The covariant density functional theory(CDFT)and five-dimensional collective Hamiltonian(5DCH)are used to analyze the experimental deformation parameters and moments of inertia(MoIs)of 12 triaxial nuclei as extracted ...The covariant density functional theory(CDFT)and five-dimensional collective Hamiltonian(5DCH)are used to analyze the experimental deformation parameters and moments of inertia(MoIs)of 12 triaxial nuclei as extracted by Allmond and Wood[J.M.Allmond and J.L.Wood,Phys.Lett.B 767,226(2017)].We find that the CDFT MoIs are generally smaller than the experimental values but exhibit qualitative consistency with the irrotational flow and experimental data for the relative MoIs,indicating that the intermediate axis exhibites the largest MoI.Additionally,it is found that the pairing interaction collapse could result in nuclei behaving as a rigid-body flow,as exhibited in the^(186-192)Os case.Furthermore,by incorporating enhanced CDFT MoIs(factor of f≈1.55)into the 5DCH,the experimental low-lying energy spectra and deformation parameters are reproduced successfully.Compared with both CDFT and the triaxial rotor model,the 5DCH demonstrates superior agreement with the experimental deformation parameters and low-lying energy spectra,respectively,emphasizing the importance of considering shape fluctuations.展开更多
The octupole deformation and collectivity in octupole double-magic nucleus 144Ba are investigated using the Cranking covariant density functional theory in a three-dimensional lattice space.The reduced B(E3)transition...The octupole deformation and collectivity in octupole double-magic nucleus 144Ba are investigated using the Cranking covariant density functional theory in a three-dimensional lattice space.The reduced B(E3)transition probability is implemented for the first time in semiclassical approximation based on the microscopically calculated electric octupole moments.The available data,including the I-ωrelation and electric transitional probabilities B(E2)and B(E3)are well reproduced.Furthermore,it is shown that the ground state of 144Ba exhibits axial octupole and quadrupole deformations that persist up to high spins(I≈24h).展开更多
This paper extends the covariant derivative un der curved coordinate systems in 3D Euclid space. Based on the axiom of the covariant form invariability, the classical covariant derivative that can only act on componen...This paper extends the covariant derivative un der curved coordinate systems in 3D Euclid space. Based on the axiom of the covariant form invariability, the classical covariant derivative that can only act on components is ex tended to the generalized covariant derivative that can act on any geometric quantity including base vectors, vectors and tensors. Under the axiom, the algebra structure of the gen eralized covariant derivative is proved to be covariant dif ferential ring. Based on the powerful operation capabilities and simple analytical properties of the generalized covariant derivative, the tensor analysis in curved coordinate systems is simplified to a large extent.展开更多
This paper extends the classical covariant deriva tive to the generalized covariant derivative on curved sur faces. The basement for the extension is similar to the pre vious paper, i.e., the axiom of the covariant fo...This paper extends the classical covariant deriva tive to the generalized covariant derivative on curved sur faces. The basement for the extension is similar to the pre vious paper, i.e., the axiom of the covariant form invariabil ity. Based on the generalized covariant derivative, a covari ant differential transformation group with orthogonal duality is set up. Through such orthogonal duality, tensor analy sis on curved surfaces is simplified intensively. Under the covariant differential transformation group, the differential invariabilities and integral invariabilities are constructed on curved surfaces.展开更多
This paper reports the new progresses in the axiomatization of tensor anal- ysis, including the thought of axiomatization, the concept of generalized components, the axiom of covariant form invariability, the axiomati...This paper reports the new progresses in the axiomatization of tensor anal- ysis, including the thought of axiomatization, the concept of generalized components, the axiom of covariant form invariability, the axiomatized definition, the algebraic structure, the transformation group, and the simple calculation of generalized covariant differentia- tions. These progresses strengthen the tendency of the axiomatization of tensor analysis.展开更多
