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Mathematical Wave Functions and 3D Finite Element Modelling of the Electron and Positron
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作者 Declan Traill 《Journal of Applied Mathematics and Physics》 2024年第4期1134-1162,共29页
The wave/particle duality of particles in Physics is well known. Particles have properties that uniquely characterize them from one another, such as mass, charge and spin. Charged particles have associated Electric an... The wave/particle duality of particles in Physics is well known. Particles have properties that uniquely characterize them from one another, such as mass, charge and spin. Charged particles have associated Electric and Magnetic fields. Also, every moving particle has a De Broglie wavelength determined by its mass and velocity. This paper shows that all of these properties of a particle can be derived from a single wave function equation for that particle. Wave functions for the Electron and the Positron are presented and principles are provided that can be used to calculate the wave functions of all the fundamental particles in Physics. Fundamental particles such as electrons and positrons are considered to be point particles in the Standard Model of Physics and are not considered to have a structure. This paper demonstrates that they do indeed have structure and that this structure extends into the space around the particle’s center (in fact, they have infinite extent), but with rapidly diminishing energy density with the distance from that center. The particles are formed from Electromagnetic standing waves, which are stable solutions to the Schrödinger and Classical wave equations. This stable structure therefore accounts for both the wave and particle nature of these particles. In fact, all of their properties such as mass, spin and electric charge, can be accounted for from this structure. These particle properties appear to originate from a single point at the center of the wave function structure, in the same sort of way that the Shell theorem of gravity causes the gravity of a body to appear to all originate from a central point. This paper represents the first two fully characterized fundamental particles, with a complete description of their structure and properties, built up from the underlying Electromagnetic waves that comprise these and all fundamental particles. 展开更多
关键词 ELECTRON POSITRON Wave Function Solution Electromagnetic Spin Mass Charge Proof Fundamental Particle Properties quantum Mechanics Classical Physics Computer 3D Model Schrödinger Equation RMS KLEIN GORDON Electric Magnetic Lorentz invariant Hertzian Vector Point Potential Field Density Phase Flow Attraction REPULSION Shell Theorem Ehrenfest VIRIAL Normalization Harmonic Oscillator
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Population Control of Equilibrium States of Quantum Systems via Lyapunov Method 被引量:5
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作者 KUANG Sen CONG Shuang 《自动化学报》 EI CSCD 北大核心 2010年第9期1257-1263,共7页
关键词 人口控制问题 平衡状态 函数 单调性 计算方法
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含时阻尼线性谐振子的量子不变量处理 被引量:4
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作者 凌瑞良 《大学物理》 北大核心 2007年第12期12-15,共4页
在适当的正则化变换下,采用Lewis-Riesenfeld量子不变量理论,得到了含时阻尼线性谐振子的精确波函数,波函数的正确性和普遍性同样得到讨论.
