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Determination of Solar Radius and Earth’s Radius by Relativistic Matter Wave 被引量:2
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作者 Huaiyang Cui 《Journal of Applied Mathematics and Physics》 2023年第1期69-84,共16页
In recent years, relativistic matter waves have been applied to the solar system to explain some quantum gravity effects. This paper shows that the solar size and Earth’s size are the consequences of Bode’s rule in ... In recent years, relativistic matter waves have been applied to the solar system to explain some quantum gravity effects. This paper shows that the solar size and Earth’s size are the consequences of Bode’s rule in terms of the relativistic matter wave. The solar radius is determined as 7e+8 (m) with a relative error of 0.72%;the Earth’s radius is determined as 6.4328e+6 (m) with a relative error of 0.86%. The Earth’s atmospheric circulation is also investigated in terms of the relativistic matter wave, the wind fields on the Earth’s surface are calculated, and the results agree well with experimental observation. These findings indicate that the solar system is under the control of the planetary relativistic matter waves. 展开更多
关键词 Relativistic matter wave Sunspot Cycle Atmospheric Circulation
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Why Energy and Mass Can Be Converted between Each Other? A New Perspective Based on a Matter Wave Model 被引量:1
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作者 Donald C. Chang 《Journal of Modern Physics》 2016年第4期395-403,共9页
It was predicted by Einstein that energy and mass can be converted between each other. But why? Energy and mass are two very different physical concepts. How can they be exchanged with each other? We think the key to ... It was predicted by Einstein that energy and mass can be converted between each other. But why? Energy and mass are two very different physical concepts. How can they be exchanged with each other? We think the key to answer this question is to recall that a particle can behave like a wave. Particle properties like energy and momentum are known to be related to their corresponding wave properties (frequency and wave vector). Mass is clearly a particle property;is it also related to a wave property? This study suggests that it is. We found that mass and energy appear to share similar physical nature in the wave perspective. Both of them are related to the curvature of bending the vacuum medium during the propagation of the excitation wave. This similarity explains why they are convertible. 展开更多
关键词 ENERGY MASS Particle wave VACUUM matter wave Special Relativity
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Remarkable Findings in Fundamental Theory of Quantum Mechanics—Matter Wave and Discrete Time in Physics 被引量:1
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作者 Takahisa Okino 《Journal of Modern Physics》 2022年第2期256-266,共11页
The relation of matter wave, which is well-known as a hypothesis proposed by de Broglie in 1923, gave basis for establishing the quantum mechanics. After that, experimental results revealed that a micro particle has a... The relation of matter wave, which is well-known as a hypothesis proposed by de Broglie in 1923, gave basis for establishing the quantum mechanics. After that, experimental results revealed that a micro particle has a wave nature. However, the theoretical validity of the relation itself has never been revealed since his proposal. Theoretical basis that a micro particle has a wave nature has been thus disregarded in the unsolved state. The diffusion equation having been accepted as Fick’s second law was derived from the theory of Markov process in mathematics. It was then revealed that the diffusivity D depends on an angular momentum of a micro particle in a local space. The fact being unable to discriminate between micro particles in a local space resulted in having to accept the existence of minimum time t<sub>0 </sub>(>0) in the quantum mechanics. Based on t<sub>0</sub> and D obtained here, the theoretical validity of relation of matter wave was confirmed. Denying the density theorem in mathematics for time in physics indicates that the probabilistic interpretation is essentially indispensable for understanding the quantum mechanics. The logical necessity of quantum theory itself is thus understandable through introducing t<sub>0</sub> into the Newton mechanics. It is remarkable that the value of t<sub>0</sub> between 1.14&times;10<sup>-17</sup> s &le; t<sub>0 </sub>&le;1.76×10<sup>-14 </sup>s obtained here is extremely larger than that of the well-known Planck time t<sub>p</sub>=5.396&times;10<sup>-44 </sup>s. 展开更多
关键词 Quantum Diffusion Particle matter wave Planck Time Minimum Time
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Fully Quantized Theory of Six-Wave Mixing with Matter Waves
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作者 ZHOU Qing Ping 《Communications in Theoretical Physics》 SCIE CAS CSCD 2008年第2期477-478,共2页
We show that Wu-Yang theory of fully quantized four-wave mixing can be generalized to the six-wave mixing and derive the analytical solution of the coupled equations describing the quantum dynamics of six-wave mixing.