This paper further extends the generalized covari ant derivative from the first covariant derivative to the sec ond one on curved surfaces. Through the linear transforma tion between the first generalized covariant de...This paper further extends the generalized covari ant derivative from the first covariant derivative to the sec ond one on curved surfaces. Through the linear transforma tion between the first generalized covariant derivative and the second one, the second covariant differential transformation group is set up. Under this transformation group, the sec ond class of differential invariants and integral invariants on curved surfaces is made clear. Besides, the symmetric struc ture of the tensor analysis on curved surfaces are revealed.展开更多
In this study,a microscopic method for calculating the nuclear level density(NLD)based on the covariant density functional theory(CDFT)is developed.The particle-hole state density is calculated by a combinatorial meth...In this study,a microscopic method for calculating the nuclear level density(NLD)based on the covariant density functional theory(CDFT)is developed.The particle-hole state density is calculated by a combinatorial method using single-particle level schemes obtained from the CDFT,and the level densities are then obtained by considering collective effects such as vibration and rotation.Our results are compared with those of other NLD models,including phenomenological,microstatisti-cal and nonrelativistic Hartree–Fock–Bogoliubov combinatorial models.This comparison suggests that the general trends among these models are essentially the same,except for some deviations among the different NLD models.In addition,the NLDs obtained using the CDFT combinatorial method with normalization are compared with experimental data,including the observed cumulative number of levels at low excitation energies and the measured NLDs.The CDFT combinatorial method yields results that are in reasonable agreement with the existing experimental data.展开更多
Based upon the covariant prolongation structures theory, we construct the sl（2, R）×R（p） prolongation structure for Konno-Asai-Kakuhata equation. By taking two and one-dimensional prolongation spaces, we obtai...Based upon the covariant prolongation structures theory, we construct the sl（2, R）×R（p） prolongation structure for Konno-Asai-Kakuhata equation. By taking two and one-dimensional prolongation spaces, we obtain the inverse scattering equations given by Konno et al. and the corresponding Riccati equation. The Baecklund transformations are also presented.展开更多
A new approach is proposed to use the covariant scalar equations of the a-coordinate （the covariant method）, in which the pressure gradient force （PGF） has only one term in each horizontal momentum equation, and t...A new approach is proposed to use the covariant scalar equations of the a-coordinate （the covariant method）, in which the pressure gradient force （PGF） has only one term in each horizontal momentum equation, and the PGF errors are much reduced in the computational space. In addition, the validity of reducing the PGF errors by this covariant method in the computational and physical space over steep terrain is investigated. First, the authors implement a set of idealized experiments of increasing terrain slope to compare the PGF errors of the covariant method and those of the classic method in the computational space. The results demonstrate that the PGF errors of the covariant method are consistently much-reduced, compared to those of the classic method. More importantly, the steeper the terrain, the greater the reduction in the ratio of the PGF errors via the covariant method. Next, the authors use geometric analysis to further investigate the PGF errors in the physical space, and the results illustrates that the PGF of the covariant method equals that of the classic method in the physical space; namely, the covariant method based on the non-orthogonal a-coordinate cannot reduce the PGF errors in the physical space. However, an orthogonal method can reduce the PGF errors in the physical space. Finally, a set of idealized experiments are carried out to validate the results obtained by the geometric analysis. These results indicate that the covariant method may improve the simulation of variables relevant to pressure, in addition to pressure itself, near steep terrain.展开更多
