In physics, there are two main energy formulas. One is kinetic energy formula and the another is Einstein equation. But kinetic energy formula can only calculate low speed motion. Einstein equation can only calculate ...In physics, there are two main energy formulas. One is kinetic energy formula and the another is Einstein equation. But kinetic energy formula can only calculate low speed motion. Einstein equation can only calculate light speed motion. The two formulas are not unified. We hope to get a unified formula. But it didn’t work. According to the principle of Lorentz contraction, we generalize the contraction of length to the contraction of mass, and obtain a unified energy formula. This is the generalized Einstein equation and the new Einstein kinetic energy formula.展开更多
In this paper the authors derive regular criteria in Lorentz spaces for LerayHopf weak solutions v of the three-dimensional Navier-Stokes equations based on the formal equivalence relationπ≌|v|^(2),whereπdenotes th...In this paper the authors derive regular criteria in Lorentz spaces for LerayHopf weak solutions v of the three-dimensional Navier-Stokes equations based on the formal equivalence relationπ≌|v|^(2),whereπdenotes the fluid pressure and v denotes the fluid velocity.It is called the mixed pressure-velocity problem(the P-V problem for short).It is shown that if(π/(e-^|(x)|^(2)+|v|^(θ)∈L^(p)(0,T;L^(q,∞)),where 0≤θ≤1 and 2/p+3/q=2-θ,then v is regular on(0,T].Note that,ifΩ,is periodic,e^(-|x|)^(2) may be replaced by a positive constant.This result improves a 2018 statement obtained by one of the authors.Furthermore,as an integral part of the contribution,the authors give an overview on the known results on the P-V problem,and also on two main techniques used by many authors to establish sufficient conditions for regularity of the so-called Ladyzhenskaya-Prodi-Serrin(L-P-S for short)type.展开更多
In this paper,by introducing the Lorentz-invariance-violation(LIV)class of dispersion relations(DR)suppressed by the second power(E/Eqg)2,we investigated the effect of the LIV on the Hawking radiation of a charged Dir...In this paper,by introducing the Lorentz-invariance-violation(LIV)class of dispersion relations(DR)suppressed by the second power(E/Eqg)2,we investigated the effect of the LIV on the Hawking radiation of a charged Dirac particle based on tunneling from a Reissner-Nordstrom(RN)black hole.It was determined that the LIV speeds up black hole evaporation.As a result,the induced Hawking temperature was very sensitive to changes in the energy of the radiation particle.However,at the same energy level,it was insensitive to changes in the charge of the radiation particle.This is phenomenological evidence in support of the LIV-DR as a candidate for describing the effect of quantum gravity.Moreover,when the effect of the LIV was in eluded,we discovered that the statistical correlations with the Planck-scale corrections between successive emissions could leak out information via radiation.We also determined that black hole radiation via tunneling is an entropy conservation process,and no information loss occurred during radiation,where the interpretatio n of the entropy of a biack hole is addressed.Fin ally,we concluded that black hole evaporation is still a unitary process in the context of quantum gravity.展开更多
Chromatic aberration-free meta-devices(e.g.,achromatic meta-devices and abnormal chromatic meta-devices)play an essential role in modern science and technology.However,current efforts suffer the issues of low efficien...Chromatic aberration-free meta-devices(e.g.,achromatic meta-devices and abnormal chromatic meta-devices)play an essential role in modern science and technology.However,current efforts suffer the issues of low efficiency,narrow operating band,and limited wavefront manipulation capability.We propose a general strategy to design chromatic aberration-free meta-devices with high-efficiency and ultrabroadband properties,which is realized by satisfying the key criteria of desirable phase dispersion and high reflection amplitudes at the target frequency interval.The phase dispersion is tuned successfully based on a multiresonant Lorentz model,and high reflection is guaranteed by the presence of the metallic ground.As proof of the concept,two microwave meta-devices are designed,fabricated,and experimentally characterized.An achromatic meta-mirror is proposed within 8 to 12 GHz,and another abnormal chromatic meta-mirror can tune the reflection angle as a linear function.Both meta-mirrors exhibit very high efficiencies(85%to 94%in the frequency band).Our findings open a door to realize chromatic aberration-free meta-devices with high efficiency and wideband properties and stimulate the realizations of chromatic aberration-free metadevices with other functionalities or working at higher frequency.展开更多
We obtain an exact slowly rotating Einstein-bumblebee black hole solution by solving the corresponding rr and tθ components of the gravitational field equations for both cases:A)b u=(0,b(r),0,0) and B) bu=(0,b(r),b(...We obtain an exact slowly rotating Einstein-bumblebee black hole solution by solving the corresponding rr and tθ components of the gravitational field equations for both cases:A)b u=(0,b(r),0,0) and B) bu=(0,b(r),b(θ),0) .Then,we check the other gravitational field equations and the bumblebee field motion equations using this solution.We find that for case A,there indeed exists a slowly rotating black hole solution for an arbitrary LV(Lorentz violation)coupling constant l;however,for case B,this slowly rotating solution exists if and only if coupling constant l is as small as or smaller than angular momentum a.Thus far,no full rotating black hole solution has been published;hence,the Newman-Janis algorithm cannot be used to generate a rotating solution in the Einstein-bumblebee theory.This is similar to the Einstein-aether theory,wherein only some slowly rotating black hole solutions exist.To study the effects of this broken Lorentz symmetry,we consider the black hole greybody factor and find that,for angular index l=0 ,LV constant l decreases the effective potential and enhances the absorption probability,which is similar to the results for the non-minimal derivative coupling theory.展开更多