关键词 multiwave mixing fully quantized theory matter waves
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On the Existence of a Minimum Universal Speed of Physical Transmissions Associated with Matter Wave in Special Relativity
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作者 Vu B. Ho 《Journal of Applied Mathematics and Physics》 2023年第5期1287-1303,共17页
In this work, we show that it is possible to establish coordinate transformations between inertial reference frames in the theory of special relativity with a minimum universal speed of physical transmissions. The est... In this work, we show that it is possible to establish coordinate transformations between inertial reference frames in the theory of special relativity with a minimum universal speed of physical transmissions. The established coordinate transformations, referred to as modified Lorentz transformations because they have almost identical form to the Lorentz transformations, also comply with the requirement of invariance of the Minkowski line element. Particularly, the minimum universal speed can be associated with the phase speed of de Broglie matter wave. As application, we also discuss the possibility to formulate relativistic classical and quantum mechanics for the special relativity associated with the modified Lorentz transformations, which describes physical processes that represent an expansion or a collapsing of massive quantum particles. 展开更多
关键词 Special Relativity Minkowski Line Element Minimum Universal Speed Modified Lorentz Transformations Phase Velocity De Broglie matter wave Relativistic Mechanics
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Weak Nonlinear Matter Waves in a Trapped Spin-1 Condensates
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作者 蔡宏强 杨树荣 薛具奎 《Communications in Theoretical Physics》 SCIE CAS CSCD 2011年第4期583-588,共6页
The dynamics of the weak non//near matter sofitary waves in a spin-1 condensates with harmonic external potential are investigated analytically by a perturbation method. It is shown that, in the small amplitude limit,... The dynamics of the weak non//near matter sofitary waves in a spin-1 condensates with harmonic external potential are investigated analytically by a perturbation method. It is shown that, in the small amplitude limit, the dynamics of the solitary waves are governed by a variable-coetficient Korteweg-de Vries (KdV) equation. The reduction to the (KdV) equation may be useful to understand the dynamics of nonlinear matter waves in spinor BECs. The analytical expressions for the evolution of soliton show that the small-amplitude vector solitons of the mixed types perform harmonic oscillations in the presence of the trap. Furthermore, the emitted radiation profiles and the soliton oscillation frequency are also obtained. 展开更多
关键词 spin-1 condensate weak nonlinear matter solitary wave variable-coefficient KdV equation
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Matter Waves in a Static Gravitational Field
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作者 Neculai Agavriloaei 《Journal of Modern Physics》 2012年第8期750-754,共5页
A new approach of the matter waves concept initiated by Louis de Broglie leads to a new model – the vacuum matter waves. By using the physics of time dilation, one can calculate a gravitational cutoff frequency, with... A new approach of the matter waves concept initiated by Louis de Broglie leads to a new model – the vacuum matter waves. By using the physics of time dilation, one can calculate a gravitational cutoff frequency, with respect to the spectrum of vacuum fluctuations, which is the upper bound of the frequency range of this new model. We described the properties of these new waves and outlined the connection between them and the dimensions at Planck length level. The calculation of velocity in circular orbits by using this new concept complies with the well-known equation. One of its consequences is that the structure of the physical vacuum is modified on the radial direction with the gravity source, but not modified on its tangential direction. This study places the space-time structure from sub-quantum level into a new light and makes the connection between this level and that of the planetary systems. 展开更多
关键词 matter waveS Quantum Vacuum De BROGLIE waveS Special RELATIVITY Theory INERTIA Mach’s PRINCIPLE
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Two-parameter estimation in a matter-wave Sagnac interferometer
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作者 Xu Yu Hong-Bin Liang Xiao-Guang Wang 《Communications in Theoretical Physics》 SCIE CAS CSCD 2020年第9期39-48,共10页