关键词 含时阻尼 量子不变量 Lewis相位
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Editorial of special issue on spatiotemporal optical fields and time-varying optical materials
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作者 万辰皓 陈伟 曹前 《Chinese Optics Letters》 SCIE EI CAS CSCD 2023年第12期1-6,共6页
Optical science is currently witnessing a surge of interest in exploring complex optical fields with intricately tailored space-time characteristics.These spatiotemporal optical fields,carefully sculpted,are opening u... Optical science is currently witnessing a surge of interest in exploring complex optical fields with intricately tailored space-time characteristics.These spatiotemporal optical fields,carefully sculpted,are opening up new facets in both classical and quantum optics studies and paving the way for many novel applications.These include,but are not limited to,superresolution imaging,nanofabrication,optical manipulation,high-dimensional communication,and quantum information processing.Simultaneously,there is a growing fascination surrounding time-varying optical materials.These dynamic materials,in stark contrast to their time-invariant counterparts,provide an innovative degree of freedom in orchestrating electromagnetic fields and light–matter interactions across time and space.Furthermore,these time-varying materials offer a promising avenue for generating and tailoring spatiotemporal optical fields. 展开更多
关键词 MATERIALS quantum invariant
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Noncyclic nonadiabatic holonomic quantum gates via shortcuts to adiabaticity 被引量:3
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作者 Sai Li Pu Shen +1 位作者 Tao Chen Zheng-Yuan Xue 《Frontiers of physics》 SCIE CSCD 2021年第5期39-46,共8页
High-fidelity quantum gates are essential for large-scale quantum computation.However,any quantum manipulation will inevitably affected by noises,systematic errors and decoherence effects,which lead to infidelity of a... High-fidelity quantum gates are essential for large-scale quantum computation.However,any quantum manipulation will inevitably affected by noises,systematic errors and decoherence effects,which lead to infidelity of a target quantum task.Therefore,implementing high-fidelity,robust and fast quantum gates is highly desired.Here,we propose a fast and robust scheme to construct high-fidelity holonomic quantum gates for universal quantum computation based on resonant interaction of three-level quantum systems via shortcuts to adiabaticity.In our proposal,the target Hamiltonian to induce noncyclic non-Abelian geometric phases can be inversely engineered with less evolution time and demanding experimentally,leading to high-fidelity quantum gates in a simple setup.Besides,our scheme is readily realizable in physical system currently pursued for implementation of quantum computation.Therefore,our proposal represents a promising way towards fault-tolerant geometric quantum computation. 展开更多
关键词 noncyclic holonomic quantum gates shortcuts to adiabaticity Lewis-Riesenfeld invariant
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Automorphism groups of some algebras 被引量:1
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作者 PARK Hong Goo LEE Jeongsig +1 位作者 CHOI Seul Hee NAM Ki-Bong 《Science China Mathematics》 SCIE 2009年第2期323-328,共6页
The automorphism groups of algebras are found in many papers. Using auto-invariance, we find the automorphism groups of the Laurent extension of the polynomial ring and the quantum n-plane (respectively, twisting poly... The automorphism groups of algebras are found in many papers. Using auto-invariance, we find the automorphism groups of the Laurent extension of the polynomial ring and the quantum n-plane (respectively, twisting polynomial ring) in this work. As an application of the results of this work, we can find the automorphism group of a twisting algebra. We define a generalized Weyl algebra and show that the generalized Weyl algebra is simple. We also find the automorphism group of a generalized Weyl algebra. We show that the generalized Weyl algebra Am,m+n is the universal enveloping algebra of the generalized Witt algebra W(m,m + n). 展开更多
