest time among the five anodes, followed by anodes Pb-0.67%Ag, Pb-0.60%Ag, Pb-0.58%Ag and Pb-0.29%Ag-0.1%Ca by measurement of open circuit potential. During immersion of the anodes, MnO4 ions accelerated the passivation and increased the corrosion current density of the anodes. After immersion in zinc electrolyte with MnO4-, the anode Pb-0.72%Ag had the best corrosion resistance, followed by anodes Pb-0.67%Ag, Pb-0.60%Ag, then the close anodes Pb-0.58%Ag and Pb-0.29%Ag-0.1%Ca by the electrochemical impedance spectroscopy (EIS) analysis.展开更多
Persulfate is considered a convenient and efficient remediation agent for organic contaminated soil.However,the potential risk of sulfur into the soil remediation by persulfate remains ignored.In this study,glass bott...Persulfate is considered a convenient and efficient remediation agent for organic contaminated soil.However,the potential risk of sulfur into the soil remediation by persulfate remains ignored.In this study,glass bottles with different persulfate dosages and groundwater tables were set up to simulate persulfate remediation of organic pollutants(aniline).The results found sulfate to be the main end-product(83.0%–99.5%)of persulfate remediation after10 days.Moreover,H_(2)S accounted for 93.4%–99.4%of sulfur reduction end-products,suggesting that H_(2)S was the final fate of sulfur.H_(2)S was released rapidly after one to three days at a maximum concentration of 33.0 ppm,which is sufficient to make a person uncomfortable.According to the fitted curve results,H_(2)S concentration decreased to a safe concentration(0.15 ppm)after 20–85 days.Meanwhile,the maximum concentration of methanethiol reached 0.6 ppm.These results indicated that secondary pollution from persulfate remediation could release harmful gases over a long time.Therefore,persulfate should be used more carefully as a remediation agent for soil contamination.展开更多
We show that supersymmetry is a simple but powerful tool to exactly solve quantum mechanics problems. Here, the supersymmetric approach is used to analyse a quantum system with periodic Poschl-Teller potential, and to...We show that supersymmetry is a simple but powerful tool to exactly solve quantum mechanics problems. Here, the supersymmetric approach is used to analyse a quantum system with periodic Poschl-Teller potential, and to find out the exact energy spectra and the corresponding band structure.展开更多
In this study, we investigate the collective directed transport of coupled Brownian particles in spatially symmetric periodic potentials under time-periodic pulsating modulations. We find that the coupling between two...In this study, we investigate the collective directed transport of coupled Brownian particles in spatially symmetric periodic potentials under time-periodic pulsating modulations. We find that the coupling between two particles can induce symmetry breaking and consequently collective directed motion. Moreover, the direction of motion can be reversed under certain conditions. The dependence of directed current on various parameters is systematically studied, reverse motion can be achieved by modulating the coupling free length and the phase shift of tile pulsating potential. The dynamical mechanism of these transport properties is understood in terms of the effective-potential theory and the space-time transformation invariance. The directed transport of coupled Brownian motors can be maniplflated and optimized by adjusting the coupling strength, pulsating frequency, or noise intensity.展开更多
Kerov[16,17] proved that Wigner's semi-circular law in Gauss[an unitary ensembles is the transition distribution of the omega curve discovered by Vershik and Kerov[34] for the limit shape of random partitions under t...Kerov[16,17] proved that Wigner's semi-circular law in Gauss[an unitary ensembles is the transition distribution of the omega curve discovered by Vershik and Kerov[34] for the limit shape of random partitions under the Plancherel measure. This establishes a close link between random Plancherel partitions and Gauss[an unitary ensembles, In this paper we aim to consider a general problem, namely, to characterize the transition distribution of the limit shape of random Young diagrams under Poissonized Plancherel measures in a periodic potential, which naturally arises in Nekrasov's partition functions and is further studied by Nekrasov and Okounkov[25] and Okounkov[28,29]. We also find an associated matrix mode[ for this transition distribution. Our argument is based on a purely geometric analysis on the relation between matrix models and SeibergWitten differentials.展开更多
Based on the numerical evidences,an analytical expression of the Dirichletto-Neumann mapping in the form of infinite product was first conjectured for the onedimensional characteristic Schrodinger equation with a sinu...Based on the numerical evidences,an analytical expression of the Dirichletto-Neumann mapping in the form of infinite product was first conjectured for the onedimensional characteristic Schrodinger equation with a sinusoidal potential in[Commun.Comput.Phys.,3(3):641-658,2008].It was later extended for the general secondorder characteristic elliptic equations with symmetric periodic coefficients in[J.Comp.Phys.,227:6877-6894,2008].In this paper,we present a proof for this Dirichlet-toNeumann mapping.展开更多
