In this paper, in Section 1, we have described some equations and theorems concerning the Lebesgue integral and the Lebesgue measure. In Section 2, we have described the possible mathematical applications, of Lebesgue...In this paper, in Section 1, we have described some equations and theorems concerning the Lebesgue integral and the Lebesgue measure. In Section 2, we have described the possible mathematical applications, of Lebesgue integration, in some equations concerning various sectors of Chern-Simons theory and Yang-Mills gauge theory, precisely the two dimensional quantum Yang-Mills theory. In conclusion, in Section 3, we have described also the possible mathematical connections with some sectors of String Theory and Number Theory, principally with some equations concerning the Ramanujan’s modular equations that are related to the physical vibrations of the bosonic strings and of the superstrings, some Ramanujan’s identities concerning π and the zeta strings.展开更多
Simulating U(1) quantum gauge theories with spatial dimensions greater than one is of great physical significance. Here we propose a simple realization of U(1) gauge theory with Rydberg and Rydberg-dressed atom arrays...Simulating U(1) quantum gauge theories with spatial dimensions greater than one is of great physical significance. Here we propose a simple realization of U(1) gauge theory with Rydberg and Rydberg-dressed atom arrays. Within the experimentally accessible range, we find that the various aspects of the U(1) gauge theory can be well simulated, such as the emergence of topological sectors, incommensurability, and the Rokhsar–Kivelson point that hosts deconfined charge excitations and degenerate topological sectors. Our proposal is promising to implement experimentally and exhibits pronounced quantum dynamics.展开更多
We have investigated the gauge dependence of physical observables in a quantum Rabi model under different potential fields arising from the Hilbert space truncation of the atomic degrees of freedom.In both the square-...We have investigated the gauge dependence of physical observables in a quantum Rabi model under different potential fields arising from the Hilbert space truncation of the atomic degrees of freedom.In both the square-well and harmonic potentials,the optimal gauge for the ground-state energy depends on the cavity frequency,which is optimal in the low-frequency limit,whereas the Coulomb gauge is optimal in the high-frequency limit.For a dynamic quantity,such as an out-of-time-order correlator,we have demonstrated the necessity of introducing an optimal dynamic gauge.This study provides deeper insight into the intricate relationship between gauge choice and the dynamics of quantum electrodynamics systems,resulting in more accurate theoretical frameworks.展开更多
The transverse-traceless gauge condition is an important concept in the theory of gravitational waves.It is well known that a vacuum is one of the key conditions to guarantee the existence of the transverse-traceless ...The transverse-traceless gauge condition is an important concept in the theory of gravitational waves.It is well known that a vacuum is one of the key conditions to guarantee the existence of the transverse-traceless gauge.Although it is thin,the interstellar medium is ubiquitous in the Universe.Therefore,it is important to understand the concept of gravitational waves when matter is presented.Bondi-Metzner-Sachs theory has solved the gauge problem related to gravitational waves.But it does not help with cases when the gravitational wave propagates in matter.This paper discusses possible extensions of the transverse-traceless gauge condition to Minkowski perturbation with matter presented.展开更多
A power splitter with a wideband arbitrary splitting ratio,which provides flexibility and adaptability in forming photonic devices such as microring resonators and Mach–Zehnder interferometers,proves to be essential ...A power splitter with a wideband arbitrary splitting ratio,which provides flexibility and adaptability in forming photonic devices such as microring resonators and Mach–Zehnder interferometers,proves to be essential in photonic integrated circuits(PICs).We designed and fabricated a directional coupler-based power splitter with a wideband arbitrary splitting ratio and a microring resonator with a wideband uniform extinction ratio(ER)based on artificial gauge field(AGF)optimization.The neural network-aided inverse design method is applied to complete the target.Less than 0.9 dB power splitting variation and 1.6 dB ER variation have been achieved experimentally over a 100-nm bandwidth.Wideband performance,design efficiency,and device compactness are obtained by utilizing this optimization,which indicates great potential and universality in PIC applications.展开更多
A new mechanism for mass generation of gauge field is discussed in this paper. By introducing two sets of gauge fields and making the variations of these two sets of gauge fields compensated each other under local gau...A new mechanism for mass generation of gauge field is discussed in this paper. By introducing two sets of gauge fields and making the variations of these two sets of gauge fields compensated each other under local gauge transformations, the mass term of gauge fields is introduced into the Lagrangian without violating the local gauge symmetry of the Lagrangian. This model is a renormalizable quantum model.展开更多
