均值量化与中值量化光栅性能的理论研究

对相移技术的投影栅相位法的传统中值量化方法提出改进,设计和制作出小误差、低高阶谐波的均值量化光栅.理论讨论了相位值、离散等级和量化等级等因素对两种量化光栅性能的影响;在标准偏差和频谱分布两方面比较后,得出均值量化光栅性能优于中值量化光栅且更接近正弦光栅的结论.     

用对应原理导出氢原子量子化能量、量子化电子轨道以及Bohr稳定轨道量子化条件

用对应原理导出了氢原子量子化能量、量子化电子轨道以及Bohr稳定轨道量子化条件(角动量量子化条件)     

Number-Phase Quantization Scheme for L-C Circuit

For a mesoscopic L-C circuit, besides the Louisell's quantization scheme in which electric charge q and electric current I are respectively quantized as the coordinate operator Q and momentum operator P, in this paper we propose a new quantization scheme in the context of number-phase quantization through the standard Lagrangian formalism. The comparison between this number-phase quantization with the Josephson junction's Cooper pair number-phase-difference quantization scheme is made.     

ADC border effect and suppression of quantization error in the digital dynamic measurement

The digital measurement and processing is an important direction in the measurement and control field. The quantization error widely existing in the digital processing is always the decisive factor that restricts the development and applications of the digital technology. In this paper, we find that the stability of the digital quantization system is obviously better than the quantization resolution. The application of a border effect in the digital quantization can greatly improve the accuracy of digital processing. Its effective precision has nothing to do with the number of quantization bits, which is only related to the stability of the quantization system. The high precision measurement results obtained in the low level quantization system with high sampling rate have an important application value for the progress in the digital measurement and processing field.     

A Deformation-Theoretical Approach to Weyl Quantization on Riemannian Manifolds

By using a sheaf-theoretical language, we introduce a notion of deformation quantization allowing not only for formal deformation parameters but also for real or complex ones as well. As a model for this approach to deformation quantization, we construct a quantization scheme for cotangent bundles of Riemannian manifolds. Here, we essentially use a complete symbol calculus for pseudodifferential operators on a Riemannian manifold. Depending on a scaling parameter, our quantization scheme corresponds to normally ordered, Weyl or antinormally ordered quantization. Finally, it is shown that our quantization scheme induces a family of pairwise isomorphic strongly closed star products on a cotangent bundle.     

The positronium negative ion: Classical properties aaand semiclassical quantization

Properties of collinear and planar periodic orbits for the positronium negative ion are examined with respect to the possibilities for semiclassical quantization. In contrast to other two-electron atomic systems as helium and H^- the relevant orbits for quantization are fully stable and permit a full torus quantization. However, for lower excitations the area of stability in phase-space is too small for a reliable torus quantization. Instead, a quasi-separability of the three-body system is used to apply effective one-dimensional (WKB) quantization. Received 19 January 2001     

量化对干涉成像仪复原光谱幅值不确定度的影响

推导并分析了干涉图量化对干涉成像光谱仪复原光谱幅值的影响。结果表明,复原光谱幅值的不确定度受量化条件的影响。在确定了干涉图采样点数后,干涉成像光谱仪复原光谱幅值的不确定度与A/D转换器的量化步长成正比;在固定了量化步长后,不确定度随干涉图采样点数的增加而增大;由干涉图量化引起的复原光谱幅值不确定度的大小还与在实际算法中选取的切趾函数形式有关。     

Are the Weyl and coherent state descriptions physically equivalent?

We investigate the consistency of coherent state quantization in regard to physical observations in the non-relativistic (or Galilean) regime. We compare this particular type of quantization of the complex plane with the canonical (Weyl) quantization and examine whether they are or not equivalent in their predictions. As far as only usual dynamical observables (position, momentum, energy, …) are concerned, the quantization through coherent states is proved to be a perfectly valid alternative. We successfully put to the test the validity of CS quantization in the case of data obtained from vibrational spectroscopy.     

THE BKS DERNEL OF BOSONIC STRINGS AND PATH INTEGRAL

The connections between geometric quantization and path integral quantization of bosonic strings are investigated.The Polyakov path integral formulation and its measure are manifestly deduced from the Blattner-Kostant-Sternberg(BKS) kernel of geometric quantization.     

The Angular Momentum Dilemma and Born–Jordan Quantization

The rigorous equivalence of the Schrödinger and Heisenberg pictures requires that one uses Born–Jordan quantization in place of Weyl quantization. We confirm this by showing that the much discussed “ angular momentum dilemma” disappears if one uses Born–Jordan quantization. We argue that the latter is the only physically correct quantization procedure. We also briefly discuss a possible redefinition of phase space quantum mechanics, where the usual Wigner distribution has to be replaced with a new quasi-distribution associated with Born–Jordan quantization, and which has proven to be successful in time-frequency analysis.     