With the circumstance of the electron strongly coupled to LO-phonon and using the variational method of Pekar type(VMPT),we study the eigenenergies and the eigenfunctions(EE) of the ground and the first excited st...With the circumstance of the electron strongly coupled to LO-phonon and using the variational method of Pekar type(VMPT),we study the eigenenergies and the eigenfunctions(EE) of the ground and the first excited states(GFES) in a RbCl crystal asymmetric Gaussian potential quantum well(AGPQW).It concludes:(i) Twoenergy-level of the AGPQW may be seen as a qubit.(ii) When the electron located in the superposition state of the two-energy-level system,the time evolution and the coordinate changes of the electron probability density oscillated periodically in the AGPQW with every certain period T0=22.475 fs.(iii) Due to the confinement that is a two dimensional x-y plane symmetric structure in the AGPQW and the asymmetrical Gaussian potential(AGP) in the AGPQW growth direction,the electron probability density presents only one peak configuration located in the coordinate of z 〉 0,whereas it is zero in the range of z 〈 0.(iv) The oscillatory period is a decreasing function of the AGPQW height and the polaron radius,(v) The oscillating period is a decreasing one in the confinement potential R 〈 0.24 nm,whereas it is an increasing one in the confinement potential R 〉 0.24 nm and it takes a minimum value in R = 0.24 nm.展开更多
The nonlinear lattice - a new and nonlinear class of periodic potentials - was recently introduced to generate various nonlinear localized modes. Several attempts failed to stabilize two-dimensional (2D) solitons ag...The nonlinear lattice - a new and nonlinear class of periodic potentials - was recently introduced to generate various nonlinear localized modes. Several attempts failed to stabilize two-dimensional (2D) solitons against their intrinsic critical collapse in Kerr media. Here, we provide a possibility for supporting 2D matter-wave solitons and vortices in an extended setting - the cubic and quintic model - by introducing another nonlinear lattice whose period is controllable and can be different from its cubic counterpart, to its quintic nonlinearity, therefore making a fully "nonlinear quasi-crystal". A variational approximation based on Gaussian ansatz is developed for the fundamental solitons and in particular, their stability exactly follows the inverted Vakhitov-Kolokolov stability criterion, whereas the vortex solitons are only studied by means of numerical methods. Stability regions for two types of localized mode -- the fundamental and vortex solitons -- are provided. A noteworthy feature of the localized solutions is that the vortex solitons are stable only when the period of the quintic nonlinear lattice is the same as the cubic one or when the quintic nonlinearity is constant, while the stable fundamental solitons can be created under looser conditions. Our physical setting (cubic-quintic model) is in the framework of the Gross-Pitaevskii equation or nonlinear Schr6dinger equation, the predicted localized modes thus may be implemented in Bose-Einstein condensates and nonlinear optical media with tunable cubic and quintic nonlinearities.展开更多
We study efficient spectral-collocation and continuation methods(SCCM)for rotating two-component Bose-Einstein condensates(BECs)and rotating two-component BECs in optical lattices,where the second kind Chebyshev polyn...We study efficient spectral-collocation and continuation methods(SCCM)for rotating two-component Bose-Einstein condensates(BECs)and rotating two-component BECs in optical lattices,where the second kind Chebyshev polynomials are used as the basis functions for the trial function space.A novel two-parameter continuation algorithm is proposed for computing the ground state and first excited state solutions of the governing Gross-Pitaevskii equations(GPEs),where the classical tangent vector is split into two constraint conditions for the bordered linear systems.Numerical results on rotating two-component BECs and rotating two-component BECs in optical lattices are reported.The results on the former are consistent with the published numerical results.展开更多
基金supported by the Ministry of Science and Technology of Taiwan,China(Grant Nos.NSC-99-2112-M-032-002-MY3 and NSC 102-2112-M-032-003-MY3)the National Center for Theoretical Sciences(North)(NCTS-n)of China
文摘We present a numerical study of a model of quantum walk in a periodic potential on a line. We take the simple view that different potentials have different affects on the way in which the coin state of the walker is changed. For simplicity and definiteness, we assume that the walker's coin state is unaffected at sites without the potential, and rotated in an unbiased way according to the Hadamard matrix at sites with the potential. This is the simplest and most natural model of a quantum walk in a periodic potential with two coins. Six generic cases of such quantum walks are studied numerically. It is found that, of the six cases, four cases display significant localization effect where the walker is confined in the neighborhood of the origin for a sufficiently long time. Associated with such a localization effect is the recurrence of the probability of the walker returning to the neighborhood of the origin.
