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wave functions of a new kind of nonlinear single-mode squeezed state

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Chinese Physics B 2014年第12期23卷 34-37页

作者：范洪义笪诚陈俊华 Department of Physics Ningbo University Department of Material Science and Engineering University of Science and Technology of China

We explore the theoretical possibility of extending the usual squeezed state to those produced by nonlinear singlemode squeezing operators. We derive the wave functions of exp[-（ig/2）（（1-X2）1/2P ＋ P（1-X2）1/2）... 详细信息

关键词： wave functions nonlinear single-mode squeezed states coordinate representation disentangling formula

Scattering of Geometric Algebra wave functions and Collapse in Measurements

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Journal of Applied Mathematics and Physics 2020年第9期8卷 1838-1844页

作者： Alexander Soiguine SOiGUINE Quantum Computing Aliso Viejo CA USA

The research considers wavelike objects that are elements of even subalgebra of geometric algebra in three dimensions. The used formalism particularly eliminates long existing confusion about the reasons behind the appearance of the imaginary unit in quantum mechanics and introduces clear definition of wave functions. When a wave function acts through the Hopf fibration on a localized geometric algebra element, that is executing a measurement, the result can be named as “collapse” of the wave function.

关键词： wave functions Geometric Algebra Measurements Scattering Entanglement Dualism

Quantum Computingvia Entanglement in Geometric Algebra Approach

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Journal of Applied Mathematics and Physics 2024年第2期12卷 445-457页

作者： Alexander Soiguine SOiGUINE Quantum Computing Aliso Viejo USA

The superiority of hypothetical quantum computers is not due to faster calculations but due to different scheme of calculations running on special hardware. At the same time, one should realize that quantum computers would only provide dramatic speedups for a few specific problems, for example, factoring integers and breaking cryptographic codes in the conventional quantum computing approach. The core of quantum computing follows the way a state of a quantum system is defined when basic things interact with each other. In the conventional approach, it is implemented through the tensor product of qubits. In the suggested geometric algebra formalism simultaneous availability of all the results for non-measured observables is based on the definition of states as points on a three-dimensional sphere, which is very different from the usual Hilbert space scheme.

关键词： Geometric Algebra wave functions Entanglement Maxwell Equations Three-Dimensional Sphere

Parallelizable Calculation of Observables Values on Analog Quantum Computer

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Journal of Applied Mathematics and Physics 2024年第7期12卷 2400-2406页

作者： Alexander Soiguine SOiGUINE Quantum Computing Aliso Viejo USA

The superiority of hypothetical quantum computers is not due to faster calculations but due to different schemes of calculations running on special hardware. The core of quantum computing follows the way a state of a quantum system is defined when basic things interact with each other. In conventional approach it is implemented through tensor product of qubits. In the geometric algebra formalism simultaneous availability of all the results for non-measured observables is based on the definition of states as points on three-dimensional sphere.

关键词： Geometric Algebra wave functions Entanglement Maxwell Equations Three-Dimensional Sphere States Observables Measurements GPU Multithreading OpenCL

Measuring the Wigner functions of Two-Mode Cavity Fields and Testing the Bell＇s Inequalities

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Chinese Physics Letters 2004年第1期21卷 5-8页

作者：张智明 DepartmentofPhysics ShanghaiJiaoTongUniversityShanghai200240

We propose a scheme for measuring the Wigner function of a two-mode cavity field. The scheme bases on the interaction between the two-mode cavity field and three-level atoms. We find a simple relation between the Wigner function and the atomic population. One can obtain the Wigner function by measuring the atomic population with a micromaser-like experiment and doing a numerical integral. By using the two-mode Wigner function one can obtain the Clauser–Horne combination and test the Bell's inequalities. We test our equations with a two-mode entanglement state and the results are rather good.

