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
Classical phase-space variables are normally chosen to promote to quantum operators in order to quantize a given classical system. While classical variables can exploit coordinate transformations to address the same p...Classical phase-space variables are normally chosen to promote to quantum operators in order to quantize a given classical system. While classical variables can exploit coordinate transformations to address the same problem, only one set of quantum operators to address the same problem can give the correct analysis. Such a choice leads to the need to find the favored classical variables in order to achieve a valid quantization. This article addresses the task of how such favored variables are found that can be used to properly solve a given quantum system. Examples, such as non-renormalizable scalar fields and gravity, have profited by initially changing which classical variables to promote to quantum operators.展开更多
Chaotic dynamics of highly excited vibration of deuterium cyanide is explored by two independent approaches： （1） the Lyapunov analysis, based on the classical phase space for the levels, and （2） the Dixon dip ana...Chaotic dynamics of highly excited vibration of deuterium cyanide is explored by two independent approaches： （1） the Lyapunov analysis, based on the classical phase space for the levels, and （2） the Dixon dip analysis based on the concepts of pendulum dynamics and quantized levels. The results show that there is evident correlation between these two algorithms. We also propose that the reciprocal of energy difference between two nearby Dixon dips can be taken as a qualitative measure for the degree of dynamical chaos.展开更多
We propose a non-stationary method to measure the energy relaxation time of Josephson tunnel junctions from microwave enhanced escape phenomena. Compared with the previous methods, our method possesses simple and accu...We propose a non-stationary method to measure the energy relaxation time of Josephson tunnel junctions from microwave enhanced escape phenomena. Compared with the previous methods, our method possesses simple and accurate features. Moreover, having determined the energy relaxation time, we can further obtain the coupling strength between the microwave source and the junction by changing the microwave power.展开更多
It is pointed out that the property of a constant energy characteristic for the circular motions of macroscopic bodies in classical mechanics does not hold when the quantum conditions for the motion are applied. This ...It is pointed out that the property of a constant energy characteristic for the circular motions of macroscopic bodies in classical mechanics does not hold when the quantum conditions for the motion are applied. This is so because any macroscopic body—lo-cated in a high-energy quantum state—is in practice forced to change this state to a state having a lower energy. The rate of the energy decrease is usually extremely small which makes its effect uneasy to detect in course of the observations, or experiments. The energy of the harmonic oscillator is thoroughly examined as an example. Here our point is that not only the energy, but also the oscillator amplitude which depends on energy, are changing with time. In result, no constant positions of the turning points of the oscillator can be specified;consequently the well-known variational procedure concerning the calculation of the action function and its properties cannot be applied.展开更多
The uncertainty principle is a fundamental principle of quantum mechanics, but its exact mathematical expression cannot obtain correct results when used to solve theoretical problems such as the energy levels of hydro...The uncertainty principle is a fundamental principle of quantum mechanics, but its exact mathematical expression cannot obtain correct results when used to solve theoretical problems such as the energy levels of hydrogen atoms, one-dimensional deep potential wells, one-dimensional harmonic oscillators, and double-slit experiments. Even after approximate treatment, the results obtained are not completely consistent with those obtained by solving Schrödinger’s equation. This indicates that further research on the uncertainty principle is necessary. Therefore, using the de Broglie matter wave hypothesis, we quantize the action of an elementary particle in natural coordinates and obtain the quantization condition and a new deterministic relation. Using this quantization condition, we obtain the energy level formulas of an elementary particle in different conditions in a classical way that is completely consistent with the results obtained by solving Schrödinger’s equation. A new physical interpretation is given for the particle eigenfunction independence of probability for an elementary particle: an elementary particle is in a particle state at the space-time point where the action is quantized, and in a wave state in the rest of the space-time region. The space-time points of particle nature and the wave regions of particle motion constitute the continuous trajectory of particle motion. When an elementary particle is in a particle state, it is localized, whereas in the wave state region, it is nonlocalized.展开更多
在网络化控制系统(Networked Control Systems,简记为NCSs)中,由于网络的介入使控制系统的规模和复杂性显著增加,且产生了各种新问题,为了使控制更加容易,需要设计合理的估计策略。主要从控制和通信2个角度出发,集中考虑了在量化影响、...在网络化控制系统(Networked Control Systems,简记为NCSs)中,由于网络的介入使控制系统的规模和复杂性显著增加,且产生了各种新问题,为了使控制更加容易,需要设计合理的估计策略。主要从控制和通信2个角度出发,集中考虑了在量化影响、时延与丢包、不确定性等通信受限因素下状态估计策略的研究与进展。一直以来,状态估计都是诸如过程监控、故障诊断等控制领域中不可缺少的重要部分,当前已成为网络化控制系统研究的热点和难点,为抵消网络环境不确定性对闭环系统性能的影响,设计最优的状态估计策略必将成为不可缺少的因素之一。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.