The self-consistent tilted axis cranking covariant density functional theory based on the point-coupling interaction is applied to investigate the tilted axis rotation in ^57 Mn. The observed data for band C are repro...The self-consistent tilted axis cranking covariant density functional theory based on the point-coupling interaction is applied to investigate the tilted axis rotation in ^57 Mn. The observed data for band C are reproduced well with the assigned configuration eonfig 1. The shears mechanism for magnetic rotation is examined by investigating microscopically the orientation of angular momentum and the corresponding contributions. It is found that config 1 and config 3 correspond to a rotation of high-K character. Config 2 corresponds to a rotation of magnetic character. However, due to the presence of electromagnetic transition B（M1） and B（E2）, collective rotation plays an essential role in the competition with magnetic rotation.展开更多
This paper discusses Hawking radiation from the charged and magnetized Bafiados-Teitelboim-Zanelli （BTZ） black hole from the viewpoint of anomaly, initiated by Robinson and Wilczek recently. It reconstructs the elec...This paper discusses Hawking radiation from the charged and magnetized Bafiados-Teitelboim-Zanelli （BTZ） black hole from the viewpoint of anomaly, initiated by Robinson and Wilczek recently. It reconstructs the electromagnetic field tensor and the Lagrangian of the field corresponding to the source with electric and magnetic charges to redefine an equivalent charge and gauge potential. It employs the covariant anomaly cancellation method to determine the compensating fluxes of charge flow and energy-momentum tensor, which are shown to match with those of the 2- dimensional blackbody radiation at the Hawking temperature exactly.展开更多
We investigate the coupled inhomogeneous nonlinear Schrodinger equation by the covariant prolongationstructure theory, and obtain its Lax's representation. Moreover, we present the corresponding Riccati equations,...We investigate the coupled inhomogeneous nonlinear Schrodinger equation by the covariant prolongationstructure theory, and obtain its Lax's representation. Moreover, we present the corresponding Riccati equations, Backlundtransformation, and one-soliton solution.展开更多
Based on the covariant anomaly cancellation method, which is believed to be more refined than the initial approach of Robinson and Wilczek, we discuss Hawking radiation from the plane symmetric black hole. The result ...Based on the covariant anomaly cancellation method, which is believed to be more refined than the initial approach of Robinson and Wilczek, we discuss Hawking radiation from the plane symmetric black hole. The result shows that Hawking radiation from the non-spherical symmetric black holes also can be derived from the viewpoint of anomaly.展开更多
Very recently, via the covariant form of the adiabatic invariant I = ∮pidqi instead of I = ∮pidqi, an equally spaced spectroscopy of a Schwarzschild black hole was derived. The emphasis was given to the covariant of...Very recently, via the covariant form of the adiabatic invariant I = ∮pidqi instead of I = ∮pidqi, an equally spaced spectroscopy of a Schwarzschild black hole was derived. The emphasis was given to the covariant of results. In this paper, we extend that work in a spherically symmetric spacetime to the case of a rotating Bafiados-Teitelboim-Zanelli （BTZ） black hole. It is noteworthy that the adiabatic covariant action I = ∮pidqi gives the same value for the black hole spectroscopy in different coordinates. The result shows that the area spectrum is △A = 8πl2p, which confirms Bekenstein＇s initial proposal. And the result is consistent with that already obtained by other methods.展开更多
Adopting the anomaly cancellation method, initiated by Robinson and Wilczek recently, this paper discusses Hawking radiation from the dilaton-（anti） de Sitter black hole. To save the underlying gauge and general cov...Adopting the anomaly cancellation method, initiated by Robinson and Wilczek recently, this paper discusses Hawking radiation from the dilaton-（anti） de Sitter black hole. To save the underlying gauge and general covariance, it introduces covariant fluxes of gauge and energy-momentum tensor to cancel the gauge and gravitational anomalies. The result shows that the introduced compensating fluxes are equivalent to those of a 2-dimensional blackbody radiation at Hawking temperature with appropriate chemical potential.展开更多
