摘要 :AbstractWe consider the Schr?dinger equation?y′′+q(x)y=λy,on a finite interval with Dirichlet boundary conditions, whereq(x)is of indefinite sign. In the case of symmetric potentials, we prove the optimal lower boundλnλ1≥n2(...
展开AbstractWe consider the Schr?dinger equation?y′′+q(x)y=λy,on a finite interval with Dirichlet boundary conditions, whereq(x)is of indefinite sign. In the case of symmetric potentials, we prove the optimal lower boundλnλ1≥n2(resp. upper boundλnλ收起
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A new group of spherical single-particle potentials applicable to a wide nuclidic region are obtained. The central component of each potential is a five-parameter refinement of the Woods-Saxon potential including two new parameter...
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A new group of spherical single-particle potentials applicable to a wide nuclidic region are obtained. The central component of each potential is a five-parameter refinement of the Woods-Saxon potential including two new parameters, of which one parameter governs the behavior at large distances and the other produces a dip in the surface region. These five potential parameters as well as the parameters in the spin-orbit component are assumed to vary smoothly with Z and N. In evaluating the Coulomb energy of a single proton, occasional deviations of that proton from the single-particle state to more complicated states are taken into account by including an adjustable parameter. The adjustable parameters introduced are fixed by comparison with experimental data of single-particle levels in the vicinities of 15 doubly magic or magic-submagic nuclides ranging from He-4 to Pb-208, and a reasonable agreement with experiment is obtained. (C) 2000 Elsevier Science B.V. All rights reserved. [References: 18]
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Using the self-consistent Hartree-Fock calculation plus RPA with Skyrme interactions, the RPA quadrupole strength function is estimated in the coordinate space, including simultaneously both the isoscalar and the isovector correla...
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Using the self-consistent Hartree-Fock calculation plus RPA with Skyrme interactions, the RPA quadrupole strength function is estimated in the coordinate space, including simultaneously both the isoscalar and the isovector correlation. We discuss the result of the isoscalar, the isovector and the electric quadrupole polarization of the Ca-isotopes from the proton drip line towards the neutron drip line. We study also the comparison of the polarizations in the A = 48 mirror nuclei, Ni-48(28)20 and Ca-48(20)28, and the dependence of the polarization of O-28(8)20 on various Skyrme interactions. (C) 1997 Elsevier Science B.V. [References: 12]
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The state of a single particle injected onto the surface of the Fermi sea is a pure state if the temperature is zero and is a mixed state if the temperature is finite. Moreover, the state of an injected particle is orthogonal to t...
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The state of a single particle injected onto the surface of the Fermi sea is a pure state if the temperature is zero and is a mixed state if the temperature is finite. Moreover, the state of an injected particle is orthogonal to the state of the Fermi sea at zero temperature, while it is not orthogonal at nonzero temperature. These changes in the quantum state of the injected particles can be detected using the temperature dependence of the shot noise that is generated when the particles one by one pass through a semitransparent quantum point contact. Namely, the shot noise produced by the mixed state is suppressed in comparison with the noise of the pure state. In addition, the correlations between the injected particles and the underlying Fermi sea, present at nonzero temperature, do enhance the shot noise. Furthermore, antibunching of injected particles with possible thermal excitations coming from another input channel of a quantum point contact does suppress shot noise. Here I analyze in detail these three effects, which are responsible for the temperature dependence of the shot noise, and discuss how to distinguish them experimentally.
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When using standard deterministic particle methods, point values of the computed solutions have to be recovered from their singular particle approximations by using some smoothing procedure. The choice of the smoothing procedure i...
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When using standard deterministic particle methods, point values of the computed solutions have to be recovered from their singular particle approximations by using some smoothing procedure. The choice of the smoothing procedure is rather flexible. Moreover, there is always a parameter associated with the smoothing procedure: if this parameter is too large, the numerical solution loses its accuracy; if it is too small, oscillation appears. No explicit formula has been given on how to choose this parameter. In this paper, we develop a particle method for the semiclassical limit of the Schr?dinger equation and the Vlasov-Poisson equations, in which we use the property of conservation of charge, which was studied in [D. Wei, Kinetic and Related Models, 3 (2010), pp. 729- 754], to construct the density. This method avoids the recovery step of the particle methods; thus it is simpler and more accurate. In particular it gives more accurate field quantities. Consequently, we apply this method to the Vlasov-Poisson equations, which yield more accurate density and electric field in each time step. We carry out numerical experiments in both one and two dimensions for the Schr?dinger equation and Vlasov-Poisson equations to verify the method. Some comparisons with other particle methods are also made.