Christoffel connection (or Levi-Civita affine connection) did not enter gravity as an axiom of minimal length for the free fall of particles (where anyway length action is not defined for massless particles), nor out ...Christoffel connection (or Levi-Civita affine connection) did not enter gravity as an axiom of minimal length for the free fall of particles (where anyway length action is not defined for massless particles), nor out of economy, but from the weak equivalence principle (gravitational force is equivalent to acceleration according to Einstein) together with the identification of the local inertial frame with the local Lorentz one. This identification implies that the orbits of all particles are given by the geodesics of the Christoffel connection. Here, we show that in the presence of only massless particles (absence of massive particles), the above identification is inconsistent and does not lead to any connection. The proof is based on the existence of projectively equivalent connections and the absence of proper time for null particles. If a connection derived by some kinematical principles for the particles is to be applied in the world, it is better for these principles to be valid in all relevant spacetime rather than different principles to give different connections in different spacetime regions. Therefore, our result stated above may imply a conceptual insufficiency of the use of the Christoffel connection in the early universe where only massless particles are expected to be present (whenever at least some notions, like orbits, are meaningful), and thus of the total use of this connection. If in the early universe, the notion of a massive particle, which appears latter in time, cannot be used, in an analogous way in a causally disconnected high-energy region (maybe deep interior of astrophysical objects or black holes), the same conclusions could be extracted if only massless particles are present.展开更多
The aim of the paper is to get an insight into the time interval of electron emission done between two neighbouring energy levels of the hydrogen atom. To this purpose, in the first step, the formulae of the special r...The aim of the paper is to get an insight into the time interval of electron emission done between two neighbouring energy levels of the hydrogen atom. To this purpose, in the first step, the formulae of the special relativity are applied to demonstrate the conditions which can annihilate the electrostatic force acting between the nucleus and electron in the atom. This result is obtained when a suitable electron speed entering the Lorentz transformation is combined with the strength of the magnetic field acting normally to the electron orbit in the atom. In the next step, the Maxwell equation characterizing the electromotive force is applied to calculate the time interval connected with the change of the magnetic field necessary to produce the force. It is shown that the time interval obtained from the Maxwell equation, multiplied by the energy change of two neighbouring energy levels considered in the atom, does satisfy the Joule-Lenz formula associated with the quantum electron energy emission rate between the levels.展开更多
We present the theoretical considerations for the case of looking into a generalization of quantum theory corresponding to having an inner product with an indefinite signature on the Hilbert space. The latter is essen...We present the theoretical considerations for the case of looking into a generalization of quantum theory corresponding to having an inner product with an indefinite signature on the Hilbert space. The latter is essentially a direct analog of having the Minkowski spacetime with an indefinite signature generalizing the metric geometry of the Newtonian space. In fact, the explicit physics setting we have in mind is exactly a Lorentz covariant formulation of quantum mechanics, which has been discussed in the literature for over half a century yet without a nice full picture. From the point of view of the Lorentz symmetry, indefiniteness of the norm for a Minkowski vector may be the exact correspondence of the indefiniteness of the norm for a quantum state vector on the relevant Hilbert space. That, of course, poses a challenge to the usual requirement of unitarity. The related issues will be addressed.展开更多
In this note we give a geometrical presentation to the 4D Riemannian curvature as it relates to the Newtonian gravity in the 4D Lorentz manifold. The compacting of the proper time as is necessary for the unification w...In this note we give a geometrical presentation to the 4D Riemannian curvature as it relates to the Newtonian gravity in the 4D Lorentz manifold. The compacting of the proper time as is necessary for the unification with the Maxwell electrodynamics, as given by Einstein and Kaluza-Klein, should the universe be only of 4D space-time, led to the concept of gravitational field singularity sinks known as black holes, that would not be acceptable under a 5D homogeneous manifold through which the 4D Lorentz manifold evolved by application of the Perelman-Ricci Flow entropy mapping, which is consistent with both Maxwell suggested magnetic monopole, the quantum Higgs vacuum theory and the Gell-Mann standard model for hadrons.展开更多