We explore the general characteristics of a matter-wave Sagnac interferometer in a two-parameter estimation scheme. We find that the measurement precisions of both parameters cannot reach the Heisenberg limit(HL) simu... We explore the general characteristics of a matter-wave Sagnac interferometer in a two-parameter estimation scheme. We find that the measurement precisions of both parameters cannot reach the Heisenberg limit(HL) simultaneously when the input state is maximally entangled. Only one of the parameters' uncertainties can approach the HL while the other is scaled by the standard quantum limit.We provide the conditions with which the measurement precision of the specific parameter can reach the HL. We also discuss and figure out the concrete expressions of the constraint conditions for saturating the quantum Cramér–Rao bound. To satisfy these constraint conditions, the evolution time has to be a series of discrete values. Additionally, we calculate the variances of the parameters through some examples under these constraint conditions. The results provided in our work show some intrinsic features of the matter-wave Sagnac interferometer for the two-parameter estimation, which can be valuable in actual experiments. 展开更多
关键词 multi-parameter estimation matter wave Sagnac interferometer Heisenberg limit
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Durational Exposure to Particulate Matter and Changes in Fertility Intentions:A Study of Adults in China
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作者 Jia-yu Wang Xin Yun +6 位作者 Rui Qu Wei-qian Zhang Jia Liang Yu Guan Dong-dong Tang Yu Chen Tai-lang Yin 《Current Medical Science》 2025年第2期363-372,共10页
Objective The effects of prolonged exposure to persistently elevated atmospheric pollutants,commonly termed air pollution waves,on fertility intentions remain inadequately understood.This study aims to investigate the... Objective The effects of prolonged exposure to persistently elevated atmospheric pollutants,commonly termed air pollution waves,on fertility intentions remain inadequately understood.This study aims to investigate the association between particulate matter(PM)exposure and fertility intentions.Methods In this nationwide cross-sectional study,we analyzed data from 10,747 participants(5496 females and 5251 males).PM waves were defined as periods lasting 3‒6 consecutive days during which the daily average concentrations exceeded China’s Ambient Air Quality Standards Grade II thresholds(PM2.5>75μg/m3 and PM10>150μg/m3).We employed multivariate logistic regression models to assess the association between exposure to PM waves and fertility intentions.Results Significant inverse associations were detected between exposure to PM2.5 wave events(characterized by concentrations exceeding 75μg/m3 for durations of 4‒6 days,P<0.05)and PM10 wave events(defined as concentrations exceeding 150μg/m3 for 6 consecutive days,P<0.05)and fertility intentions among females.In contrast,neither the PM2.5 wave nor the PM10 wave events demonstrated statistically significant correlations with fertility intentions in males(P>0.05 for all comparisons).The potentially susceptible subgroup was identified as females aged 20–30 years.Conclusions Our results provide the first evidence that PM2.5 and PM10 waves are associated with a reduction in female fertility intentions,offering critical insights for the development of public health policies and strategies aimed at individual protection. 展开更多
关键词 Fine particulate matter wave Air pollution Fertility intention
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Matter-wave interference in an axial triple-well optical dipole trap 被引量:2
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作者 周琦 陆俊发 印建平 《Chinese Physics B》 SCIE EI CAS CSCD 2010年第9期323-330,共8页
This paper proposes a scheme of axial triple-well optical dipole trap by employing a simple optical system composed of a circular cosine grating and a lens. Three optical wells separated averagely by -37 μm were crea... This paper proposes a scheme of axial triple-well optical dipole trap by employing a simple optical system composed of a circular cosine grating and a lens. Three optical wells separated averagely by -37 μm were created when illuminating by a YAG laser with power 1 mW. These wells with average trapping depth -0.5 μK and volume -74 μm^3 are suitable to trap and manipulate an atomic Bose-Einstein condensation (BEC). Due to a controllable grating implemented by a spatial light modulator, an evolution between a triple-well trap and a single-well one is achievable by adjusting the height of potential barrier between adjacent wells. Based on this novel triple-well potentials, the loading and splitting of BEC, as well as the interference between three freely expanding BECs, are also numerically stimulated within the framework of mean-field treatment. By fitting three cosine functions with three Gaussian envelopes to interference fringe, the information of relative phases among three condensates is extracted. 展开更多
关键词 triple-well optical trap matter-wave interference spatial light modulator
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Dynamic stability and manipulation of bright matter-wave solitons by optical lattices in Bose-Einstein condensates 被引量:1
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作者 Song Chang-Sheng Li Jing Zong Feng-De 《Chinese Physics B》 SCIE EI CAS CSCD 2012年第2期98-106,共9页
