Canonical quantization covers a broad class of classical systems, but that does not include all the problems of interest. Affine quantization has the benefit of providing a successful quantization of many important pr...Canonical quantization covers a broad class of classical systems, but that does not include all the problems of interest. Affine quantization has the benefit of providing a successful quantization of many important problems including the quantization of half-harmonic oscillators [1], non-renormalizable scalar fields, such as (<i>ϕ</i><sup>12</sup>)<sub>3</sub> [2] and (<i>ϕ</i><sup>12</sup>)<sub>3</sub> [3], as well as the quantum theory of Einstein’s general relativity [4]. The features that distinguish affine quantization are emphasized, especially, that affine quantization differs from canonical quantization only by the choice of classical variables promoted to quantum operators. Coherent states are used to ensure proper quantizations are physically correct. While quantization of non-renormalizable covariant scalars and gravity are difficult, we focus on appropriate ultralocal scalars and gravity that are fully soluble while, in that case, implying that affine quantization is the proper procedure to ensure the validity of affine quantizations for non-renormalizable covariant scalar fields and Einstein’s gravity.展开更多
In this paper, we analyze the physical layer abstraction for bit interleaved coded orthogonal frequency division multiplexing(BIC-OFDM) system from a parallel bit channel perspective. By combining the exponential effe...In this paper, we analyze the physical layer abstraction for bit interleaved coded orthogonal frequency division multiplexing(BIC-OFDM) system from a parallel bit channel perspective. By combining the exponential effective SNR(signal-to-noise ratio) mapping(EESM) with the maximum a posteriori(MAP) algorithm, a bit LLR(log-likelihood ratio) wise EESM(BL-EESM) method is proposed. This method can abstract the link performance with high accuracy, especially for the case when channel estimation is imperfect. Afterward, the BL-EESM method is simplified by utilizing the non-linear quantization idea, which can reduce the times of exponential operation by two orders of magnitude at wide system bandwidth, yet shows little loss in accuracy. Our proposal can be applied to both system level simulations to save the time consumption and to practical terminals to facilitate the adaptive modulation and coding(AMC) procedure, bringing about throughput improvement at low hardware cost.展开更多
研究带宽受限下信息物理系统中虚假数据注入(false data injection,FDI)攻击的检测问题.首先,将执行器遭受的FDI攻击信号建模为系统的未知输入信号,基于给定的H∞性能指标,设计局部残差产生器以实时逼近攻击信号.其次,为提高检测系统预...研究带宽受限下信息物理系统中虚假数据注入(false data injection,FDI)攻击的检测问题.首先,将执行器遭受的FDI攻击信号建模为系统的未知输入信号,基于给定的H∞性能指标,设计局部残差产生器以实时逼近攻击信号.其次,为提高检测系统预警速度,在分布式融合框架下将所有经对数量化后的残差信号发送至检测中心,并设计优化目标将分布式加权融合准则的求解问题转化为线性矩阵不等式形式下的凸优化问题.与单个传感器情况下的检测方法相比,基于分布式融合方法所确定的检测阈值更加精准,从而可大幅度提高对攻击信号的预警速度.最后,通过移动目标系统的仿真验证所提方法的有效性.展开更多
The similarity between classical and quantum physics is large enough to make an investigation of quantization methods a worthwhile endeavour. As history has shown, Dirac's canonical quantization method works reaso...The similarity between classical and quantum physics is large enough to make an investigation of quantization methods a worthwhile endeavour. As history has shown, Dirac's canonical quantization method works reasonably well in the case of conventional quantum mechanics over R<sup>n</sup> but it may fail in non-trivial phase spaces and also suffer from ordering problems. Affine quantization is an alternative method, similar to the canonical quantization, that may offer a positive result in situations for which canonical quantization fails. In this paper we revisit the affine quantization method on the half-line. We formulate and solve some simple models, the free particle and the harmonic oscillator.展开更多
Loop Quantum Gravity is widely developed using canonical quantization in an effort to find the correct quantization for gravity. Affine quantization, which is like canonical quantization augmented and bounded in one o...Loop Quantum Gravity is widely developed using canonical quantization in an effort to find the correct quantization for gravity. Affine quantization, which is like canonical quantization augmented and bounded in one orientation, e.g., a strictly positive coordinate. We open discussion using canonical and affine quantizations for two simple problems so each procedure can be understood. That analysis opens a modest treatment of quantum gravity gleaned from some typical features that exhibit the profound differences between aspects of seeking the quantum treatment of Einstein’s gravity.展开更多
A simple phenomenological model is developed, which indicates the existence of a direct link between the concept of rest mass of a particle and magnetodynamic energies associated to the formation of the particle. The ...A simple phenomenological model is developed, which indicates the existence of a direct link between the concept of rest mass of a particle and magnetodynamic energies associated to the formation of the particle. The model is based upon the principles of quantization and conservation of flux, well known for their application in superconductivity. The charge of particles is considered as forming vortices of superconducting currents, which we postulate are created by electromagnetic fluctuations from vacuum (or related processes). A new quantization rule gathers the size, the magnetic moment, and the rest mass of the particle and associates these quantities to the integer number of flux quanta that should be stored in the vortices corresponding to each particle. The model is applied to the electron, the muon, the proton, and the neutron. Quantitative consistency with available experimental data for these subatomic particles is obtained.展开更多
文摘Canonical quantization covers a broad class of classical systems, but that does not include all the problems of interest. Affine quantization has the benefit of providing a successful quantization of many important problems including the quantization of half-harmonic oscillators [1], non-renormalizable scalar fields, such as (<i>ϕ</i><sup>12</sup>)<sub>3</sub> [2] and (<i>ϕ</i><sup>12</sup>)<sub>3</sub> [3], as well as the quantum theory of Einstein’s general relativity [4]. The features that distinguish affine quantization are emphasized, especially, that affine quantization differs from canonical quantization only by the choice of classical variables promoted to quantum operators. Coherent states are used to ensure proper quantizations are physically correct. While quantization of non-renormalizable covariant scalars and gravity are difficult, we focus on appropriate ultralocal scalars and gravity that are fully soluble while, in that case, implying that affine quantization is the proper procedure to ensure the validity of affine quantizations for non-renormalizable covariant scalar fields and Einstein’s gravity.