A theory employing the vortex shape of the electron was presented to resolve the enigma of the wave-particle duality. Conventions such as “particle” and “wave” were used to describe the behavior of quantum objects...A theory employing the vortex shape of the electron was presented to resolve the enigma of the wave-particle duality. Conventions such as “particle” and “wave” were used to describe the behavior of quantum objects such as electrons. A superfluid vacuum formed the base to describe the basic vortex structure and properties of the electron, whereas various formulations derived from hydrodynamic laws described the electron vortex circumference, radius, angular velocity and angular frequency, angular momentum (spin) and magnetic momentum. A vortex electron fully explained the associations between momentum and wave, and hydrodynamic laws were essential in deriving the energy and angular frequency of the electron. In general, an electron traveling in space possesses internal and external motions. To derive the angular frequency of its internal motion, the Compton wavelength was used to represent the length of one cycle of the internal motion that is equal to the circumference of the electron vortex. The angular frequency of the electron vortex was calculated to obtain the same value according to Planck’s theory. A traveling vortex electron has internal and external motions that create a three-dimensional helix trajectory. The magnitude of the instantaneous velocity of the electron is the resultant of its internal and external velocities, being equal to the internal velocity reduced by the Lorentz factor (whose essence is presented in a detailed formulation). The wavelength of the helix trajectory represents the distance traveled by a particle along its axis during one period of revolution around the axis, resulting in the same de Broglie wavelength that corresponds to the helix pitch of the helix. Mathematical formulations were presented to demonstrate the relation between the energy of the vortex and its angular frequency and de Broglie’s wavelength;furthermore, Compton’s and de Broglie’s wavelengths were also differentiated.展开更多
According to a corrected dispersion relation proposed in the study on the string theory and quantum gravity theory,the Rarita-Schwinger equation was precisely modified,which resulted in the Rarita-Schwinger-Hamilton-J...According to a corrected dispersion relation proposed in the study on the string theory and quantum gravity theory,the Rarita-Schwinger equation was precisely modified,which resulted in the Rarita-Schwinger-Hamilton-Jacobi equation.Using this equation,the characteristics of arbitrary spin fermion quantum tunneling radiation from non-stationary Kerr-de Sitter black holes were determined.A number of accurately corrected physical quantities,such as surface gravity,chemical potential,tunneling probability,and Hawking temperature,which describe the properties of black holes,were derived.This research has enriched the research methods and enabled increased precision in black hole physics research.展开更多
The 3D viscous incompressible magneto-hydrodynamic (MHD) system comprised by the 3D incompressible viscous Navier-Stokes equation couples with Maxwell equation.The global well-posedness of the coupled system is still ...The 3D viscous incompressible magneto-hydrodynamic (MHD) system comprised by the 3D incompressible viscous Navier-Stokes equation couples with Maxwell equation.The global well-posedness of the coupled system is still an open problem.In this paper,we study the Cauchy problem of this coupled system and establish some logarithmical type of blow-up criterion for smooth solution in Lorentz spaces.展开更多
The effective vacuum energy density contributed by the non-trivial contortion distribution and the bare vacuumenergy density can be viewed as the energy density of the auxiliary quintessence field potential.We find th...The effective vacuum energy density contributed by the non-trivial contortion distribution and the bare vacuumenergy density can be viewed as the energy density of the auxiliary quintessence field potential.We find thatthe negative bare vacuum energy density from string landscape leads to a monotonically decreasing quintessence potentialwhile the positive one from swampland leads to the metastable or stable de Sitter-like potential.Moreover,thenon-trivial Brans-Dicke like coupling between the quintessence field and gravitation field is necessary in the lattercase.展开更多
Even for a 100 nm interparticle distance or a small change in particle shape,optical Fano-like plasmonic resonance mode usually vanishes completely.It would be remarkable if stable Fano-like resonance could somehow be...Even for a 100 nm interparticle distance or a small change in particle shape,optical Fano-like plasmonic resonance mode usually vanishes completely.It would be remarkable if stable Fano-like resonance could somehow be achieved in distinctly shaped nanoparticles for more than 1μm interparticle distance,which corresponds to the far electromagnetic field region.If such far-field Fano-like plasmonic resonance can be achieved,controlling the reversal of the far-field binding force can be attained,like the currently reported reversals for near-field cases.In this work,we have proposed an optical set-up to achieve such a robust and stable Fano-like plasmonic resonance,and comparatively studied its remarkable impact on controlling the reversal of near-and far-field optical binding forces.In our proposed set-up,the distinctly shaped plasmonic tetramers are half immersed(i.e.air-benzene)in an inhomogeneous dielectric interface and illuminated by?circular?polarized light.We have demonstrated significant differences between near-and far-field optical binding forces along with the Lorentz force field,which partially depends on the object’s shape.A clear connection is shown between the far-field binding force and the resonant modes,along with a generic mechanism to achieve controllable Fano-like plasmonic resonance and the reversal of the optical binding force in both far-and near-field configurations.展开更多
We investigate quantum effects on a nonrelativistic neutral particle with a permanent magnetic dipole moment that interacts with an electric field.This neutral particle is also under the influence of a background that...We investigate quantum effects on a nonrelativistic neutral particle with a permanent magnetic dipole moment that interacts with an electric field.This neutral particle is also under the influence of a background that breaks the Lorentz symmetry.We focus on the Lorentz symmetry violation background determined by a space-like vector field.Then,we show that the effects of the violation of Lorentz symmetry can yield an attractive Coulomb-type potential.Furthermore,we obtain the bound state solutions to the SchrÖdinger–Pauli equation and show that the spectrum of energy is a function of the Aharonov–Casher geometric quantum phase.Finally,we discuss the arising of persistent spin currents.展开更多