The covariant derivative is a generalization of differentiating vectors.The Euclidean derivative is a special case of the covariant derivative in Euclidean space.The covariant derivative gathers broad attention,partic...The covariant derivative is a generalization of differentiating vectors.The Euclidean derivative is a special case of the covariant derivative in Euclidean space.The covariant derivative gathers broad attention,particularly when computing vector derivatives on curved surfaces and volumes in various applications.Covariant derivatives have been computed using the metric tensor from the analytically known curved axes.However,deriving the global axis for the domain has been mathematically and computationally challenging for an arbitrary two-dimensional(2D)surface.Consequently,computing the covariant derivative has been difficult or even impossible.A novel high-order numerical scheme is proposed for computing the covariant derivative on any 2D curved surface.A set of orthonormal vectors,known as moving frames,expand vectors to compute accurately covariant derivatives on 2D curved surfaces.The proposed scheme does not require the construction of curved axes for the metric tensor or the Christoffel symbols.The connectivity given by the Christoffel symbols is equivalently provided by the attitude matrix of orthonormal moving frames.Consequently,the proposed scheme can be extended to the general 2D curved surface.As an application,the Helmholtz‐Hodge decomposition is considered for a realistic atrium and a bunny.展开更多
The integrability of a （2＋1）-dimensional super nonlinear evolution equation is analyzed in the framework of the fermionie covariant prolongation structure theory. We construct the prolongation structure of the mult...The integrability of a （2＋1）-dimensional super nonlinear evolution equation is analyzed in the framework of the fermionie covariant prolongation structure theory. We construct the prolongation structure of the multidimen- sional super integrable equation and investigate its Lax representation. Furthermore, the Backlund transformation is presented and we derive a solution to the super integrable equation.展开更多
In this paper, we investigate the Gross-Pitaevskii (GP) equation which describes the propagation of an electron plasma wave packet with a large wavelength and small amplitude in a medium with a parabolic density and c...In this paper, we investigate the Gross-Pitaevskii (GP) equation which describes the propagation of an electron plasma wave packet with a large wavelength and small amplitude in a medium with a parabolic density and constant interactional damping by the Covariant Prolongation Structure Theory. As a result, we obtain general forms of Lax-Pair representations. In addition, some hidden structural symmetries that govern the dynamics of the GP equation such as SL(2,R), SL(2,C), Virasoro algebra, SU(1,1) and SU(2) are unearthed. Using the Riccati form of the linear eigenvalue problem, infinite number of conservation laws of the GP equation is explicitly constructed and the exact analytical soliton solutions are obtained by employing the simple and straightforward Hirota’s bilinear method.展开更多
Starting from classical Lagrangian with the nonlinear system-beth interaction,a covariantform of generalized Langevin equation is derived.The transformation properties of the equation and itsquantities under a time-in...Starting from classical Lagrangian with the nonlinear system-beth interaction,a covariantform of generalized Langevin equation is derived.The transformation properties of the equation and itsquantities under a time-independent coordinate transformation in phase space are studied.展开更多
The Galilei covariant generalizations of the EM field equations (1984) (including moving media), Schroedinger, and Dirac (1985, 1993) equations for inertial frames S(w) with substratum velocity w are re- viewed. By G...The Galilei covariant generalizations of the EM field equations (1984) (including moving media), Schroedinger, and Dirac (1985, 1993) equations for inertial frames S(w) with substratum velocity w are re- viewed. By G-covariant electrodynamics, physical variables, e.g., rod length, clock rate, particle mass, momentum, and energy are G-invariants, determined by the object velocity v-w= vo=G-inv relative to the substratum frame, So(w=0) [v=object velocity relative to observer in S(w)] Galilean measurements using standard (i) contracted rods and (ii) retarded clocks, anisotropic light propagation, and conservation of EM energy and momentum in IFs S(w) are discussed. Fundamental experiments are formulated which permit measurement of substratum (w) induced EM and charge fields, the substratum velocity w, and verification of the G-invariance of the magnetic field, B= Bo=G-inv. The G-invariant Lagrangian and Hamiltonian of a charged particle in EM fields, and the momentum and energy