关键词： wave functions

Spectroscopic properties of thulium ions in bismuth silicate glass

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Chinese Optics Letters 2012年第10期10卷 44-48页

作者：王欣胡丽丽李科峰田颖凡思军 Shanghai Institute of Optics and Fine Mechanics Chinese Academy of Science Graduate Universitiy of Chinese Academy of Science Beijing 100049China

A new type of bismuth silicate glass （Bi2O3-SiO2-ZnO-Al2O3-La2O3） doped with Tm2O3 is prepared by melt-quenching method. The thermal stability of the glass is examined by differential scanning calorimetry. No crystallization peak is found. Using the absorption and emission spectra, the absorption and emission cross-sections are calculated. Their maximum data are 2.9×10^-21cm^2 at 1663 nm and 4.7×10^-21cm^2 at 1826 nm, respectively. Using the Judd-Ofelt theory, the radiation transition probabilities and radiative lifetimes are obtained. The extended overlap integral method is applied to analyze energy transfer process among the Tm3＋ ions. The transfer constants of cross-relaxation and energy migration among the Tm^3＋ ions at the 3H4 level are 7.60×10^-40 and 14.98×10^-40 cm^6 /s, respectively. The critical transfer radius for cross-relaxation is 0.99 nm. The cross relaxation process is easy to realize and is favorable for obtaining ～2-μm laser.

关键词： Bismuth Chemical bonds Differential scanning calorimetry Emission spectroscopy Energy transfer Glass Lanthanum oxides Molecular orbitals Silicates wave functions Zinc oxide

Spectral Statistics in the Cranking Model

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Chinese Physics Letters 2002年第2期19卷 184-186页

作者：周先荣孟杰等 InstituteofTheoreticalPhysics ChineseAcademyofSciencesP.O.Box2735beijing100080

The difference of spectral statistics properties between single-j and two-j shell models has been studied in the frame of the cranking model. The results show that the system becomes more regular when single-j space (i13/2) is replaced by a two-j shell (g7/2 + d5/2), although the basis size of the configuration space is unchanged. However, the degree of chaos of the system changes slightly when configuration space is enlarged by extending the single-j shell (i13/2) to two-j (i13/2 + g9/2) shell.

关键词： wave functions

Acoustic radiation from the submerged circular cylindrical shell treated with active constrained layer damping

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Chinese Physics B 2015年第12期24卷 361-372页

作者：袁丽芸向宇陆静蒋红华 Department of Automotive and Transportation Guangxi University of Science and Technology Guangxi Key Laboratory of Automobile Components and Vehicle Technology Guangxi University of Science and Technology

Based on the transfer matrix method of exploring the circular cylindrical shell treated with active constrained layer damping（i.e., ACLD）, combined with the analytical solution of the Helmholtz equation for a point source, a multi-point multipole virtual source simulation method is for the first time proposed for solving the acoustic radiation problem of a submerged ACLD shell. This approach, wherein some virtual point sources are assumed to be evenly distributed on the axial line of the cylindrical shell, and the sound pressure could be written in the form of the sum of the wave functions series with the undetermined coefficients, is demonstrated to be accurate to achieve the radiation acoustic pressure of the pulsating and oscillating spheres respectively. Meanwhile, this approach is proved to be accurate to obtain the radiation acoustic pressure for a stiffened cylindrical shell. Then, the chosen number of the virtual distributed point sources and truncated number of the wave functions series are discussed to achieve the approximate radiation acoustic pressure of an ACLD cylindrical shell. Applying this method, different radiation acoustic pressures of a submerged ACLD cylindrical shell with different boundary conditions, different thickness values of viscoelastic and piezoelectric layer, different feedback gains for the piezoelectric layer and coverage of ACLD are discussed in detail. Results show that a thicker thickness and larger velocity gain for the piezoelectric layer and larger coverage of the ACLD layer can obtain a better damping effect for the whole structure in general. Whereas, laying a thicker viscoelastic layer is not always a better treatment to achieve a better acoustic characteristic.

关键词： active constrained layer damping submerged circular cylindrical shell acoustic radiation multipoint multipole nethod wave functions

DIRICHLET PROBLEMS FOR STATIONARY VON NEUMANN-LANDAU wave EQUATIONS

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Acta Mathematica Scientia 2009年第5期29卷 1225-1232页

作者：陈泽乾 Wuhan Institute of Physics and Mathematics Chinese Academy of Sciences

In this article, we are concerned with the Dirichlet problem of the stationary von Neumann-Landau wave equation：{（-△x＋△y）φ（x,y）=0,x,y∈Ωφ｜δΩxδΩ=fwhere Ω is a bounded domain in R^n. By introducing anti-inner product spaces, we show the existence and uniqueness of the generalized solution for the above Dirichlet problem by functional-analytic methods.

关键词： von Neumann-Landau equation wave functions Dirichlet problem