The wetting behavior of liquid metals is of great importance for many processes. For brazing, however, a targeted modification beyond the adjustment of conventional process parameters or the actual set-up was not poss...The wetting behavior of liquid metals is of great importance for many processes. For brazing, however, a targeted modification beyond the adjustment of conventional process parameters or the actual set-up was not possible in the past. Therefore, the effect of direct electric current along the surface of a steel substrate on the wetting behavior and the formation of the spreading pattern of an industrial nickel-based filler metal was investigated at a temperature above T = 1000 °C in a vacuum brazing furnace. By applying direct current up to I = 60 A the wetted surface area could be increased and the spreading of the molten filler metal could be controlled in dependence of the polarity of the electric current. The electric component of the Lorentz force is supposed to be feasible reasons for the observed dependence of the electrical polarity on the filler metal spreading direction. To evaluate the influence of the electric current on the phase formation subsequent selective electron microscope analyses of the spreading pattern were carried out.展开更多
The present study reveals the significance of the magnetic field or Lorentz force on the unsteady natural convection flow and heat transfer in the suddenly expanded cavity.The Lorentz force based magnetohydrodynamics(...The present study reveals the significance of the magnetic field or Lorentz force on the unsteady natural convection flow and heat transfer in the suddenly expanded cavity.The Lorentz force based magnetohydrodynamics(MHD)solver using electric potential formulation coupled with the energy equation by the means of Boussinesq approximation is developed in the open-source CFD tool OpenFOAM.The unsteady flow is generated by the buoyancy force keeping the Rayleigh number(Ra)at 109,at the fixed Prandtl number(Pr)of 0.71.The effects of the magnetic field on the flow and heat transfer are explained for various orientations of magnetic field(Bx,B45,and By)in terms of Hartmann number(Ha=0,50,100,300 and 500).The increase in the magnetic field increases the strength of the Lorentz force,which regulates the flow pattern and suppresses down the unsteady nature of flow and heat transfer into the steady-state.It is perceived that the average Nusselt number decreases as the intensity of Bx and B45 magnetic field increases.However,for By magnetic field the average Nusselt number increases up to Ha of 100 as compared to the non-MHD case(Ha=0).The distribution of Lorentz force in the domain plays a significant role in the governing of the fluid flow and heat transfer.展开更多
The quintessence-like potential of vacuum energy can meet the requirements from both quantum gravity and the accelerating expansion of the universe.The anti-de Sitter(AdS)vacuum in string theory must be lifted to the ...The quintessence-like potential of vacuum energy can meet the requirements from both quantum gravity and the accelerating expansion of the universe.The anti-de Sitter(AdS)vacuum in string theory must be lifted to the meta-stable dS vacuum with a positive vacuum energy density to explain the accelerating expansion of the universe.Based on possible large-scale Lorentz violation,we define an effective cosmological constant that depends not only on the bare cosmological constant but also on the Lorentz violation effect.We find that the evolution of the effective cosmological constant exhibits the behavior of the quintessence potential when the bare cosmological constant originates from the string landscape,in contrast to the existence of a local minimum during evolution when the bare cosmological constant is supplied by the swampland.The critical value of the bare cosmological constant is approximately zero for the behavior transition.The frozen large-scale Lorentz violation can uplift the AdS vacua to an effective quintessence-like one in this sense.展开更多
Using time-dependent Ginzburg-Landau formalism,we investigate the multiple reversals of ratchet effects in an unpatterned superconducting strip by the tilted dynamic pinning potential.In the case of collinear sliding ...Using time-dependent Ginzburg-Landau formalism,we investigate the multiple reversals of ratchet effects in an unpatterned superconducting strip by the tilted dynamic pinning potential.In the case of collinear sliding potential and Lorentz force,vortices are always confined in the channels induced by sliding potential.However,due to the inclination angle of sliding pinning potential with respect to the Lorentz force,vortices could be driven out of the channels,and unexpected results with multiple reversals of vortex rectifications are observed.The mechanism of multiple reversals of vortex rectifications is explored by analyzing different vortex motion scenarios with increasing ac current amplitudes.The multiple reversals of transverse and longitudinal ratchet effects can be highly controlled by ac amplitude and dynamic pinning velocity.What's more,at certain large current the ratchet effect reaches strongest within a wide range of pinning sliding velocity.展开更多
文摘In physics, there are two main energy formulas. One is kinetic energy formula and the another is Einstein equation. But kinetic energy formula can only calculate low speed motion. Einstein equation can only calculate light speed motion. The two formulas are not unified. We hope to get a unified formula. But it didn’t work. According to the principle of Lorentz contraction, we generalize the contraction of length to the contraction of mass, and obtain a unified energy formula. This is the generalized Einstein equation and the new Einstein kinetic energy formula.