Quantization: Deformation and/or Functor?

After a short presentation of the difference in motivation between the Berezin and deformation quantization approaches, we start with a reminder of Berezin’s view of quantization as a functor followed by a brief overview of deformation quantization in contrast with the latter. We end by a short survey of two main avatars of deformation quantization, quantum groups and quantum spaces (especially noncommutative geometry) presented in that perspective.     

Geometric quantization and constraints in field theory

The main objective of this series of lectures is a discussion of the problem of quantization of systems with constraints, first studied by P.A.M. Dirac. I want to reinterprete Dirac's approach to quantization of constraints in the framework of geometric quantization, and then use it to discuss some aspects of quantized Yang-Mills fields. We begin with a review of geometric quantization and the implied relationship between the co-adjoint orbits and the irreducible unitary representations of Lie groups. Next, we discuss an intrinsic Hamiltonian formulation of a class of field theories which includes gauge theories and general relativity. Quantization of this class of field theories is discussed. Dirac's approach to quantization of constraints is reinterpreted in the framework of geometric quantization.     

Extended GIPQ description of the RPA excitations

The work presents an application of the GIPQ quantization method, extended to include the wave function quantization. By explicit calculation on a particular proton-neutron system it is shown that the extended quantization gives the same excitation operator and energy as the RPA.     

Quantization of the Green-Schwarz superstring

The problem of quantization of superstrings is traced back to the nilpotency of gauge generators of the first-generation ghosts. The quantization of such theories is performed. The novel feature of this quantization is the freedom in choosing the number of ghost generations as well as gauge conditions. As an example, we perform the quantization of the heterotic string in a gauge that preserves spacetime supersymmetry. The equations of motion are those of a free theory.     

Operator Ordering Problem and Coordinate-Free Nature of Geometric Quantization

Operator ordering problem in geometric quantization is investigated. While the quantum operator for p²f(q) given by geometric quantization is found to be ordered via the rule invariant under general coordinate transformations, it is shown that the quantum operators for pⁿ f(q) when n > 2 cannot be well-defined by geometric quantization. This is considered as a natural consequence of the coordinate-free nature of geometric quantization and the Van Hove's theorem.     

Use of error diffusion with space-variant optimized weights to obtain high-quality quantized images and holograms

Error diffusion is an important procedure for image and hologram quantization. The spatial distribution of the spectrum of the quantization noise is shaped by a filter function, which depends on the diffusion weights. The customary weights applied during the whole quantization process are optimized to yield the desired filter functions. Stability restrictions limit the optimization process. We suggest optimizing new weights locally after the quantization of each pixel. In this way the eventual occurrence of instabilities can be counteracted and the quality of the filter function improved.     

一种校正相位测量轮廓术量化误差的算法

为了减小相位测量轮廓术中因数字化设备内部结构的量化处理过程引起的相位量化误差,提高相位测量精度。针对相位测量精度要求较高且表面凹凸变化不大的被扫描物体提出了一种能够有效校正相位测量轮廓术量化误差的算法,测量相位中的每一个像素点利用其相邻像素点进行校正。实验结果显示,校正之后,相位量化误差标准差减小了41.38%,相位测量的精度得到了提高。     

Optimized phase quantization for diffractive elements by use of a bias phase

Many applications of diffractive phase elements involve the calculation of a continuous phase profile that is subsequently quantized for fabrication. The quantization process maps the continuous range of phase values to a limited number of discrete steps. We report our observation of the influence of this quantization process on the performance of mode-selecting diffractive elements and show that the quantization process produces significantly better results by use of an optimized bias phase. In principle this process can be employed to a greater or lesser extent in any quantization process.     

Affine holomorphic quantization

We present a rigorous and functorial quantization scheme for affine field theories, i.e., field theories where local spaces of solutions are affine spaces. The target framework for the quantization is the general boundary formulation, allowing to implement manifest locality without the necessity for metric or causal background structures. The quantization combines the holomorphic version of geometric quantization for state spaces with the Feynman path integral quantization for amplitudes. We also develop an adapted notion of coherent states, discuss vacuum states, and consider observables and their Berezin–Toeplitz quantization. Moreover, we derive a factorization identity for the amplitude in the special case of a linear field theory modified by a source-like term and comment on its use as a generating functional for a generalized S$S$-matrix.