文摘Classical phase-space variables are normally chosen to promote to quantum operators in order to quantize a given classical system. While classical variables can exploit coordinate transformations to address the same problem, only one set of quantum operators to address the same problem can give the correct analysis. Such a choice leads to the need to find the favored classical variables in order to achieve a valid quantization. This article addresses the task of how such favored variables are found that can be used to properly solve a given quantum system. Examples, such as non-renormalizable scalar fields and gravity, have profited by initially changing which classical variables to promote to quantum operators.
基金Supported by the National Natural Science Foundation of China under Grant No 20373030, the Key Project of the Ministry of Education of China under Grant No 306020.
文摘Chaotic dynamics of highly excited vibration of deuterium cyanide is explored by two independent approaches： （1） the Lyapunov analysis, based on the classical phase space for the levels, and （2） the Dixon dip analysis based on the concepts of pendulum dynamics and quantized levels. The results show that there is evident correlation between these two algorithms. We also propose that the reciprocal of energy difference between two nearby Dixon dips can be taken as a qualitative measure for the degree of dynamical chaos.
基金Supported by the National Natural Science Foundation of China under Grant No 10674062, the Natural Science Foundation of Jiangsu Province （BK2006118）, and the Doctoral Funds of Ministry of Education of China （20060284022）. We thank Sun Guozhu, Qing Lan and Mao Ting for useful discussions.
文摘We propose a non-stationary method to measure the energy relaxation time of Josephson tunnel junctions from microwave enhanced escape phenomena. Compared with the previous methods, our method possesses simple and accurate features. Moreover, having determined the energy relaxation time, we can further obtain the coupling strength between the microwave source and the junction by changing the microwave power.
文摘It is pointed out that the property of a constant energy characteristic for the circular motions of macroscopic bodies in classical mechanics does not hold when the quantum conditions for the motion are applied. This is so because any macroscopic body—lo-cated in a high-energy quantum state—is in practice forced to change this state to a state having a lower energy. The rate of the energy decrease is usually extremely small which makes its effect uneasy to detect in course of the observations, or experiments. The energy of the harmonic oscillator is thoroughly examined as an example. Here our point is that not only the energy, but also the oscillator amplitude which depends on energy, are changing with time. In result, no constant positions of the turning points of the oscillator can be specified;consequently the well-known variational procedure concerning the calculation of the action function and its properties cannot be applied.
文摘The uncertainty principle is a fundamental principle of quantum mechanics, but its exact mathematical expression cannot obtain correct results when used to solve theoretical problems such as the energy levels of hydrogen atoms, one-dimensional deep potential wells, one-dimensional harmonic oscillators, and double-slit experiments. Even after approximate treatment, the results obtained are not completely consistent with those obtained by solving Schrödinger’s equation. This indicates that further research on the uncertainty principle is necessary. Therefore, using the de Broglie matter wave hypothesis, we quantize the action of an elementary particle in natural coordinates and obtain the quantization condition and a new deterministic relation. Using this quantization condition, we obtain the energy level formulas of an elementary particle in different conditions in a classical way that is completely consistent with the results obtained by solving Schrödinger’s equation. A new physical interpretation is given for the particle eigenfunction independence of probability for an elementary particle: an elementary particle is in a particle state at the space-time point where the action is quantized, and in a wave state in the rest of the space-time region. The space-time points of particle nature and the wave regions of particle motion constitute the continuous trajectory of particle motion. When an elementary particle is in a particle state, it is localized, whereas in the wave state region, it is nonlocalized.
文摘在网络化控制系统(Networked Control Systems,简记为NCSs)中,由于网络的介入使控制系统的规模和复杂性显著增加,且产生了各种新问题,为了使控制更加容易,需要设计合理的估计策略。主要从控制和通信2个角度出发,集中考虑了在量化影响、时延与丢包、不确定性等通信受限因素下状态估计策略的研究与进展。一直以来,状态估计都是诸如过程监控、故障诊断等控制领域中不可缺少的重要部分,当前已成为网络化控制系统研究的热点和难点,为抵消网络环境不确定性对闭环系统性能的影响,设计最优的状态估计策略必将成为不可缺少的因素之一。