基金Project supported by the Scientific and Technologial Innovation Program of the Higher Education Institutions in Shanxi Province,China(Grant Nos.2019L0813,2019L0785,and 2019L0808).
文摘We investigate the ground states of spin-1 Bose–Einstein condensates (BECs) with spin–orbit coupling in a radiallyperiodic potential by numerically solving the coupled Gross–Pitaevskii equations. In the radially periodic potential, wefirst demonstrate that spin–orbit-coupled antiferromagnetic BECs support a multiring petal phase. Polar–core vortex canbe observed from phase profiles, which is manifested as circularly symmetric distribution. We further show that spin–orbitcoupling can induce multiring soliton structure in ferromagnetic BECs. It is confirmed especially that the wave-functionphase of the ring corresponding to uniform distribution satisfies the rotational symmetry, and the wave-function phase ofthe ring corresponding to partial splitting breaks the rotational symmetry. Adjusting the spin–orbit coupling strength cancontrol the number of petal in antiferromagnetic BECs and the winding numbers of wave-function in ferromagnetic BECs.Finally, we discuss effects of spin-independent and spin-dependent interactions on the ground states.
基金Science and Technology Project of Hebei Education Department,China(Grant No.ZD2020200)。
文摘We numerically investigate the gap solitons in Bose–Einstein condensates(BECs)with spin–orbit coupling(SOC)in the parity–time(PT)-symmetric periodic potential.We find that the depths and periods of the imaginary lattice have an important influence on the shape and stability of these single-peak gap solitons and double-peak gap solitons in the first band gap.The dynamics of these gap solitons are checked by the split-time-step Crank–Nicolson method.It is proved that the depths of the imaginary part of the PT-symmetric periodic potential gradually increase,and the gap solitons become unstable.But the different periods of imaginary part hardly affect the stability of the gap solitons in the corresponding parameter interval.
文摘Motivated by developing a simple model to calculate the diffusion coefficient in moderate friction region, a simplified model is proposed to deal with the diffusion of Brownian particles in a periodic potential. Where the internal noise is a Gaussian white noise, and the basic cell of the periodic potential is composed of a parabolic potential linked with a harmonic potential. When the particles cross the joint point of the potential, a time coarse-graining scheme is used to obtain a simple analytical expression of the probability distribution. The particles drift and diffuse from the first barrier to the second barrier, the passing probability over the second barrier corresponding to the escape rate becomes decrease serves as the long-jump probability. The theoretical result is confirmed by numerical simulation results. The approach can be extended to color noise case.
基金supported by the Hunan Provincial Natural Science Foundation of China(Nos.2020JJ4240,2018JJ2078)the Scientific Research Fund of Hunan Provincial Education Department(No.19A106,18C0699)the Postgraduate University-Level Research Programme of Jishou University(No.Jdy22043)。
文摘We investigate the topological properties of an antiferromagnetic(AFM)chain with an on-site periodic potential,considering the intrinsic spin–orbit coupling and an external Zeeman field along with the nanowire.Our results indicate that Majorana zero modes(MZMs)can be observed by adjusting the strength of the periodic potential.We have calculated the energy spectrum,the wave-function and transport properties,and all these results support the existence of MZMs in the AFM chain.Additionally,multiple topological phase transitions occur as the strength of the periodic potential changes,and several regions support MZMs.
文摘We present a formula approximating the mean escape time(MST)of a particle from a tilted multi-periodic potential well.The potential function consists of a weighted sum of a finite number of component functions,each of which is periodic.For this particular case,the least period of the potential function is a common period amongst all of its component functions.An approximation of the MST for the potential function is derived,and this approximation takes the form of a product of the MSTs for each of the individual periodic component functions.Our first example illustrates the computational advantages of using the approximation for model validation and parameter tuning in the context of the biological application of DNA transcription.We also use this formula to approximate the MST for an arbitrary tilted periodic potential by the product of MSTs of a finite number of its Fourier modes.Two examples using truncated Fourier series are presented and analyzed.
基金supported by the research project UTAustin/MAT/066/2008.