基金supported by FCT(Portugal)under the project UIDB/MAT/04561/2020the Fundamental Research Funds for the Central Universities under grant G2019KY05114。
文摘In this paper the authors derive regular criteria in Lorentz spaces for LerayHopf weak solutions v of the three-dimensional Navier-Stokes equations based on the formal equivalence relationπ≌|v|^(2),whereπdenotes the fluid pressure and v denotes the fluid velocity.It is called the mixed pressure-velocity problem(the P-V problem for short).It is shown that if(π/(e-^|(x)|^(2)+|v|^(θ)∈L^(p)(0,T;L^(q,∞)),where 0≤θ≤1 and 2/p+3/q=2-θ,then v is regular on(0,T].Note that,ifΩ,is periodic,e^(-|x|)^(2) may be replaced by a positive constant.This result improves a 2018 statement obtained by one of the authors.Furthermore,as an integral part of the contribution,the authors give an overview on the known results on the P-V problem,and also on two main techniques used by many authors to establish sufficient conditions for regularity of the so-called Ladyzhenskaya-Prodi-Serrin(L-P-S for short)type.
基金Supported by the National Natural Science Foundation of China(11903025)by the starting fund of China West Normal University(18Q062)+1 种基金by the Natural Science Foundation of Sichuan Education Department(17ZA0294)by the Research Project of Si Chuan MinZu College(XYZB18003ZA)。
文摘In this paper,by introducing the Lorentz-invariance-violation(LIV)class of dispersion relations(DR)suppressed by the second power(E/Eqg)2,we investigated the effect of the LIV on the Hawking radiation of a charged Dirac particle based on tunneling from a Reissner-Nordstrom(RN)black hole.It was determined that the LIV speeds up black hole evaporation.As a result,the induced Hawking temperature was very sensitive to changes in the energy of the radiation particle.However,at the same energy level,it was insensitive to changes in the charge of the radiation particle.This is phenomenological evidence in support of the LIV-DR as a candidate for describing the effect of quantum gravity.Moreover,when the effect of the LIV was in eluded,we discovered that the statistical correlations with the Planck-scale corrections between successive emissions could leak out information via radiation.We also determined that black hole radiation via tunneling is an entropy conservation process,and no information loss occurred during radiation,where the interpretatio n of the entropy of a biack hole is addressed.Fin ally,we concluded that black hole evaporation is still a unitary process in the context of quantum gravity.
基金This work was supported by the National Natural Science Foundation of China under Grant Nos.61871394,61901512,11604167,61625502,11961141010,61975176,and 62071423Postdoctoral Innovation Talents Support Program of China under Grant No.BX20190293,and Natural Science Foundation of Shaanxi Province under Grant No.2019JQ-013.
文摘Chromatic aberration-free meta-devices(e.g.,achromatic meta-devices and abnormal chromatic meta-devices)play an essential role in modern science and technology.However,current efforts suffer the issues of low efficiency,narrow operating band,and limited wavefront manipulation capability.We propose a general strategy to design chromatic aberration-free meta-devices with high-efficiency and ultrabroadband properties,which is realized by satisfying the key criteria of desirable phase dispersion and high reflection amplitudes at the target frequency interval.The phase dispersion is tuned successfully based on a multiresonant Lorentz model,and high reflection is guaranteed by the presence of the metallic ground.As proof of the concept,two microwave meta-devices are designed,fabricated,and experimentally characterized.An achromatic meta-mirror is proposed within 8 to 12 GHz,and another abnormal chromatic meta-mirror can tune the reflection angle as a linear function.Both meta-mirrors exhibit very high efficiencies(85%to 94%in the frequency band).Our findings open a door to realize chromatic aberration-free meta-devices with high efficiency and wideband properties and stimulate the realizations of chromatic aberration-free metadevices with other functionalities or working at higher frequency.