An extended variation approach to describing the dynamic evolution of self-attractive Bose-Einstein condensates is developed. We consider bright matter-wave solitons in the presence of a parabolic magnetic potential a... An extended variation approach to describing the dynamic evolution of self-attractive Bose-Einstein condensates is developed. We consider bright matter-wave solitons in the presence of a parabolic magnetic potential and a timespace periodic optical lattice. The dynamics of condensates is shown to be well approximated by four coupled nonlinear differential equations. A noteworthy feature is that the extended variation approach gives a critical strength ratio to support multiple stable lattice sites for the condensate. We further examine the existence of the solitons and their stabilities at the multiple stable lattice sites. In this case, the analytical predictions of Bose-Einstein condensates variational dynamics are found to be in good agreement with numerical simulations. We then find a stable region for successful manipulating matter-wave solitons without collapse, which are dragged from an initial stationary to a prescribed position by a moving periodic optical lattice. 展开更多
关键词 Bose-Einstein condensates Gross-Pitaevskii equation matter-wave solitons controlled manipulation
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Oscillation properties of matter–wave bright solitons in harmonic potentials
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作者 Shu-Wen Guan Ling-Zheng Meng Li-Chen Zhao 《Chinese Physics B》 SCIE EI CAS CSCD 2022年第8期317-324,共8页
We investigate the oscillation periods of bright soliton pair or vector bright soliton pair in harmonic potentials. We demonstrate that periods of low-speed solitons are greatly affected by the position shift during t... We investigate the oscillation periods of bright soliton pair or vector bright soliton pair in harmonic potentials. We demonstrate that periods of low-speed solitons are greatly affected by the position shift during their collisions. The modified oscillation periods are described by defining a characterized speed, with the aid of asymptotic analysis on related exact analytic soliton solutions in integrable cases. The oscillation period can be used to distinguish the inter-and intra-species interactions between solitons. However, a bright soliton cannot oscillate in a harmonic trap, when it is coupled with a dark soliton(without any trapping potentials). Interestingly, it can oscillate in an anti-harmonic potential, and the oscillation behavior is explained by a quasi-particle theory. The modified period of two dark-bright solitons can be also described well by the characterized speed. These results address well the effects of position shift during soliton collision, which provides an important supplement for previous studies without considering phase shift effects. 展开更多
关键词 matterwave bright soliton harmonic potential oscillation period
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Dark Matter and Gravitational Waves
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作者 Joseph J. Smulsky 《Natural Science》 2021年第3期76-87,共12页
Two reviews of papers are considered. The first paper for a galaxy model uses matter consisting of neutrinos, bosons and other similar particles. It is shown that these particles were introduced as a result of an inco... Two reviews of papers are considered. The first paper for a galaxy model uses matter consisting of neutrinos, bosons and other similar particles. It is shown that these particles were introduced as a result of an incorrect description of interactions in the Theory of Relativity. In reality, with the relative motion of interacting particles, their interactions force changes, and not their mass. It is shown that models of such stellar associations as globular clusters and galaxies should be created on the basis of the substance that exists on Earth. The second peer-reviewed paper proposes to create LIGO on the Moon. It is shown that gravitational waves do not exist. They were introduced to explain the excessive rotation of the Mercury’s perihelion. However, the excessive rotation of the Mercury’s perihelion is due to the Sun oblateness. The paper shows that gravitational waves, the Big Bang, the expanding Universe, dark matter, dark energy, etc. appeared on the basis of unfounded hypotheses. The urgent task is to eliminate them from science. 展开更多
关键词 Dark matter Gravitational waves Hypotheses INTERACTION Charged Particles Newtonian Gravity
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Complex Field Theory: A Unifying Framework for Dark Matter and Dark Energy with the Material Universe
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作者 Hossin Abdeldayem 《Journal of Modern Physics》 2025年第1期140-151,共12页
Complex Field Theory (CFT) proposes that dark matter (DM) and dark energy (DE) are pervasive, complex fields of charged complex masses of equally positive and negative complex charges, respectively. It proposes that e... Complex Field Theory (CFT) proposes that dark matter (DM) and dark energy (DE) are pervasive, complex fields of charged complex masses of equally positive and negative complex charges, respectively. It proposes that each material object, including living creatures, is concomitant with a fraction of the charged complex masses of DM and DE in proportion to its mass. This perception provides new insights into the physics of nature and its constituents from subatomic to cosmic scales. This complex nature of DM and DE explains our inability to see DM or harvest DE for the last several decades. The positive complex DM is responsible for preserving the integrity of galaxies and all material systems. The negative complex charged DE induces a positive repelling force with the positively charged DM and contributes to the universe’s expansion. Both fields are Lorentz invariants in all directions and entangle the whole universe. The paper uses CFT to investigate zero-point energy, particle-wave duality, relativistic mass increase, and entanglement phenomenon and unifies Coulomb’s and Newton’s laws. The paper also verifies the existence of tachyons and explains the spooky action of quantum mechanics at a distance. The paper encourages further research into how CFT might resolve several physical mysteries in physics. 展开更多