关键词 Laurent extension quantum n-plane (generalized) Weyl algebra AUTOMORPHISM auto-invariant 17B40 17B56
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含时阻尼谐振子的量子不变量算符及其本征值和本征函数 被引量:2
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作者 凌瑞良 《常熟理工学院学报》 2005年第4期35-39,共5页
在适当的正则变换下,使含时阻尼谐振子纳入量子化轨道,并以此找到含时阻尼谐振子的不变量算符、不变量算符的本征值和本征函数。
关键词 含时阻尼 谐振子 量子不变量 Lewis相
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动边界量子含时谐振子系统的Lewis-Riesenfeld相位与Berry相位 被引量:1
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作者 李玲 李伯臧 梁九卿 《物理学报》 SCIE EI CAS CSCD 北大核心 2001年第11期2077-2082,共6页
根据Lewis Riesenfeld的量子不变量理论 ,计算了一维动壁无限深势阱内频率随时间变化的谐振子的Lewis Riesenfeld相位 ,发现刘登云文中“非绝热Berry相位”与Lewis Riesenfeld相位中的几何部分完全一致 .也许更为重要的是 ,证明了至少... 根据Lewis Riesenfeld的量子不变量理论 ,计算了一维动壁无限深势阱内频率随时间变化的谐振子的Lewis Riesenfeld相位 ,发现刘登云文中“非绝热Berry相位”与Lewis Riesenfeld相位中的几何部分完全一致 .也许更为重要的是 ,证明了至少对于做正弦振动的边界 ,在绝热近似下 ,该系统不存在非零的Berry相位 . 展开更多
关键词 BERRY相位 Lewis-Riesenfeld相位 量子不变量 动边界 量子力学
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The Quantum sl<sub>2</sub>-Invariant of a Family of Knots
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作者 Abdul Rauf Nizami Mobeen Munir Malka Shah Bano 《Applied Mathematics》 2014年第1期70-78,共9页
We give a general formula of the quantum sl2-invariant of a family of braid knots. To compute the quantum invariant of the links we use the Lie algebra g=sl2 in its standard two-dimensional representation. We also rec... We give a general formula of the quantum sl2-invariant of a family of braid knots. To compute the quantum invariant of the links we use the Lie algebra g=sl2 in its standard two-dimensional representation. We also recover the Jones polynomial of these knots as a special case of this quantum invariant. 展开更多
关键词 quantum invariant Jones Polynomial Braid KNOT
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OHTSUKI’S INVARIANT CANNOT DETERMINE THE FULL SO(3) QUANTUM INVARIANTS
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作者 李邦河 李天军 《Acta Mathematica Scientia》 SCIE CSCD 2009年第3期642-644,共3页
Two lens spaces are given to show, that Ohtsuki’sτ for rational homology spheres does not determine Kirby-Melvin’s {τ r′, r odd ≥ 3}.
关键词 Ohtsuki's invariant SO(3) quantum invariants lens space
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Gravitation and Electromagnetism Conciliated Following Einstein’s Program
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作者 Claude Elbaz 《Journal of Modern Physics》 2015年第5期660-669,共10页
The Einstein’s program permits to conciliate gravitation and electromagnetism. Besides the standard model, it forms a consistent system for universe description, founded upon a scalar field propagating at the speed o... The Einstein’s program permits to conciliate gravitation and electromagnetism. Besides the standard model, it forms a consistent system for universe description, founded upon a scalar field propagating at the speed of light c. Matter corresponds to standing waves. Adiabatic variations of frequencies lead to electromagnetic interaction constituted by progressive waves. Classical domain corresponds to geometrical optics approximation, when frequencies are infinitely high, and then hidden. As interactions for matter, Gravitation and Electromagnetism derive from variations of its energy E = mc2. Electromagnetic interaction energy derives from mass variation dE = c2dm, and gravitation from speed of light variation dE = mdc2. Contrarily to gravitation, only electromagnetic interaction serves as a bridge between classical and quantum frames, since it leans directly upon the wave property of matter: its energy dE = hdν = c2dm derives from variations of matter energy E = hν = mc2. 展开更多
关键词 General RELATIVITY GRAVITATION Electromagnetism ADIABATIC invariant Standard Model quantum PHYSICS CLASSICAL PHYSICS
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构造不变子空间计算光子克隆的保真度