基金the Shanghai Basic Research KeyProject(No.11DZ1500206)the NationalScience and Technology Major Project of China(No.2012ZX03001013-003)
文摘In this paper, we analyze the physical layer abstraction for bit interleaved coded orthogonal frequency division multiplexing(BIC-OFDM) system from a parallel bit channel perspective. By combining the exponential effective SNR(signal-to-noise ratio) mapping(EESM) with the maximum a posteriori(MAP) algorithm, a bit LLR(log-likelihood ratio) wise EESM(BL-EESM) method is proposed. This method can abstract the link performance with high accuracy, especially for the case when channel estimation is imperfect. Afterward, the BL-EESM method is simplified by utilizing the non-linear quantization idea, which can reduce the times of exponential operation by two orders of magnitude at wide system bandwidth, yet shows little loss in accuracy. Our proposal can be applied to both system level simulations to save the time consumption and to practical terminals to facilitate the adaptive modulation and coding(AMC) procedure, bringing about throughput improvement at low hardware cost.
文摘研究带宽受限下信息物理系统中虚假数据注入(false data injection,FDI)攻击的检测问题.首先,将执行器遭受的FDI攻击信号建模为系统的未知输入信号,基于给定的H∞性能指标,设计局部残差产生器以实时逼近攻击信号.其次,为提高检测系统预警速度,在分布式融合框架下将所有经对数量化后的残差信号发送至检测中心,并设计优化目标将分布式加权融合准则的求解问题转化为线性矩阵不等式形式下的凸优化问题.与单个传感器情况下的检测方法相比,基于分布式融合方法所确定的检测阈值更加精准,从而可大幅度提高对攻击信号的预警速度.最后,通过移动目标系统的仿真验证所提方法的有效性.
文摘The similarity between classical and quantum physics is large enough to make an investigation of quantization methods a worthwhile endeavour. As history has shown, Dirac's canonical quantization method works reasonably well in the case of conventional quantum mechanics over R<sup>n</sup> but it may fail in non-trivial phase spaces and also suffer from ordering problems. Affine quantization is an alternative method, similar to the canonical quantization, that may offer a positive result in situations for which canonical quantization fails. In this paper we revisit the affine quantization method on the half-line. We formulate and solve some simple models, the free particle and the harmonic oscillator.
文摘Loop Quantum Gravity is widely developed using canonical quantization in an effort to find the correct quantization for gravity. Affine quantization, which is like canonical quantization augmented and bounded in one orientation, e.g., a strictly positive coordinate. We open discussion using canonical and affine quantizations for two simple problems so each procedure can be understood. That analysis opens a modest treatment of quantum gravity gleaned from some typical features that exhibit the profound differences between aspects of seeking the quantum treatment of Einstein’s gravity.
文摘A simple phenomenological model is developed, which indicates the existence of a direct link between the concept of rest mass of a particle and magnetodynamic energies associated to the formation of the particle. The model is based upon the principles of quantization and conservation of flux, well known for their application in superconductivity. The charge of particles is considered as forming vortices of superconducting currents, which we postulate are created by electromagnetic fluctuations from vacuum (or related processes). A new quantization rule gathers the size, the magnetic moment, and the rest mass of the particle and associates these quantities to the integer number of flux quanta that should be stored in the vortices corresponding to each particle. The model is applied to the electron, the muon, the proton, and the neutron. Quantitative consistency with available experimental data for these subatomic particles is obtained.