With the popularity of the automatic precipitation gauges in national weather stations,testing their performance and adjusting their measurements are top priorities. Additionally,because different climatic conditions ...With the popularity of the automatic precipitation gauges in national weather stations,testing their performance and adjusting their measurements are top priorities. Additionally,because different climatic conditions may have different effects on the performance of the precipitation gauges, it is also necessary to test the gauges in different areas. This study mainly analyzed precipitation measurements from the single-Altershielded TRwS204 automatic weighing gauge(TRwS_(SA)) relative to the adjusted manual measurements(reference precipitation) from the Chinese standard precipitation gauge in a doublefence wind shield(CSPG_(DF)) in the Hulu watershed in the Qilian Mountains, China. The measurements were compared over the period from August 2014 to July2017, and the transfer function derived from the work by Kochendorfer et al.(2017 a) for correcting windinduced losses was applied to the TRwS_(SA) measurements. The results show that the average loss of TRwS_(SA) measurements relative to the reference precipitation decreased from 0.55 mm(10.7%) to 0.51 mm(9.9%) for rainfall events, from 0.35 mm(8.5%)to 0.22 mm(5.3%) for sleet events, and from 0.49 mm(18.9%) to 0.33 mm(12.7%) for snowfall events after adjustment. The uncorrected large biases of TRwS_(SA) measurements are considered to be mainly caused by specific errors of TRwS_(SA), different gauge orifice area and random errors. These types of errors must be considered when comparing precipitation measurements for different gauge types, especially in the mountains.展开更多
In order to provide manufacturers of carding machines and relevant accessories with theoretical references,how cylinder radius,setover and heel-toe difference affect cylinder-flat gauge of a carding machine was theore...In order to provide manufacturers of carding machines and relevant accessories with theoretical references,how cylinder radius,setover and heel-toe difference affect cylinder-flat gauge of a carding machine was theoretically studied.The relationship between cylinder-flat gauge and cylinder radius,setover and heel-toe difference was geometrically discussed.Numerical calculation and illustration about the relationship were made with MATLAB in accordance with practical settings.A general formula about the relationship is derived.A concept,the small-gauge zone length,has been defined for the first time,and some relevant results thus obtained.Given setover and heel-toe difference,the greater the cylinder radius,the greater the average gauge.If a smaller overall cylinder-flat gauge is desirable,it is not necessary to emphasize the tangential direction of the heel of clothed surface to the cylinder.Their intersection within a small zone is acceptable.In many cases,small-gauge zone can reduce average gauge which may be helpful to the carding action;given cylinder radius and setover,the smaller the heel-toe difference,the more helpful to reduce the overall gauge;given cylinder radius and heel-toe difference,the small-gauge zone length will increase with the increase of setover,so does the difference between the smallest gauge and outlet gauge.展开更多
Karma alloy thin film strain gauges were fabricated on alumina substrates by magnetron sputtering. The electrical properties of strain gauges annealed at different temperatures were then tested. The surface morphology...Karma alloy thin film strain gauges were fabricated on alumina substrates by magnetron sputtering. The electrical properties of strain gauges annealed at different temperatures were then tested. The surface morphology and phase structure of the Karma alloy thin films were analyzed using X-ray diffraction and scanning electron microscopy. The effect of the annealing temperature on the performance of the Karma alloy thin film strain gauge was also investigated. As the annealing temperature increased, it was found that the resistivity of the thin films decreased, whereas the temperature coefficient of resistance (TCR) of the thin films increased. A Karma alloy thin film strain gauge was annealed at 200 °C, thereby obtaining a gauge factor of 1.7 and a corresponding TCR of 64.8 × 10−6 K−1. The prepared Karma alloy thin film strain gauge had a lower TCR than other strain gauges at room temperature. This result can provide a reference for the preparation and application of Karma alloy thin film strain gauges in specific scenarios.展开更多
We summarize our results about the quantization of a charged particle motion without spin inside a flat box under a static electromagnetic field with Landau’s gauge for the magnetic field, where Fourier’s transforma...We summarize our results about the quantization of a charged particle motion without spin inside a flat box under a static electromagnetic field with Landau’s gauge for the magnetic field, where Fourier’s transformation was used to analyze the problem, to point out that there exists a wave function which is different to that one given by Landau with the same Landau’s levels. The quantization of the magnetic flux is deduced differently to previous one, and a new solution is presented for the case of symmetric gauge of the magnetic field, and having the same Landau’s levels.展开更多
A new mechanism to introduce the mass of gauge field in supersymmetric gauge theory is discussed. The model has the strict local gauge symmetry and supersymmetry. Because we introduce two vector superfields simulta...A new mechanism to introduce the mass of gauge field in supersymmetric gauge theory is discussed. The model has the strict local gauge symmetry and supersymmetry. Because we introduce two vector superfields simultaneously, the model contains a massive gauge field as well as a massless gauge field.展开更多