关键词 Dark Energy Dark matter Complex Field Theory Entanglement Zero-Point Energy Particle-wave Duality Gravity Unification of Coulomb’s and Newton’s Laws TACHYONS Spooky Action Effect
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Primary Assumptions and Guidance Laws in Wave Mechanics
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作者 Adriano Orefice Raffaele Giovanelli Domenico Ditto 《Journal of Applied Mathematics and Physics》 2018年第12期2621-2634,共14页
In an article written by Louis de Broglie in 1959 (30 years after the Nobel prize rewarding his foundation of Wave Mechanics), the most challenging problem raised by the Bohr, Heisenberg and Born Standard Quantum Mech... In an article written by Louis de Broglie in 1959 (30 years after the Nobel prize rewarding his foundation of Wave Mechanics), the most challenging problem raised by the Bohr, Heisenberg and Born Standard Quantum Mechanics (SQM) was pointed out in the renunciation to describe “a permanent localization in space, and therefore a well-defined trajectory” for any moving particle. This challenge is taken up in the present paper, showing that de Broglie’s Primary Assumption p=hk, predicting the wave-particle duality, does also allow to obtain from the energy-dependent form of the Schr&#246;dinger and/or Klein-Gordon equations the Guidance Laws piloting particles along well-defined trajectories. The energy-independent equations, on the other hand, may only give rise—both in SQM and in the Bohmian approach—to probabilistic descriptions, overshadowing the role of de Broglie’s matter waves in physical space. 展开更多
关键词 Helmholtz Equation wave Potential Hamilton-Jacobi Equations wave Mechanics de Broglie’s Duality matter waves Guidance Laws Schrodinger Equations Klein-Gordon Equations
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The Dynamics of Wave-Particle Duality
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作者 Adriano Orefice Raffaele Giovanelli Domenico Ditto 《Journal of Applied Mathematics and Physics》 2018年第9期1840-1859,共20页
Both classical and wave-mechanical monochromatic waves may be treated in terms of exact ray-trajectories (encoded in the structure itself of Helmholtz-like equations) whose mutual coupling is the one and only cause of... Both classical and wave-mechanical monochromatic waves may be treated in terms of exact ray-trajectories (encoded in the structure itself of Helmholtz-like equations) whose mutual coupling is the one and only cause of any diffraction and interference process. In the case of Wave Mechanics, de Broglie’s merging of Maupertuis’s and Fermat’s principles (see Section 3) provides, without resorting to the probability-based guidance-laws and flow-lines of the Bohmian theory, the simple law addressing particles along the Helmholtz rays of the relevant matter waves. The purpose of the present research was to derive the exact Hamiltonian ray-trajectory systems concerning, respectively, classical electromagnetic waves, non-relativistic matter waves and relativistic matter waves. We faced then, as a typical example, the numerical solution of non-relativistic wave-mechanical equation systems in a number of numerical applications, showing that each particle turns out to “dances a wave-mechanical dance” around its classical trajectory, to which it reduces when the ray-coupling is neglected. Our approach reaches the double goal of a clear insight into the mechanism of wave-particle duality and of a reasonably simple computability. We finally compared our exact dynamical approach, running as close as possible to Classical Mechanics, with the hydrodynamic Bohmian theory, based on fluid-like “guidance laws”. 展开更多
关键词 Helmholtz Equation wave Potential Hamilton-Jacobi Equation wave Mechanics De Broglie’s Duality matter waves Guidance Laws Schrodinger Equations Klein-Gordon Equation
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Describe Quantum Mechanics in Dual 4 d Complex Space-Time and the Ontological Basis of Wave Function 被引量:3
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作者 Guoqiu Zhao 《Journal of Modern Physics》 2014年第16期1684-1697,共14页