conservation equations in Particle collisions are given for velocities |v-w|<co. The EM Doppler effects for moving source or moving observer are shown to exhibit measurable substratum effects. The spectral lines from a recoiling atom exhibit superimposed Doppler and substratum (w) shifts. The measurable substratum effects in the (i) aberration of light and (ii) reflection of light from a moving mirror are evaluated. The EM fields of accelerated charges in the substratum flow w are given, and applied to the anisotropic emission of x-rays in IFs S(w). G-covariant electrodynamics is examined for subluminal and superluminal electron velocities. Both the Cerenkov effect in (i) dielectrics for Iv--wl> c(ro) and (ii) vacuum for |v-w| > co are relative to the substratum So, and demonstrate the anisotropy of the vacuum in IFs S(w). G-covariant electrodynamics (relative to substratum) contains Lorentz covariant electrodynamics (relative to observer) in the special case w = 0 (So).展开更多
基金supported by the National Natural Science Foundation of China(No.12205103)。
文摘The covariant density functional theory(CDFT)and five-dimensional collective Hamiltonian(5DCH)are used to analyze the experimental deformation parameters and moments of inertia(MoIs)of 12 triaxial nuclei as extracted by Allmond and Wood[J.M.Allmond and J.L.Wood,Phys.Lett.B 767,226(2017)].We find that the CDFT MoIs are generally smaller than the experimental values but exhibit qualitative consistency with the irrotational flow and experimental data for the relative MoIs,indicating that the intermediate axis exhibites the largest MoI.Additionally,it is found that the pairing interaction collapse could result in nuclei behaving as a rigid-body flow,as exhibited in the^(186-192)Os case.Furthermore,by incorporating enhanced CDFT MoIs(factor of f≈1.55)into the 5DCH,the experimental low-lying energy spectra and deformation parameters are reproduced successfully.Compared with both CDFT and the triaxial rotor model,the 5DCH demonstrates superior agreement with the experimental deformation parameters and low-lying energy spectra,respectively,emphasizing the importance of considering shape fluctuations.
基金supported by the National Natural Science Foundation of China(NSFC)(No.12205097)the Fundamental Research Funds for the Central Universities(No.2024MS071)。
文摘The octupole deformation and collectivity in octupole double-magic nucleus 144Ba are investigated using the Cranking covariant density functional theory in a three-dimensional lattice space.The reduced B(E3)transition probability is implemented for the first time in semiclassical approximation based on the microscopically calculated electric octupole moments.The available data,including the I-ωrelation and electric transitional probabilities B(E2)and B(E3)are well reproduced.Furthermore,it is shown that the ground state of 144Ba exhibits axial octupole and quadrupole deformations that persist up to high spins(I≈24h).
基金supported by the NSFC(11072125 and 11272175)the NSF of Jiangsu Province(SBK201140044)the Specialized Research Fund for Doctoral Program of Higher Education(20130002110044)
文摘This paper extends the covariant derivative un der curved coordinate systems in 3D Euclid space. Based on the axiom of the covariant form invariability, the classical covariant derivative that can only act on components is ex tended to the generalized covariant derivative that can act on any geometric quantity including base vectors, vectors and tensors. Under the axiom, the algebra structure of the gen eralized covariant derivative is proved to be covariant dif ferential ring. Based on the powerful operation capabilities and simple analytical properties of the generalized covariant derivative, the tensor analysis in curved coordinate systems is simplified to a large extent.
基金supported by the NSFC(11072125 and 11272175)the NSF of Jiangsu Province(SBK201140044)the Specialized Research Fund for Doctoral Program of Higher Education(20130002110044)
文摘This paper extends the classical covariant deriva tive to the generalized covariant derivative on curved sur faces. The basement for the extension is similar to the pre vious paper, i.e., the axiom of the covariant form invariabil ity. Based on the generalized covariant derivative, a covari ant differential transformation group with orthogonal duality is set up. Through such orthogonal duality, tensor analy sis on curved surfaces is simplified intensively. Under the covariant differential transformation group, the differential invariabilities and integral invariabilities are constructed on curved surfaces.