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We consider \(N\)-body Schr?dinger operators with \(N\geq 3\) quantum particles interacting via short-range potentials in dimension \(d\geq 3\), where the essential spectrum coincides with the half line \([0,\infty)\). We give the...
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We consider \(N\)-body Schr?dinger operators with \(N\geq 3\) quantum particles interacting via short-range potentials in dimension \(d\geq 3\), where the essential spectrum coincides with the half line \([0,\infty)\). We give the asymptotic behaviour of eigenfunctions corresponding to the eigenvalue at the threshold of the essential spectrum under the condition that the eigenfunctions are not orthogonal to the sum of the pair interactions. This condition is fulfilled when zero is the smallest eigenvalue and the pair interactions are negative. We also give examples of systems when this condition is not met.
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Phase functions for hexagonal ice plates randomly oriented in the horizontal plane are calculated with a facet-tracing code. The bright optical phenomena like sundog and parhelion 120 degrees are quantified by their weight coeffic...
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Phase functions for hexagonal ice plates randomly oriented in the horizontal plane are calculated with a facet-tracing code. The bright optical phenomena like sundog and parhelion 120 degrees are quantified by their weight coefficients that are tabulated as functions of both incident angles and particle aspect ratios. Dependence of the scattered intensity on azimuth scattering angles is studied in details. (C) 2007 Elsevier Ltd. All rights reserved.
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High channel capacity always plays an important role in quantum communication. Dense coding is an effective way to improve channel capacity, whose core idea is to apply as few particles as possible to carry information. Quantum en...
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High channel capacity always plays an important role in quantum communication. Dense coding is an effective way to improve channel capacity, whose core idea is to apply as few particles as possible to carry information. Quantum entanglement exists not only between multiple particles but also in various degrees of freedom of a single-particle (intraparticle entanglement). Compared with the former (entanglement among multi-particles), firstly, the latter (intraparticle entanglement) can enable more bits of information to be transmitted in one-time communication by utilizing more degrees of freedom of single-particle. Secondly, the latter is more robust than the former. Thus, in this paper, based on the current experiment technology level, a scheme is designed to encode, transmit, and process 3 bits of classical information by applying the intraparticle entanglement state of a single-photon with three degrees of freedom in theory. Based on the literature survey, this scheme reaches the level at which a single-photon currently carries the most information with good security and robustness, and this work reveals a good idea for realizing superdense coding.
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In this paper, we consider a class of two-particle tight-binding Hamiltonians, describing pairs of interacting quantum particles on the lattice ?~d, d ≥ 1, subject to a common external potential V(x) which we assume quasi-periodi...
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In this paper, we consider a class of two-particle tight-binding Hamiltonians, describing pairs of interacting quantum particles on the lattice ?~d, d ≥ 1, subject to a common external potential V(x) which we assume quasi-periodic and depending on auxiliary parameters. Such parametric families of ergodic deterministic potentials ("grands ensembles") have been introduced earlier in Chulaevsky (2007), in the framework of single-particle lattice systems, where it was proved that a non-uniform analog of the Wegner bound holds true for a class of quasi-periodic grands ensembles. Using the approach proposed in Chulaevsky and Suhov (Commun Math Phys 283(2):479-489, 2008), we establish volume-dependent Wegner-type bounds for a class of quasi-periodic two-particle lattice systems with a non-random short-range interaction.
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Investigation of the heterogeneity of protein adsorption on particle surfaces has attracted enormous research attention owing to its great importance in fundamental studies and quality control. Herein we, for the first time, repor...
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Investigation of the heterogeneity of protein adsorption on particle surfaces has attracted enormous research attention owing to its great importance in fundamental studies and quality control. Herein we, for the first time, report a new method for label-free analysis of the heterogeneity of protein adsorption on single nanoparticles, based on particle collision events at the orifice of a nanopipette. The dwell time was strongly dependent on the amount of protein adsorbed on polystyrene particles, which could be used to analyze the heterogeneity of protein adsorption at the single particle level. This method presents a label-free, sensitive, reproducible and easily-operated way to analyze adsorption behavior at the single particle level, which opens a new approach to the study of the heterogeneity of physicochemical parameters at the surface of nanoparticles.
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