Micro-object is both particle and wave, so the traditional Particle Model (mass point model) is actually not applicable for it. Here to describe its motion, we expand the definition of time and space and pick up the s... Micro-object is both particle and wave, so the traditional Particle Model (mass point model) is actually not applicable for it. Here to describe its motion, we expand the definition of time and space and pick up the spatial degrees of freedom hidden by particle model. We say that micro-object is like a rolling field-matter-ball, which has four degrees of freedom including one surface curvature degree and three mapping degrees in the three-dimensional phenomenal space. All the degrees are described by four curvature coordinate components, namely “k1, k2, k3, k4”, which form the imaginary part of a complex phase space, respectively. While as to the real part, we use “x1, x2, x3, x4” to describe the micro object’s position in our real space. Consequently, we build a Dual 4-dimensional complex phase space whose imaginary part is 4-dimension k space and real part is 4-dimension x space to describe the micro-object’s motion. Furthermore, we say that wave function can describe the information of a field-matter-ball’s rotation & motion and also matter-wave can spread the information of micro-object’s spatial structure & density distribution. Matter-wave and probability-wave can transform to each other though matter-wave is a physical wave. The non-point property is the foundational source of the probability in Quantum Mechanics. 展开更多
关键词 Field-matter matter-wave Probability CURVATURE CURVATURE Coordinate
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Gravitational wave radiation from a double white dwarf system inside our galaxy: a potential method for seeking strange dwarfs
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作者 Zhan-Kui Lu Shi-Wei Wu Zhi-Cheng Zeng 《Research in Astronomy and Astrophysics》 SCIE CAS CSCD 2009年第7期745-750,共6页
Like the investigation of double white dwarf (DWD) systems, strange dwarf (SD) - white dwarf (WD) system evolution in Laser Interferometer Space Antenna (LISA)'s absolute amplitude-frequency diagram is invest... Like the investigation of double white dwarf (DWD) systems, strange dwarf (SD) - white dwarf (WD) system evolution in Laser Interferometer Space Antenna (LISA)'s absolute amplitude-frequency diagram is investigated. Since there is a strange quark core inside an SD, SDs' radii are significantly smaller than the value predicted by the standard WD model, which may strongly affect the gravitational wave (GW) signal in the mass-transferring phases of binary systems. We study how an SD-WD binary evolves across LISA's absolute amplitude-frequency diagram. In principle, we provide an executable way to detect SDs in the Galaxy's DWD systems by radically new windows offered by GW detectors. 展开更多
关键词 ACCRETION accretion disks - binaries close - dense matter - gravitational waves
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Influence of laser fields on the vibrational population of molecules and its wave-packet dynamical investigation 被引量:4
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作者 王军 刘芳 +4 位作者 岳大光 赵娟 许燕 孟庆田 Liu Wing-Ki 《Chinese Physics B》 SCIE EI CAS CSCD 2010年第12期193-202,共10页
The time-dependent wave packet method is used to investigate the influence of laser-fields on the vibrational population of molecules. For a two-state system in laser fields, the populations on different vibrational l... The time-dependent wave packet method is used to investigate the influence of laser-fields on the vibrational population of molecules. For a two-state system in laser fields, the populations on different vibrational levels of the upper and lower electronic states are given by wavefunctions obtained by solving the Schrbdinger equation with the split- operator method. The calculation shows that the field parameters, such as intensity, wavelength, duration, and delay time etc. can have different influences on the vibrational population. By varying the laser parameters appropriately one can control the evolution of wave packet and so the vibrational population in each state, which will benefit the light manipulation of atomic and molecular processes. 展开更多
关键词 intense laser field time-dependent wave packet method light-matter interaction vibrational population
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Properties of surface waves in granular media under gravity
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作者 郑鹤鹏 《Chinese Physics B》 SCIE EI CAS CSCD 2014年第5期355-359,共5页
Acoustical waves propagating along the free surface of granular media under gravity are investigated in the framework of elasticity theory. The influence of stress on a surface wave is analyzed. The results have shown... Acoustical waves propagating along the free surface of granular media under gravity are investigated in the framework of elasticity theory. The influence of stress on a surface wave is analyzed. The results have shown that two types of surface waves, namely sagittal and transverse modes exist depending on initial stress states, which may have some influence on the dispersion relations of surface waves, but the influence is not great. Considering that the present experimental accuracy is far from distinguishing this detail, the validity of elasticity theory on the surface waves propagating in granular media can still be maintained. 展开更多
关键词 granular matter STRESS surface waves
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