In this paper, spinor and vector decompositions of SU（2） gauge potential are presented and their equivalence is constructed using a simply proposal. We also obtain the action of Faddeev nonlinear 0（3） sigma model ...In this paper, spinor and vector decompositions of SU（2） gauge potential are presented and their equivalence is constructed using a simply proposal. We also obtain the action of Faddeev nonlinear 0（3） sigma model from the SU（2） mass/ve gauge field theory, which is proposed according to the gauge invariant principle. At last, the knot structure in SU（2） Chern-Simons filed theory is discussed in terms of the Φ-mapping topological current theory, The topological charge of the knot is characterized by the Hopf indices and the Brouwer degrees of Φ-mapping.展开更多
Gauge potential plays an important role in exploring exotic phenomena in the single- and many-body quantum systems.In this paper,we propose a scheme to create both new Abelian and non-Abelian gauge potentials by adiab...Gauge potential plays an important role in exploring exotic phenomena in the single- and many-body quantum systems.In this paper,we propose a scheme to create both new Abelian and non-Abelian gauge potentials by adiabatically controlling the degenerate Dicke model in cavity quantum electrodynamics.It is shown that a non-Abelian gauge potential is achieved only for a single atom,whereas an Abelianizen diagonal gauge potential is realized for the atomic ensemble.More importantly,two interesting quantum phenomena such as the geometric phase and the magnetic monopole induced by our created gauge potentials are also predicted.The possible physical realization is presented in the macroscopic circuit quantum electrodynamics with the Cooper pair boxes,which act as the artificial two-level atoms controlled by the gate voltage and the external magnetic flux.展开更多
A systematic method is developed to studY the classical motion of a mass point in gravitational gauge field. First, by using Mathematica, a spherical symmetric solution of the field equation of gravitational gauge fie...A systematic method is developed to studY the classical motion of a mass point in gravitational gauge field. First, by using Mathematica, a spherical symmetric solution of the field equation of gravitational gauge field is obtained, which is just the traditional Schwarzschild solution. Combining the principle of gauge covariance and Newton＇s second law of motion, the equation of motion of a mass point in gravitational field is deduced. Based on the spherical symmetric solution of the field equation and the equation of motion of a mass point in gravitational field, we can discuss classical tests of gauge theory of gravity, including the deflection of light by the sun, the precession of the perihelia of the orbits of the inner planets and the time delay of radar echoes passing the sun. It is found that the theoretical predictions of these classical tests given by gauge theory of gravity are completely the same as those given by general relativity.展开更多
This paper suggests a principle to find a unitary operator U which transforms non-physical quantity, zero-potential Hamiltonian H<SUB>0</SUB>, into true physical quantity UH<SUB>0</SUB>U<SUP...This paper suggests a principle to find a unitary operator U which transforms non-physical quantity, zero-potential Hamiltonian H<SUB>0</SUB>, into true physical quantity UH<SUB>0</SUB>U<SUP>?</SUP> for a charged particle in classical electromagnetic field, and puts forward a unified form of constructing gauge-independent transition probabilities in this case. Different methods correspond to different unitary operators which satisfy the above-mentioned principle.展开更多
A primordial field Self-interaction Principle, analyzed in Hestenes’ Geometric Calculus, leads to Heaviside’s equations of the gravitomagnetic field. When derived from Einstein’s nonlinear field equations Heaviside...A primordial field Self-interaction Principle, analyzed in Hestenes’ Geometric Calculus, leads to Heaviside’s equations of the gravitomagnetic field. When derived from Einstein’s nonlinear field equations Heaviside’s “linearized” equations are known as the “weak field approximation”. When derived from the primordial field equation, there is no mention of field strength;the assumption that the primordial field was predominant at the big bang rather suggests that ultra-strong fields are governed by the equations. This aspect has physical significance, so we explore the assumption by formulating the gauge field version of Heaviside’s theory. We compare with recent linearized gravity formulations and discuss the significance of differences.展开更多
文摘In this paper, in Section 1, we have described some equations and theorems concerning the Lebesgue integral and the Lebesgue measure. In Section 2, we have described the possible mathematical applications, of Lebesgue integration, in some equations concerning various sectors of Chern-Simons theory and Yang-Mills gauge theory, precisely the two dimensional quantum Yang-Mills theory. In conclusion, in Section 3, we have described also the possible mathematical connections with some sectors of String Theory and Number Theory, principally with some equations concerning the Ramanujan’s modular equations that are related to the physical vibrations of the bosonic strings and of the superstrings, some Ramanujan’s identities concerning π and the zeta strings.