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作者 孙晋串 《河北大学学报(自然科学版)》 CAS 北大核心 2022年第5期468-473,共6页
研究了双模辐射场和几个三能级原子的相互作用,计算了光子克隆的平均保真度随时间的变化,对数值计算过程进行了简化.在对量子态的演化进行数值计算中,一般是在整个Hilbert空间进行计算.如果系统的空间维度很大,则数值计算需要处理大量... 研究了双模辐射场和几个三能级原子的相互作用,计算了光子克隆的平均保真度随时间的变化,对数值计算过程进行了简化.在对量子态的演化进行数值计算中,一般是在整个Hilbert空间进行计算.如果系统的空间维度很大,则数值计算需要处理大量的数据,花费大量的计算时间,有时候可以根据系统的特殊物理性质简化数值计算.如果在整个Hilbert空间找到每个量子态所在的不变子空间,对于每个量子态,在时间演化算符的作用下始终在自己的不变子空间内演化.不需要在全空间数值计算量子态的演化,而只需要在初态所在的子空间计算即可.通过比较分析得知,在数值计算少数三能级原子对光子的克隆时,在全空间计算量子态的演化需要处理的数据量比在各自子空间计算要大1个数量级. 展开更多
关键词 量子克隆 受激辐射 保真度 不变子空间
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Quantum Phases of Pancharatnam Type for a General Spin in a Time-Dependent Magnetic Field 被引量:1
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作者 ZHAO Yue-gang LI Bo-zang 《Chinese Physics Letters》 SCIE CAS CSCD 1997年第11期801-804,共4页
Based on the quantum invariant theory,the quantum phases,including the total phase as well as its dynamical and geometric parts,of Pancharatnam type are derived for a general spin in a time-dependent magnetic field,wi... Based on the quantum invariant theory,the quantum phases,including the total phase as well as its dynamical and geometric parts,of Pancharatnam type are derived for a general spin in a time-dependent magnetic field,without the constraint of adiabatic,cyclic or unitary condition.The geometric meaning of geometric phase is expounded. 展开更多
关键词 quantum GEOMETRIC invariant
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Gauge Invariance of a Time-Dependent Harmonic Oscillator in Magnetic Dipole Approximation
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作者 QIAN Shang-Wu WANG Jing-Shan 《Communications in Theoretical Physics》 SCIE CAS CSCD 2008年第2期308-310,共3页
A manifestly gauge-invariant formulation of non-relativistic quantum mechanics is applied to the case of time-dependent harmonic oscillator in the magnetic dipole approximation. A general equation for obtaining gauge-... A manifestly gauge-invariant formulation of non-relativistic quantum mechanics is applied to the case of time-dependent harmonic oscillator in the magnetic dipole approximation. A general equation for obtaining gauge-invariant transition probability amplitudes is derived. 展开更多
关键词 gauge-invariant formulation of non-relativistic quantum mechanics time-dependent harmonic oscillator magnetic dipole approximation gauge-invariant transition probability amplitude
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Oriented quantum coalgebra structure on the tensor product of an oriented quantum coalgebra with itself
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作者 马天水 王栓宏 《Journal of Southeast University(English Edition)》 EI CAS 2009年第2期286-288,共3页
Oriented quantum algebras (coalgebras) are generalizations of quasitriangular Hopf algebras (coquasitriangular Hopf algebras) and account for regular isotopy invariants of oriented 1-1 tangles, oriented knots and ... Oriented quantum algebras (coalgebras) are generalizations of quasitriangular Hopf algebras (coquasitriangular Hopf algebras) and account for regular isotopy invariants of oriented 1-1 tangles, oriented knots and links. Let (H, or, D, U) be an oriented quantum coalgebra over the field k. Then (H×H, φ, D×D, U× U) is a trivial oriented quantum coalgebra structure on the tensor product of coalgebra H with itself, where φ (a × b, c × d) = σ-( a, c)σ (b, d). This paper presents the oriented quantum coalgebra structure ( H×H, σ, D×D, U× U) on coalgebra H× H, where σ( a × b, c× d) = σ ^-1 ( d1, a1 ) σ( a2, c1 ) σ^-1 ( d2, b1 ) σ( b2, c2 ). So a nontrivial oriented quantum coalgebra structure is obtained and it is dual to Radford's results in the paper "On the tensor product of an oriented quantum algebra with itself" published in 2007. Theoretically, the results of this paper are important in constructing the invariants of oriented knots and links. 展开更多
关键词 oriented quantum coalgebra twisted oriented quantum coalgebra knot invariant
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哈密顿量明显与时间有关系统的量子论