文摘Numerical solutions of a non-Fickian diffusion equation belonging to a hyperbolic type are presented in one space dimension.The Brownian particle modelled by this diffusion equation is subjected to a symmetric periodic potential whose spatial shape can be varied by a single parameter.We consider a numerical method which consists of applying Laplace transform in time;we then obtain an elliptic diffusion equation which is discretized using a finite difference method.We analyze some aspects of the convergence of the method.Numerical results for particle density,flux and mean-square-displacement(covering both inertial and diffusive regimes)are presented.
基金Permanent address: Institute of Mathematics, Academia Sinica, Beijing 100080, China.
文摘Recently there has been a considerable amount of work on the existence of Tperiodic solutions for Hamiltonian systems with singular potentials, (see [1]—[7],[10], [11], [13], [14]). In this paper we will study the existence of T-periodic solutions for nonconservative second-order dynamical systems
基金Project(RDCPJ346365-06)supported by the Natural Sciences and Engineering Research Council of CanadaProject(51208193)supported by the National Natural Science Foundation of ChinaProject(11jj6034)supported by the Hunan Provincial Natural Science Foundation
文摘The effect of MnO4- and silver content on electrochemical behaviour of five commercial Pb-Ag alloy anodes was studied in acid zinc sulphate electrolyte with and without MnO4- ions at 38 °C during potential decay periods. When the anodes were immersed into acid zinc sulphate electrolyte without MnO4- ions, the Pb-0.72%Ag anode entered complete passivation state in the shortest time among the five anodes, followed by anodes Pb-0.67%Ag, Pb-0.60%Ag, Pb-0.58%Ag and Pb-0.29%Ag-0.1%Ca by measurement of open circuit potential. During immersion of the anodes, MnO4 ions accelerated the passivation and increased the corrosion current density of the anodes. After immersion in zinc electrolyte with MnO4-, the anode Pb-0.72%Ag had the best corrosion resistance, followed by anodes Pb-0.67%Ag, Pb-0.60%Ag, then the close anodes Pb-0.58%Ag and Pb-0.29%Ag-0.1%Ca by the electrochemical impedance spectroscopy (EIS) analysis.
基金supported by the National Key R&D Program of China (No.2018YFC1800506)the Key R&D Program of Zhejiang Province (No.2020C03083)。
文摘Persulfate is considered a convenient and efficient remediation agent for organic contaminated soil.However,the potential risk of sulfur into the soil remediation by persulfate remains ignored.In this study,glass bottles with different persulfate dosages and groundwater tables were set up to simulate persulfate remediation of organic pollutants(aniline).The results found sulfate to be the main end-product(83.0%–99.5%)of persulfate remediation after10 days.Moreover,H_(2)S accounted for 93.4%–99.4%of sulfur reduction end-products,suggesting that H_(2)S was the final fate of sulfur.H_(2)S was released rapidly after one to three days at a maximum concentration of 33.0 ppm,which is sufficient to make a person uncomfortable.According to the fitted curve results,H_(2)S concentration decreased to a safe concentration(0.15 ppm)after 20–85 days.Meanwhile,the maximum concentration of methanethiol reached 0.6 ppm.These results indicated that secondary pollution from persulfate remediation could release harmful gases over a long time.Therefore,persulfate should be used more carefully as a remediation agent for soil contamination.
文摘We show that supersymmetry is a simple but powerful tool to exactly solve quantum mechanics problems. Here, the supersymmetric approach is used to analyse a quantum system with periodic Poschl-Teller potential, and to find out the exact energy spectra and the corresponding band structure.
基金This work was partially supported by the National Natural Science Foundation of China (Grant Nos. 11075016 and 11475022) and the Scientific Research Funds of Huaqiao University.
文摘In this study, we investigate the collective directed transport of coupled Brownian particles in spatially symmetric periodic potentials under time-periodic pulsating modulations. We find that the coupling between two particles can induce symmetry breaking and consequently collective directed motion. Moreover, the direction of motion can be reversed under certain conditions. The dependence of directed current on various parameters is systematically studied, reverse motion can be achieved by modulating the coupling free length and the phase shift of tile pulsating potential. The dynamical mechanism of these transport properties is understood in terms of the effective-potential theory and the space-time transformation invariance. The directed transport of coupled Brownian motors can be maniplflated and optimized by adjusting the coupling strength, pulsating frequency, or noise intensity.