基金supported by the National Key Research and Development Program of China (Grant Nos. 2022YFA1404204 and 2022YFA1403700)the National Natural Science Foundation of China (Grant Nos. 12274086, 11534001 and 11925402)+5 种基金funding from the National Science Foundation of China (Grant Nos. 12274046, 11874094, 12147102, and 12347101)Chongqing Natural Science Foundation (Grant No. CSTB2022NSCQ-JQX0018)the Fundamental Research Funds for the Central Universities (Grant No. 2021CDJZYJH-003)Xiaomi Foundation/Xiaomi Young Talents Programthe supports of the start-up funding of Westlake Universitysupport from the Natural Sciences and Engineering Research Council of Canada (NSERC) through Discovery Grants。
文摘Simulating U(1) quantum gauge theories with spatial dimensions greater than one is of great physical significance. Here we propose a simple realization of U(1) gauge theory with Rydberg and Rydberg-dressed atom arrays. Within the experimentally accessible range, we find that the various aspects of the U(1) gauge theory can be well simulated, such as the emergence of topological sectors, incommensurability, and the Rokhsar–Kivelson point that hosts deconfined charge excitations and degenerate topological sectors. Our proposal is promising to implement experimentally and exhibits pronounced quantum dynamics.
基金supported by the National Natural Science Foundation of China(Grant Nos.12174194 and 12475033)the Fundamental Research Funds for the Central Universities。
文摘We have investigated the gauge dependence of physical observables in a quantum Rabi model under different potential fields arising from the Hilbert space truncation of the atomic degrees of freedom.In both the square-well and harmonic potentials,the optimal gauge for the ground-state energy depends on the cavity frequency,which is optimal in the low-frequency limit,whereas the Coulomb gauge is optimal in the high-frequency limit.For a dynamic quantity,such as an out-of-time-order correlator,we have demonstrated the necessity of introducing an optimal dynamic gauge.This study provides deeper insight into the intricate relationship between gauge choice and the dynamics of quantum electrodynamics systems,resulting in more accurate theoretical frameworks.
基金supported in part by the National Key Research and Development Program of China Grant No.2021YFC2203001in part by the NSFC(Grant Nos.11920101003,12021003 and 12005016)+1 种基金supported by‘the Fundamental Research Funds for the Central Universities’of Beijing Normal Universitysupported by the NSF of Hunan province(Grant No.2023JJ30179)。
文摘The transverse-traceless gauge condition is an important concept in the theory of gravitational waves.It is well known that a vacuum is one of the key conditions to guarantee the existence of the transverse-traceless gauge.Although it is thin,the interstellar medium is ubiquitous in the Universe.Therefore,it is important to understand the concept of gravitational waves when matter is presented.Bondi-Metzner-Sachs theory has solved the gauge problem related to gravitational waves.But it does not help with cases when the gravitational wave propagates in matter.This paper discusses possible extensions of the transverse-traceless gauge condition to Minkowski perturbation with matter presented.
基金supported by the National Key R&D Program of China(Grant No.2023YFB2905502)the National Natural Science Foundation of China(Grant Nos.62122047 and 61935011).