基金Supported by the Scientific Research Fund of the Hunan Provincial Education Department(19A257)the National Natural Science Foundation(NNSFC)of China(11247013)Hunan Provincial Natural Science Foundation of China(2015JJ2085)。
文摘We obtain an exact slowly rotating Einstein-bumblebee black hole solution by solving the corresponding rr and tθ components of the gravitational field equations for both cases:A)b u=(0,b(r),0,0) and B) bu=(0,b(r),b(θ),0) .Then,we check the other gravitational field equations and the bumblebee field motion equations using this solution.We find that for case A,there indeed exists a slowly rotating black hole solution for an arbitrary LV(Lorentz violation)coupling constant l;however,for case B,this slowly rotating solution exists if and only if coupling constant l is as small as or smaller than angular momentum a.Thus far,no full rotating black hole solution has been published;hence,the Newman-Janis algorithm cannot be used to generate a rotating solution in the Einstein-bumblebee theory.This is similar to the Einstein-aether theory,wherein only some slowly rotating black hole solutions exist.To study the effects of this broken Lorentz symmetry,we consider the black hole greybody factor and find that,for angular index l=0 ,LV constant l decreases the effective potential and enhances the absorption probability,which is similar to the results for the non-minimal derivative coupling theory.
文摘Christoffel connection (or Levi-Civita affine connection) did not enter gravity as an axiom of minimal length for the free fall of particles (where anyway length action is not defined for massless particles), nor out of economy, but from the weak equivalence principle (gravitational force is equivalent to acceleration according to Einstein) together with the identification of the local inertial frame with the local Lorentz one. This identification implies that the orbits of all particles are given by the geodesics of the Christoffel connection. Here, we show that in the presence of only massless particles (absence of massive particles), the above identification is inconsistent and does not lead to any connection. The proof is based on the existence of projectively equivalent connections and the absence of proper time for null particles. If a connection derived by some kinematical principles for the particles is to be applied in the world, it is better for these principles to be valid in all relevant spacetime rather than different principles to give different connections in different spacetime regions. Therefore, our result stated above may imply a conceptual insufficiency of the use of the Christoffel connection in the early universe where only massless particles are expected to be present (whenever at least some notions, like orbits, are meaningful), and thus of the total use of this connection. If in the early universe, the notion of a massive particle, which appears latter in time, cannot be used, in an analogous way in a causally disconnected high-energy region (maybe deep interior of astrophysical objects or black holes), the same conclusions could be extracted if only massless particles are present.
文摘The aim of the paper is to get an insight into the time interval of electron emission done between two neighbouring energy levels of the hydrogen atom. To this purpose, in the first step, the formulae of the special relativity are applied to demonstrate the conditions which can annihilate the electrostatic force acting between the nucleus and electron in the atom. This result is obtained when a suitable electron speed entering the Lorentz transformation is combined with the strength of the magnetic field acting normally to the electron orbit in the atom. In the next step, the Maxwell equation characterizing the electromotive force is applied to calculate the time interval connected with the change of the magnetic field necessary to produce the force. It is shown that the time interval obtained from the Maxwell equation, multiplied by the energy change of two neighbouring energy levels considered in the atom, does satisfy the Joule-Lenz formula associated with the quantum electron energy emission rate between the levels.
文摘We present the theoretical considerations for the case of looking into a generalization of quantum theory corresponding to having an inner product with an indefinite signature on the Hilbert space. The latter is essentially a direct analog of having the Minkowski spacetime with an indefinite signature generalizing the metric geometry of the Newtonian space. In fact, the explicit physics setting we have in mind is exactly a Lorentz covariant formulation of quantum mechanics, which has been discussed in the literature for over half a century yet without a nice full picture. From the point of view of the Lorentz symmetry, indefiniteness of the norm for a Minkowski vector may be the exact correspondence of the indefiniteness of the norm for a quantum state vector on the relevant Hilbert space. That, of course, poses a challenge to the usual requirement of unitarity. The related issues will be addressed.
文摘In this note we give a geometrical presentation to the 4D Riemannian curvature as it relates to the Newtonian gravity in the 4D Lorentz manifold. The compacting of the proper time as is necessary for the unification with the Maxwell electrodynamics, as given by Einstein and Kaluza-Klein, should the universe be only of 4D space-time, led to the concept of gravitational field singularity sinks known as black holes, that would not be acceptable under a 5D homogeneous manifold through which the 4D Lorentz manifold evolved by application of the Perelman-Ricci Flow entropy mapping, which is consistent with both Maxwell suggested magnetic monopole, the quantum Higgs vacuum theory and the Gell-Mann standard model for hadrons.