基金supported by the National Natural Science Foundation of China(Nos.11072125 and11272175)the Natural Science Foundation of Jiangsu Province(No.SBK201140044)the Specialized Research Fund for Doctoral Program of Higher Education(No.20130002110044)
文摘This paper reports the new progresses in the axiomatization of tensor anal- ysis, including the thought of axiomatization, the concept of generalized components, the axiom of covariant form invariability, the axiomatized definition, the algebraic structure, the transformation group, and the simple calculation of generalized covariant differentia- tions. These progresses strengthen the tendency of the axiomatization of tensor analysis.
基金supported by the NSFC(11072125 and 11272175)the NSF of Jiangsu Province(SBK201140044)the Specialized Research Fund for Doctoral Program of Higher Education(20130002110044)
文摘This paper further extends the generalized covari ant derivative from the first covariant derivative to the sec ond one on curved surfaces. Through the linear transforma tion between the first generalized covariant derivative and the second one, the second covariant differential transformation group is set up. Under this transformation group, the sec ond class of differential invariants and integral invariants on curved surfaces is made clear. Besides, the symmetric struc ture of the tensor analysis on curved surfaces are revealed.
基金supported by the Natural Science Foundation of Jilin Province(No.20220101017JC)National Natural Science Foundation of China(No.11675063)Key Laboratory of Nuclear Data Foundation(JCKY2020201C157).
文摘In this study,a microscopic method for calculating the nuclear level density(NLD)based on the covariant density functional theory(CDFT)is developed.The particle-hole state density is calculated by a combinatorial method using single-particle level schemes obtained from the CDFT,and the level densities are then obtained by considering collective effects such as vibration and rotation.Our results are compared with those of other NLD models,including phenomenological,microstatisti-cal and nonrelativistic Hartree–Fock–Bogoliubov combinatorial models.This comparison suggests that the general trends among these models are essentially the same,except for some deviations among the different NLD models.In addition,the NLDs obtained using the CDFT combinatorial method with normalization are compared with experimental data,including the observed cumulative number of levels at low excitation energies and the measured NLDs.The CDFT combinatorial method yields results that are in reasonable agreement with the existing experimental data.
文摘Based upon the covariant prolongation structures theory, we construct the sl（2, R）×R（p） prolongation structure for Konno-Asai-Kakuhata equation. By taking two and one-dimensional prolongation spaces, we obtain the inverse scattering equations given by Konno et al. and the corresponding Riccati equation. The Baecklund transformations are also presented.
基金supported by the National Basic Research Program of China(973 Program)[grant number 2015CB954102]the National Natural Science Foundation of China[grant number41305095],[grant number 41175064]
文摘A new approach is proposed to use the covariant scalar equations of the a-coordinate （the covariant method）, in which the pressure gradient force （PGF） has only one term in each horizontal momentum equation, and the PGF errors are much reduced in the computational space. In addition, the validity of reducing the PGF errors by this covariant method in the computational and physical space over steep terrain is investigated. First, the authors implement a set of idealized experiments of increasing terrain slope to compare the PGF errors of the covariant method and those of the classic method in the computational space. The results demonstrate that the PGF errors of the covariant method are consistently much-reduced, compared to those of the classic method. More importantly, the steeper the terrain, the greater the reduction in the ratio of the PGF errors via the covariant method. Next, the authors use geometric analysis to further investigate the PGF errors in the physical space, and the results illustrates that the PGF of the covariant method equals that of the classic method in the physical space; namely, the covariant method based on the non-orthogonal a-coordinate cannot reduce the PGF errors in the physical space. However, an orthogonal method can reduce the PGF errors in the physical space. Finally, a set of idealized experiments are carried out to validate the results obtained by the geometric analysis. These results indicate that the covariant method may improve the simulation of variables relevant to pressure, in addition to pressure itself, near steep terrain.