文摘A power splitter with a wideband arbitrary splitting ratio,which provides flexibility and adaptability in forming photonic devices such as microring resonators and Mach–Zehnder interferometers,proves to be essential in photonic integrated circuits(PICs).We designed and fabricated a directional coupler-based power splitter with a wideband arbitrary splitting ratio and a microring resonator with a wideband uniform extinction ratio(ER)based on artificial gauge field(AGF)optimization.The neural network-aided inverse design method is applied to complete the target.Less than 0.9 dB power splitting variation and 1.6 dB ER variation have been achieved experimentally over a 100-nm bandwidth.Wideband performance,design efficiency,and device compactness are obtained by utilizing this optimization,which indicates great potential and universality in PIC applications.
文摘A new mechanism for mass generation of gauge field is discussed in this paper. By introducing two sets of gauge fields and making the variations of these two sets of gauge fields compensated each other under local gauge transformations, the mass term of gauge fields is introduced into the Lagrangian without violating the local gauge symmetry of the Lagrangian. This model is a renormalizable quantum model.
基金supported primarily by the National Basic Research Program of China (2013CBA01806)the National Natural Sciences Foundation of China (41671029, 41690141, 41401040 and 41501040)
文摘With the popularity of the automatic precipitation gauges in national weather stations,testing their performance and adjusting their measurements are top priorities. Additionally,because different climatic conditions may have different effects on the performance of the precipitation gauges, it is also necessary to test the gauges in different areas. This study mainly analyzed precipitation measurements from the single-Altershielded TRwS204 automatic weighing gauge(TRwS_(SA)) relative to the adjusted manual measurements(reference precipitation) from the Chinese standard precipitation gauge in a doublefence wind shield(CSPG_(DF)) in the Hulu watershed in the Qilian Mountains, China. The measurements were compared over the period from August 2014 to July2017, and the transfer function derived from the work by Kochendorfer et al.(2017 a) for correcting windinduced losses was applied to the TRwS_(SA) measurements. The results show that the average loss of TRwS_(SA) measurements relative to the reference precipitation decreased from 0.55 mm(10.7%) to 0.51 mm(9.9%) for rainfall events, from 0.35 mm(8.5%)to 0.22 mm(5.3%) for sleet events, and from 0.49 mm(18.9%) to 0.33 mm(12.7%) for snowfall events after adjustment. The uncorrected large biases of TRwS_(SA) measurements are considered to be mainly caused by specific errors of TRwS_(SA), different gauge orifice area and random errors. These types of errors must be considered when comparing precipitation measurements for different gauge types, especially in the mountains.
基金Fund of Scientific and Technological Key Project Plan of Liaoning Province,China (No2003220026)
文摘In order to provide manufacturers of carding machines and relevant accessories with theoretical references,how cylinder radius,setover and heel-toe difference affect cylinder-flat gauge of a carding machine was theoretically studied.The relationship between cylinder-flat gauge and cylinder radius,setover and heel-toe difference was geometrically discussed.Numerical calculation and illustration about the relationship were made with MATLAB in accordance with practical settings.A general formula about the relationship is derived.A concept,the small-gauge zone length,has been defined for the first time,and some relevant results thus obtained.Given setover and heel-toe difference,the greater the cylinder radius,the greater the average gauge.If a smaller overall cylinder-flat gauge is desirable,it is not necessary to emphasize the tangential direction of the heel of clothed surface to the cylinder.Their intersection within a small zone is acceptable.In many cases,small-gauge zone can reduce average gauge which may be helpful to the carding action;given cylinder radius and setover,the smaller the heel-toe difference,the more helpful to reduce the overall gauge;given cylinder radius and heel-toe difference,the small-gauge zone length will increase with the increase of setover,so does the difference between the smallest gauge and outlet gauge.
文摘Karma alloy thin film strain gauges were fabricated on alumina substrates by magnetron sputtering. The electrical properties of strain gauges annealed at different temperatures were then tested. The surface morphology and phase structure of the Karma alloy thin films were analyzed using X-ray diffraction and scanning electron microscopy. The effect of the annealing temperature on the performance of the Karma alloy thin film strain gauge was also investigated. As the annealing temperature increased, it was found that the resistivity of the thin films decreased, whereas the temperature coefficient of resistance (TCR) of the thin films increased. A Karma alloy thin film strain gauge was annealed at 200 °C, thereby obtaining a gauge factor of 1.7 and a corresponding TCR of 64.8 × 10−6 K−1. The prepared Karma alloy thin film strain gauge had a lower TCR than other strain gauges at room temperature. This result can provide a reference for the preparation and application of Karma alloy thin film strain gauges in specific scenarios.
