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
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
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
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
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
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
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
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
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
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
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
文摘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.
基金Supported by National Key Basic Research Program of China（973 Program）（2006CB922004） National Natural Science Foundation of China（60904033 60774098）+1 种基金 the Chinese Postdoctoral Science Foundation（20100470848） K.C.Wong Education Foundation HongKong
文摘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.
基金This work was supported by the Key R&D Program of Guangdong Province(Grant No.2018B030326001)the National Natural Science Foundation of China(Grant No.11874156)Science and Technology Program of Guangzhou(Grant No.2019050001).
文摘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.
基金supported by 2007 Research fund of Hanyang University
文摘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).
文摘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.
文摘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.
基金Supported by the National Natural Science Foundation of China under Grant No.19677101
文摘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.
文摘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.
基金The National Natural Science Foundation of China(No.10871042)
文摘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.
基金support from the FRG scheme of National Institute of Technology Calicut。
文摘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.
基金Project supported by the National Key R&D Program of China(Grant No.2017YFA0304203)the National Natural National Science Foundation of China(Grant Nos.11604392 and 11674200)+1 种基金the Changjiang Scholars and Innovative Research Team in Universities of Ministry of Education of China(Grant No.IRT 17R70)the Fund for Shanxi“1331 Project”Key Subjects Construction,and the 111 Project,China(Grant No.D18001).
文摘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.