基金Supported by the National Natural Science Foundation of China under Grant No 11461141002the Open Project Program of State Key Laboratory of Theoretical Physics of Institute of Theoretical Physics of Chinese Academy of Sciences under Grant No Y4KF041CJ1
文摘The self-consistent tilted axis cranking covariant density functional theory based on the point-coupling interaction is applied to investigate the tilted axis rotation in ^57 Mn. The observed data for band C are reproduced well with the assigned configuration eonfig 1. The shears mechanism for magnetic rotation is examined by investigating microscopically the orientation of angular momentum and the corresponding contributions. It is found that config 1 and config 3 correspond to a rotation of high-K character. Config 2 corresponds to a rotation of magnetic character. However, due to the presence of electromagnetic transition B（M1） and B（E2）, collective rotation plays an essential role in the competition with magnetic rotation.
基金supported by the National Natural Science Foundation of China (Grant No 10773008)
文摘This paper discusses Hawking radiation from the charged and magnetized Bafiados-Teitelboim-Zanelli （BTZ） black hole from the viewpoint of anomaly, initiated by Robinson and Wilczek recently. It reconstructs the electromagnetic field tensor and the Lagrangian of the field corresponding to the source with electric and magnetic charges to redefine an equivalent charge and gauge potential. It employs the covariant anomaly cancellation method to determine the compensating fluxes of charge flow and energy-momentum tensor, which are shown to match with those of the 2- dimensional blackbody radiation at the Hawking temperature exactly.
基金Supported by Beijing Jiao-Wei Key Project KZ200810028013the Natural Science Foundation of China under Grant No. 10871135
文摘We investigate the coupled inhomogeneous nonlinear Schrodinger equation by the covariant prolongationstructure theory, and obtain its Lax's representation. Moreover, we present the corresponding Riccati equations, Backlundtransformation, and one-soliton solution.
基金supported by National Natural Science Foundation of China under Grant No. 10773008
文摘Based on the covariant anomaly cancellation method, which is believed to be more refined than the initial approach of Robinson and Wilczek, we discuss Hawking radiation from the plane symmetric black hole. The result shows that Hawking radiation from the non-spherical symmetric black holes also can be derived from the viewpoint of anomaly.
基金Project supported by the Scientific Research Foundation of the Education Department of Liaoning Province, China (Grant No. L2011195)
文摘Very recently, via the covariant form of the adiabatic invariant I = ∮pidqi instead of I = ∮pidqi, an equally spaced spectroscopy of a Schwarzschild black hole was derived. The emphasis was given to the covariant of results. In this paper, we extend that work in a spherically symmetric spacetime to the case of a rotating Bafiados-Teitelboim-Zanelli （BTZ） black hole. It is noteworthy that the adiabatic covariant action I = ∮pidqi gives the same value for the black hole spectroscopy in different coordinates. The result shows that the area spectrum is △A = 8πl2p, which confirms Bekenstein＇s initial proposal. And the result is consistent with that already obtained by other methods.
基金Project supported by the Scientific and Technological Foundation of Chongqing Municipal Education Commission of China (Grant No KJ0707011)
文摘Adopting the anomaly cancellation method, initiated by Robinson and Wilczek recently, this paper discusses Hawking radiation from the dilaton-（anti） de Sitter black hole. To save the underlying gauge and general covariance, it introduces covariant fluxes of gauge and energy-momentum tensor to cancel the gauge and gravitational anomalies. The result shows that the introduced compensating fluxes are equivalent to those of a 2-dimensional blackbody radiation at Hawking temperature with appropriate chemical potential.
基金the National Research Foundation of Korea(NRF-2021R1A2C109297811).