基金Supported by the National Natural Science Foundation of China(No.10671176)
文摘Kerov[16,17] proved that Wigner's semi-circular law in Gauss[an unitary ensembles is the transition distribution of the omega curve discovered by Vershik and Kerov[34] for the limit shape of random partitions under the Plancherel measure. This establishes a close link between random Plancherel partitions and Gauss[an unitary ensembles, In this paper we aim to consider a general problem, namely, to characterize the transition distribution of the limit shape of random Young diagrams under Poissonized Plancherel measures in a periodic potential, which naturally arises in Nekrasov's partition functions and is further studied by Nekrasov and Okounkov[25] and Okounkov[28,29]. We also find an associated matrix mode[ for this transition distribution. Our argument is based on a purely geometric analysis on the relation between matrix models and SeibergWitten differentials.
基金The authors would like to thank Prof.Matthias Ehrhardt for the inspiring discussion on this work.C.Zheng was supported by the National Natural Science Foundation of China under Grant No.11371218.
文摘Based on the numerical evidences,an analytical expression of the Dirichletto-Neumann mapping in the form of infinite product was first conjectured for the onedimensional characteristic Schrodinger equation with a sinusoidal potential in[Commun.Comput.Phys.,3(3):641-658,2008].It was later extended for the general secondorder characteristic elliptic equations with symmetric periodic coefficients in[J.Comp.Phys.,227:6877-6894,2008].In this paper,we present a proof for this Dirichlet-toNeumann mapping.
基金Project supported by the National Natural Science Foundation of China(No.11464033)the Mongolia University for Nationalities Fund(No.NMDYB1445)
文摘With the circumstance of the electron strongly coupled to LO-phonon and using the variational method of Pekar type(VMPT),we study the eigenenergies and the eigenfunctions(EE) of the ground and the first excited states(GFES) in a RbCl crystal asymmetric Gaussian potential quantum well(AGPQW).It concludes:(i) Twoenergy-level of the AGPQW may be seen as a qubit.(ii) When the electron located in the superposition state of the two-energy-level system,the time evolution and the coordinate changes of the electron probability density oscillated periodically in the AGPQW with every certain period T0=22.475 fs.(iii) Due to the confinement that is a two dimensional x-y plane symmetric structure in the AGPQW and the asymmetrical Gaussian potential(AGP) in the AGPQW growth direction,the electron probability density presents only one peak configuration located in the coordinate of z 〉 0,whereas it is zero in the range of z 〈 0.(iv) The oscillatory period is a decreasing function of the AGPQW height and the polaron radius,(v) The oscillating period is a decreasing one in the confinement potential R 〈 0.24 nm,whereas it is an increasing one in the confinement potential R 〉 0.24 nm and it takes a minimum value in R = 0.24 nm.
文摘The nonlinear lattice - a new and nonlinear class of periodic potentials - was recently introduced to generate various nonlinear localized modes. Several attempts failed to stabilize two-dimensional (2D) solitons against their intrinsic critical collapse in Kerr media. Here, we provide a possibility for supporting 2D matter-wave solitons and vortices in an extended setting - the cubic and quintic model - by introducing another nonlinear lattice whose period is controllable and can be different from its cubic counterpart, to its quintic nonlinearity, therefore making a fully "nonlinear quasi-crystal". A variational approximation based on Gaussian ansatz is developed for the fundamental solitons and in particular, their stability exactly follows the inverted Vakhitov-Kolokolov stability criterion, whereas the vortex solitons are only studied by means of numerical methods. Stability regions for two types of localized mode -- the fundamental and vortex solitons -- are provided. A noteworthy feature of the localized solutions is that the vortex solitons are stable only when the period of the quintic nonlinear lattice is the same as the cubic one or when the quintic nonlinearity is constant, while the stable fundamental solitons can be created under looser conditions. Our physical setting (cubic-quintic model) is in the framework of the Gross-Pitaevskii equation or nonlinear Schr6dinger equation, the predicted localized modes thus may be implemented in Bose-Einstein condensates and nonlinear optical media with tunable cubic and quintic nonlinearities.
基金supported by the National Science Council of R.O.C.(Taiwan)through Project NSC 98-2115-M-231-001-MY3.
文摘We study efficient spectral-collocation and continuation methods(SCCM)for rotating two-component Bose-Einstein condensates(BECs)and rotating two-component BECs in optical lattices,where the second kind Chebyshev polynomials are used as the basis functions for the trial function space.A novel two-parameter continuation algorithm is proposed for computing the ground state and first excited state solutions of the governing Gross-Pitaevskii equations(GPEs),where the classical tangent vector is split into two constraint conditions for the bordered linear systems.Numerical results on rotating two-component BECs and rotating two-component BECs in optical lattices are reported.The results on the former are consistent with the published numerical results.