文摘We summarize our results about the quantization of a charged particle motion without spin inside a flat box under a static electromagnetic field with Landau’s gauge for the magnetic field, where Fourier’s transformation was used to analyze the problem, to point out that there exists a wave function which is different to that one given by Landau with the same Landau’s levels. The quantization of the magnetic flux is deduced differently to previous one, and a new solution is presented for the case of symmetric gauge of the magnetic field, and having the same Landau’s levels.
文摘A new mechanism to introduce the mass of gauge field in supersymmetric gauge theory is discussed. The model has the strict local gauge symmetry and supersymmetry. Because we introduce two vector superfields simultaneously, the model contains a massive gauge field as well as a massless gauge field.
基金＊The project supported by National Natural Science Foundation of China and the Doctoral Foundation of the Ministry of Education of China
文摘In this paper, spinor and vector decompositions of SU（2） gauge potential are presented and their equivalence is constructed using a simply proposal. We also obtain the action of Faddeev nonlinear 0（3） sigma model from the SU（2） mass/ve gauge field theory, which is proposed according to the gauge invariant principle. At last, the knot structure in SU（2） Chern-Simons filed theory is discussed in terms of the Φ-mapping topological current theory, The topological charge of the knot is characterized by the Hopf indices and the Brouwer degrees of Φ-mapping.
基金Supported by the National Natural Science Foundation of China under Grant Nos.10904092,10934004,60978018,11074184,and 11074154the Zhejiang Provincial Natural Science Foundation under Grant No.Y6090001
文摘Gauge potential plays an important role in exploring exotic phenomena in the single- and many-body quantum systems.In this paper,we propose a scheme to create both new Abelian and non-Abelian gauge potentials by adiabatically controlling the degenerate Dicke model in cavity quantum electrodynamics.It is shown that a non-Abelian gauge potential is achieved only for a single atom,whereas an Abelianizen diagonal gauge potential is realized for the atomic ensemble.More importantly,two interesting quantum phenomena such as the geometric phase and the magnetic monopole induced by our created gauge potentials are also predicted.The possible physical realization is presented in the macroscopic circuit quantum electrodynamics with the Cooper pair boxes,which act as the artificial two-level atoms controlled by the gate voltage and the external magnetic flux.
文摘A systematic method is developed to studY the classical motion of a mass point in gravitational gauge field. First, by using Mathematica, a spherical symmetric solution of the field equation of gravitational gauge field is obtained, which is just the traditional Schwarzschild solution. Combining the principle of gauge covariance and Newton＇s second law of motion, the equation of motion of a mass point in gravitational field is deduced. Based on the spherical symmetric solution of the field equation and the equation of motion of a mass point in gravitational field, we can discuss classical tests of gauge theory of gravity, including the deflection of light by the sun, the precession of the perihelia of the orbits of the inner planets and the time delay of radar echoes passing the sun. It is found that the theoretical predictions of these classical tests given by gauge theory of gravity are completely the same as those given by general relativity.
文摘This paper suggests a principle to find a unitary operator U which transforms non-physical quantity, zero-potential Hamiltonian H<SUB>0</SUB>, into true physical quantity UH<SUB>0</SUB>U<SUP>?</SUP> for a charged particle in classical electromagnetic field, and puts forward a unified form of constructing gauge-independent transition probabilities in this case. Different methods correspond to different unitary operators which satisfy the above-mentioned principle.
文摘A primordial field Self-interaction Principle, analyzed in Hestenes’ Geometric Calculus, leads to Heaviside’s equations of the gravitomagnetic field. When derived from Einstein’s nonlinear field equations Heaviside’s “linearized” equations are known as the “weak field approximation”. When derived from the primordial field equation, there is no mention of field strength;the assumption that the primordial field was predominant at the big bang rather suggests that ultra-strong fields are governed by the equations. This aspect has physical significance, so we explore the assumption by formulating the gauge field version of Heaviside’s theory. We compare with recent linearized gravity formulations and discuss the significance of differences.