文摘The covariant derivative is a generalization of differentiating vectors.The Euclidean derivative is a special case of the covariant derivative in Euclidean space.The covariant derivative gathers broad attention,particularly when computing vector derivatives on curved surfaces and volumes in various applications.Covariant derivatives have been computed using the metric tensor from the analytically known curved axes.However,deriving the global axis for the domain has been mathematically and computationally challenging for an arbitrary two-dimensional(2D)surface.Consequently,computing the covariant derivative has been difficult or even impossible.A novel high-order numerical scheme is proposed for computing the covariant derivative on any 2D curved surface.A set of orthonormal vectors,known as moving frames,expand vectors to compute accurately covariant derivatives on 2D curved surfaces.The proposed scheme does not require the construction of curved axes for the metric tensor or the Christoffel symbols.The connectivity given by the Christoffel symbols is equivalently provided by the attitude matrix of orthonormal moving frames.Consequently,the proposed scheme can be extended to the general 2D curved surface.As an application,the Helmholtz‐Hodge decomposition is considered for a realistic atrium and a bunny.
基金Supported by the National Natural Science Foundation of China under Grant Nos 11605096,11547101 and 11601247
文摘The integrability of a （2＋1）-dimensional super nonlinear evolution equation is analyzed in the framework of the fermionie covariant prolongation structure theory. We construct the prolongation structure of the multidimen- sional super integrable equation and investigate its Lax representation. Furthermore, the Backlund transformation is presented and we derive a solution to the super integrable equation.
文摘In this paper, we investigate the Gross-Pitaevskii (GP) equation which describes the propagation of an electron plasma wave packet with a large wavelength and small amplitude in a medium with a parabolic density and constant interactional damping by the Covariant Prolongation Structure Theory. As a result, we obtain general forms of Lax-Pair representations. In addition, some hidden structural symmetries that govern the dynamics of the GP equation such as SL(2,R), SL(2,C), Virasoro algebra, SU(1,1) and SU(2) are unearthed. Using the Riccati form of the linear eigenvalue problem, infinite number of conservation laws of the GP equation is explicitly constructed and the exact analytical soliton solutions are obtained by employing the simple and straightforward Hirota’s bilinear method.
基金The project supported by the National Natural Science Foundation of China
文摘Starting from classical Lagrangian with the nonlinear system-beth interaction,a covariantform of generalized Langevin equation is derived.The transformation properties of the equation and itsquantities under a time-independent coordinate transformation in phase space are studied.
文摘The Galilei covariant generalizations of the EM field equations (1984) (including moving media), Schroedinger, and Dirac (1985, 1993) equations for inertial frames S(w) with substratum velocity w are re- viewed. By G-covariant electrodynamics, physical variables, e.g., rod length, clock rate, particle mass, momentum, and energy are G-invariants, determined by the object velocity v-w= vo=G-inv relative to the substratum frame, So(w=0) [v=object velocity relative to observer in S(w)] Galilean measurements using standard (i) contracted rods and (ii) retarded clocks, anisotropic light propagation, and conservation of EM energy and momentum in IFs S(w) are discussed. Fundamental experiments are formulated which permit measurement of substratum (w) induced EM and charge fields, the substratum velocity w, and verification of the G-invariance of the magnetic field, B= Bo=G-inv. The G-invariant Lagrangian and Hamiltonian of a charged particle in EM fields, and the momentum and energy conservation equations in Particle collisions are given for velocities |v-w|<co. The EM Doppler effects for moving source or moving observer are shown to exhibit measurable substratum effects. The spectral lines from a recoiling atom exhibit superimposed Doppler and substratum (w) shifts. The measurable substratum effects in the (i) aberration of light and (ii) reflection of light from a moving mirror are evaluated. The EM fields of accelerated charges in the substratum flow w are given, and applied to the anisotropic emission of x-rays in IFs S(w). G-covariant electrodynamics is examined for subluminal and superluminal electron velocities. Both the Cerenkov effect in (i) dielectrics for Iv--wl> c(ro) and (ii) vacuum for |v-w| > co are relative to the substratum So, and demonstrate the anisotropy of the vacuum in IFs S(w). G-covariant electrodynamics (relative to substratum) contains Lorentz covariant electrodynamics (relative to observer) in the special case w = 0 (So).