文摘A theory employing the vortex shape of the electron was presented to resolve the enigma of the wave-particle duality. Conventions such as “particle” and “wave” were used to describe the behavior of quantum objects such as electrons. A superfluid vacuum formed the base to describe the basic vortex structure and properties of the electron, whereas various formulations derived from hydrodynamic laws described the electron vortex circumference, radius, angular velocity and angular frequency, angular momentum (spin) and magnetic momentum. A vortex electron fully explained the associations between momentum and wave, and hydrodynamic laws were essential in deriving the energy and angular frequency of the electron. In general, an electron traveling in space possesses internal and external motions. To derive the angular frequency of its internal motion, the Compton wavelength was used to represent the length of one cycle of the internal motion that is equal to the circumference of the electron vortex. The angular frequency of the electron vortex was calculated to obtain the same value according to Planck’s theory. A traveling vortex electron has internal and external motions that create a three-dimensional helix trajectory. The magnitude of the instantaneous velocity of the electron is the resultant of its internal and external velocities, being equal to the internal velocity reduced by the Lorentz factor (whose essence is presented in a detailed formulation). The wavelength of the helix trajectory represents the distance traveled by a particle along its axis during one period of revolution around the axis, resulting in the same de Broglie wavelength that corresponds to the helix pitch of the helix. Mathematical formulations were presented to demonstrate the relation between the energy of the vortex and its angular frequency and de Broglie’s wavelength;furthermore, Compton’s and de Broglie’s wavelengths were also differentiated.
基金Supported by National Natural Science Foundation of China(11573022)National Natural Science Foundation of China(11273020)Natural Science Foundation of Shandong Province,China(ZR2019MA059)。
文摘According to a corrected dispersion relation proposed in the study on the string theory and quantum gravity theory,the Rarita-Schwinger equation was precisely modified,which resulted in the Rarita-Schwinger-Hamilton-Jacobi equation.Using this equation,the characteristics of arbitrary spin fermion quantum tunneling radiation from non-stationary Kerr-de Sitter black holes were determined.A number of accurately corrected physical quantities,such as surface gravity,chemical potential,tunneling probability,and Hawking temperature,which describe the properties of black holes,were derived.This research has enriched the research methods and enabled increased precision in black hole physics research.
基金Xin-Guang Yang was partially supported by the Fund of Young Backbone Teacher in Henan Province(No.2018GGJS039)Yongjin Lu is partially supported by NSF(Award No:1601127).
文摘The 3D viscous incompressible magneto-hydrodynamic (MHD) system comprised by the 3D incompressible viscous Navier-Stokes equation couples with Maxwell equation.The global well-posedness of the coupled system is still an open problem.In this paper,we study the Cauchy problem of this coupled system and establish some logarithmical type of blow-up criterion for smooth solution in Lorentz spaces.
基金Supported by the National Natural Science Foundation of China(11775080,11865016)。
文摘The effective vacuum energy density contributed by the non-trivial contortion distribution and the bare vacuumenergy density can be viewed as the energy density of the auxiliary quintessence field potential.We find thatthe negative bare vacuum energy density from string landscape leads to a monotonically decreasing quintessence potentialwhile the positive one from swampland leads to the metastable or stable de Sitter-like potential.Moreover,thenon-trivial Brans-Dicke like coupling between the quintessence field and gravitation field is necessary in the lattercase.
基金the support of the internal grant of North South University 2018–19 and 2019–20(approved by the members of BOT,North South University,Bangladesh)along with the support of a TWAS international grant 2018–19(18-121 RG/PHYS/AS_I).
文摘Even for a 100 nm interparticle distance or a small change in particle shape,optical Fano-like plasmonic resonance mode usually vanishes completely.It would be remarkable if stable Fano-like resonance could somehow be achieved in distinctly shaped nanoparticles for more than 1μm interparticle distance,which corresponds to the far electromagnetic field region.If such far-field Fano-like plasmonic resonance can be achieved,controlling the reversal of the far-field binding force can be attained,like the currently reported reversals for near-field cases.In this work,we have proposed an optical set-up to achieve such a robust and stable Fano-like plasmonic resonance,and comparatively studied its remarkable impact on controlling the reversal of near-and far-field optical binding forces.In our proposed set-up,the distinctly shaped plasmonic tetramers are half immersed(i.e.air-benzene)in an inhomogeneous dielectric interface and illuminated by?circular?polarized light.We have demonstrated significant differences between near-and far-field optical binding forces along with the Lorentz force field,which partially depends on the object’s shape.A clear connection is shown between the far-field binding force and the resonant modes,along with a generic mechanism to achieve controllable Fano-like plasmonic resonance and the reversal of the optical binding force in both far-and near-field configurations.