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作者 姜迅东 胡荣泽 《中国粉体技术》 CAS 2004年第1期1-4,共4页
给出了明显与时间有关量子振动系统的哈密顿量的普遍形式。由量子湮灭算符和量子产生算符,构造了一组满足特定对易关系的量子算符,并由这组算符构造一个不变量算符,建立算符代数理论,由此得到量子振动系统的能级和波函数的具体表示。以... 给出了明显与时间有关量子振动系统的哈密顿量的普遍形式。由量子湮灭算符和量子产生算符,构造了一组满足特定对易关系的量子算符,并由这组算符构造一个不变量算符,建立算符代数理论,由此得到量子振动系统的能级和波函数的具体表示。以一维量子阻尼振动系统为例,对该量子系统的量子力学问题进行了讨论。 展开更多
关键词 哈密顿量 量子算符 不变量 量子论
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交流源作用下介观串联RLC电路系统量子态随时间的演化
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作者 刘清 欧阳晶 +3 位作者 胡菊菊 蔡十华 闵秋应 邹丹 《量子电子学报》 CAS CSCD 北大核心 2006年第5期652-658,共7页
介观串联RLC电路系统在交流电压源的作用下,同时介观电容器极板间电子波函数的耦合作用和电路的耗散也考虑进来,由拉格朗日函数推导出系统的含时哈密顿量,根据量子不变量理论,系统的量子态将随时间演化到压缩态。分析结果表明,介观电路... 介观串联RLC电路系统在交流电压源的作用下,同时介观电容器极板间电子波函数的耦合作用和电路的耗散也考虑进来,由拉格朗日函数推导出系统的含时哈密顿量,根据量子不变量理论,系统的量子态将随时间演化到压缩态。分析结果表明,介观电路系统由任意的初态演化到一般的压缩态。 展开更多
关键词 量子光学 时间演化算符 不变量理论 介观RLC电路 拉格朗日函数
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Revisiting novel symmetries in coupled N=2 supersymmetric quantum systems:examples and supervariable approach
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作者 Aditi Pradeep Anjali S +1 位作者 Binu M Nair Saurabh Gupta 《Communications in Theoretical Physics》 SCIE CAS CSCD 2020年第10期103-112,共10页
We revisit the novel symmetries in N=2 supersymmetric quantum mechanical models by considering specific examples of coupled systems.Further,we extend our analysis to a general case and list out all the novel symmetrie... We revisit the novel symmetries in N=2 supersymmetric quantum mechanical models by considering specific examples of coupled systems.Further,we extend our analysis to a general case and list out all the novel symmetries.In each case,we show the existence of two sets of discrete symmetries that correspond to the Hodge duality operator of differential geometry.Thus,we are able to provide a proof of the conjecture which points out the existence of more than one set of discrete symmetry transformations corresponding to the Hodge duality operator.Moreover,we derive on-shell nilpotent symmetries for a generalized superpotential within the framework of supervariable approach. 展开更多
关键词 N=2 SUSY quantum mechanical system continuous and discrete symmetries de Rham cohomological operators (anti-)chiral supervariable approach SUSY invariant restrictions
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Probe of topological invariants using quantum walks of a trapped ion in coherent state space
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作者 Ya Meng Feng Mei +1 位作者 Gang Chen Suo-Tang Jia 《Chinese Physics B》 SCIE EI CAS CSCD 2020年第7期257-264,共8页
We present a protocol to realize topological discrete-time quantum walks,which comprise a sequence of spindependent flipping displacement operations and quantum coin tossing operations,with a single trapped ion.It is ... We present a protocol to realize topological discrete-time quantum walks,which comprise a sequence of spindependent flipping displacement operations and quantum coin tossing operations,with a single trapped ion.It is demonstrated that the information of bulk topological invariants can be extracted by measuring the average projective phonon number when the walk takes place in coherent state space.Interestingly,the specific chiral symmetry owned by our discrete-time quantum walks simplifies the measuring process.Furthermore,we prove the robustness of such bulk topological invariants by introducing dynamical disorder and decoherence.Our work provides a simple method to measure bulk topological features in discrete-time quantum walks,which can be experimentally realized in the system of single trapped ions. 展开更多
关键词 topological quantum walk topological invariant trapped ion coherent state space
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超微粒子量子振动系统的不变量理论
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作者 姜迅东 胡荣泽 《中国粉体技术》 CAS 2003年第3期8-9,共2页
对超微粒子量子振动系统的不变量理论进行详细分析和研讨,指出由文献[1]给出的超微粒子量子振动系统哈密顿量的不变量的正确性。
关键词 超微粒子 量子振动 不变量
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