基金CNPq(Conselho Nacional de Desenvolvimento Científico e Tecnológico—Brazil)for financial support。
文摘We investigate quantum effects on a nonrelativistic neutral particle with a permanent magnetic dipole moment that interacts with an electric field.This neutral particle is also under the influence of a background that breaks the Lorentz symmetry.We focus on the Lorentz symmetry violation background determined by a space-like vector field.Then,we show that the effects of the violation of Lorentz symmetry can yield an attractive Coulomb-type potential.Furthermore,we obtain the bound state solutions to the SchrÖdinger–Pauli equation and show that the spectrum of energy is a function of the Aharonov–Casher geometric quantum phase.Finally,we discuss the arising of persistent spin currents.
基金The presented investigations were carried out at RWTH Aachen University within the framework of the Collaborative Research Centre SFB1120-236616214“Precision Melt Engineering”and funded by the German Research Foundation(DFG e.V.).
文摘The wetting behavior of liquid metals is of great importance for many processes. For brazing, however, a targeted modification beyond the adjustment of conventional process parameters or the actual set-up was not possible in the past. Therefore, the effect of direct electric current along the surface of a steel substrate on the wetting behavior and the formation of the spreading pattern of an industrial nickel-based filler metal was investigated at a temperature above T = 1000 °C in a vacuum brazing furnace. By applying direct current up to I = 60 A the wetted surface area could be increased and the spreading of the molten filler metal could be controlled in dependence of the polarity of the electric current. The electric component of the Lorentz force is supposed to be feasible reasons for the observed dependence of the electrical polarity on the filler metal spreading direction. To evaluate the influence of the electric current on the phase formation subsequent selective electron microscope analyses of the spreading pattern were carried out.
文摘The present study reveals the significance of the magnetic field or Lorentz force on the unsteady natural convection flow and heat transfer in the suddenly expanded cavity.The Lorentz force based magnetohydrodynamics(MHD)solver using electric potential formulation coupled with the energy equation by the means of Boussinesq approximation is developed in the open-source CFD tool OpenFOAM.The unsteady flow is generated by the buoyancy force keeping the Rayleigh number(Ra)at 109,at the fixed Prandtl number(Pr)of 0.71.The effects of the magnetic field on the flow and heat transfer are explained for various orientations of magnetic field(Bx,B45,and By)in terms of Hartmann number(Ha=0,50,100,300 and 500).The increase in the magnetic field increases the strength of the Lorentz force,which regulates the flow pattern and suppresses down the unsteady nature of flow and heat transfer into the steady-state.It is perceived that the average Nusselt number decreases as the intensity of Bx and B45 magnetic field increases.However,for By magnetic field the average Nusselt number increases up to Ha of 100 as compared to the non-MHD case(Ha=0).The distribution of Lorentz force in the domain plays a significant role in the governing of the fluid flow and heat transfer.
基金Supported by the National Natural Science Foundation of China(11775080,11865016)。
文摘The quintessence-like potential of vacuum energy can meet the requirements from both quantum gravity and the accelerating expansion of the universe.The anti-de Sitter(AdS)vacuum in string theory must be lifted to the meta-stable dS vacuum with a positive vacuum energy density to explain the accelerating expansion of the universe.Based on possible large-scale Lorentz violation,we define an effective cosmological constant that depends not only on the bare cosmological constant but also on the Lorentz violation effect.We find that the evolution of the effective cosmological constant exhibits the behavior of the quintessence potential when the bare cosmological constant originates from the string landscape,in contrast to the existence of a local minimum during evolution when the bare cosmological constant is supplied by the swampland.The critical value of the bare cosmological constant is approximately zero for the behavior transition.The frozen large-scale Lorentz violation can uplift the AdS vacua to an effective quintessence-like one in this sense.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11702034,11972298,and 11702218)the China Postdoctoral Science Foundation(Grant No.2019M663812)+1 种基金the Fundamental Research Funds for the Central Universities,China(Grant Nos.300102129104,3102018zy013,and 3102017jc01003)the Young Talent Fund of University Association for Science and Technology in Shaanxi,China(Grant Nos.20180503 and 20180501).
文摘Using time-dependent Ginzburg-Landau formalism,we investigate the multiple reversals of ratchet effects in an unpatterned superconducting strip by the tilted dynamic pinning potential.In the case of collinear sliding potential and Lorentz force,vortices are always confined in the channels induced by sliding potential.However,due to the inclination angle of sliding pinning potential with respect to the Lorentz force,vortices could be driven out of the channels,and unexpected results with multiple reversals of vortex rectifications are observed.The mechanism of multiple reversals of vortex rectifications is explored by analyzing different vortex motion scenarios with increasing ac current amplitudes.The multiple reversals of transverse and longitudinal ratchet effects can be highly controlled by ac amplitude and dynamic pinning velocity.What's more,at certain large current the ratchet effect reaches strongest within a wide range of pinning sliding velocity.