Solving the Dirac equation has played an important role in many areas of fundamental physics.In this work,we present the Dirac equation solver DiracSVT,which solves the Dirac equation with scalar,vector,and tensor nuc...Solving the Dirac equation has played an important role in many areas of fundamental physics.In this work,we present the Dirac equation solver DiracSVT,which solves the Dirac equation with scalar,vector,and tensor nuclear potentials in spherical coordinate space.The shooting method was used with a Runge–Kutta 4 integration scheme.The potentials are parameterized in a Woods–Saxon form,which reproduce well the known single-particle states around all doubly magic nuclei and can be applied to study the shell evolution of exotic nuclei.The code can be easily extended to the study of other systems,including atomic,hadron,and molecular physics.展开更多
In this paper,we solve the Dirac equation under spin symmetry limit for attractive radial potential including a Coulomb-like tensor interaction.By using the parametric generalization of the Nikiforov-Uvarov method,the...In this paper,we solve the Dirac equation under spin symmetry limit for attractive radial potential including a Coulomb-like tensor interaction.By using the parametric generalization of the Nikiforov-Uvarov method,the energy eigenvalues equation and the corresponding wave functions have been obtained in closed forms.Some numerical results are given too.展开更多
The bound state solutions of Dirac equations for a trigonometric Scarf potential with a new tensor potential under spin and pseudospin symmetry limits are investigated using Romanovski polynomials. The proposed new te...The bound state solutions of Dirac equations for a trigonometric Scarf potential with a new tensor potential under spin and pseudospin symmetry limits are investigated using Romanovski polynomials. The proposed new tensor potential is inspired by superpotential form in supersymmetric （SUSY） quantum mechanics. The Dirac equations with trigonometric Scarf potential coupled by a new tensor potential for the pseudospin and spin symmetries reduce to Schrtdinger-type equations with a shape invariant potential since the proposed new tensor potential is similar to the superpotential of trigonometric Scarf potential. The relativistic wave functions are exactly obtained in terms of Romanovski polynomials and the relativistic energy equations are also exactly obtained in the approximation scheme of centrifugal term. The new tensor potential removes the degeneracies both for pseudospin and spin symmetries.展开更多
Approximate analytical solutions of the Dirac equation for Tietz-Hua （TH） potential including Coulomb-like tensor （CLT） potential with arbitrary spin-orbit quantum number K are obtained within the Pekeris approxim...Approximate analytical solutions of the Dirac equation for Tietz-Hua （TH） potential including Coulomb-like tensor （CLT） potential with arbitrary spin-orbit quantum number K are obtained within the Pekeris approximation scheme to deal with the spin-orbit coupling terms K（K± 1）r^-2. Under the exact spin and pseudospin symmetric limitation, bound state energy eigenvalues and associated unnormalized two-component wave functions of the Dirac particle in the field of both attractive and repulsive TH potential with tensor potential are found using the parametric Nikiforov-Uvarov （NU） method. The cases of the Morse oscillator with tensor potential, the generalized Morse oscillator with tensor potential, and the non-relativistic limits have been investigated.展开更多
We approximately solve the Dirac equation for attractive radial potential including a Coulomb-like tensor interaction under pseudospin and the spin symmetry limit for any arbitrary spin-orbit quantum number, by employ...We approximately solve the Dirac equation for attractive radial potential including a Coulomb-like tensor interaction under pseudospin and the spin symmetry limit for any arbitrary spin-orbit quantum number, by employing the supersymmetric （SUSY） quantum mechanics and supersymmetric shape invariance technique. We obtain the energy eigenvalue equation under the pseudospin and spin conditions. Some numerical results are compared with those obtained by the Nikiforove-Uvarov （NU） method.展开更多
In this paper, we introduce the notion of EF-critical map with potential with respect to the functional EF,H（u）. By using the stress-energy tensor, we obtain some monotonicity formulas and vanishing results for thes...In this paper, we introduce the notion of EF-critical map with potential with respect to the functional EF,H（u）. By using the stress-energy tensor, we obtain some monotonicity formulas and vanishing results for these maps under conditions on H.展开更多
Two fundamental hypotheses of special relativistic gravitational theory are: (1) the equivalence of gravitational mass and inertial mass, (2) the equation of the gravitational tensor potential in linear approximat...Two fundamental hypotheses of special relativistic gravitational theory are: (1) the equivalence of gravitational mass and inertial mass, (2) the equation of the gravitational tensor potential in linear approximation. Main results: (1) the values of the planetary perihelion shill, and the angle of deflection of light are the same as those of general relativity. The value of the red shill is consistent with the experiment. One cannot use these experimental values to judge whether space-time is curved. (2) In GP-B experiment, the gyroscope will be acted on by the additional gravitational fields due to the Earth's spin (S) and the orbital motion of satellite (L). The average precession rates are , where β and δ are the gyroscope's polar angles, (S) and (G) designate values deduced from special and general relativity, respectively. The GP-B experiment is the first one to judge whether space-time is flat.展开更多
The design and understanding of oxide-ion and proton transport in solid electrolytes are pivotal to the development of fuel cells that can operate at reduced temperatures of<600℃.Atomistic modelling and machine le...The design and understanding of oxide-ion and proton transport in solid electrolytes are pivotal to the development of fuel cells that can operate at reduced temperatures of<600℃.Atomistic modelling and machine learning are playing evermore crucial roles in achieving this objective.In this study,using passive and active learning techniques,we develop moment tensor potentials(MTPs)for two promising ionic conductors,namely,Ba_(7)Nb_(4)MoO_(20)and Sr_(3)V_(2)O_(8).Our MTPs accurately reproduce ab initio molecular dynamics data and demonstrate strong agreement with density functional theory calculations for forces,energies and stresses.They successfully predict diffusion coefficients and conductivities for both oxide ions and protons,showing excellent agreement with experimental data and ab initio molecular dynamics results.Additionally,the MTPs accurately estimate migration barriers,thereby underscoring their robustness and transferability.Our findings highlight the potential of MTPs in significantly reducing computational costs while maintaining high accuracy,making them invaluable for simulating complex ion transport mechanisms and supporting the development of nextgeneration solid oxide fuel cells.展开更多
We report on new attempt to investigate baryon-baryon interactions in lattice QCD.From the Bethe-Salpeter （BS） wave function,we have successfully extracted the nucleon-nucleon （NN） potentials in quenched QCD simul...We report on new attempt to investigate baryon-baryon interactions in lattice QCD.From the Bethe-Salpeter （BS） wave function,we have successfully extracted the nucleon-nucleon （NN） potentials in quenched QCD simulations,which reproduce qualitative features of modern NN potentials.The method has been extended to obtain the tensor potential as well as the central potential and also applied to the hyperonnucleon （YN） interactions,in both quenched and full QCD.展开更多
文摘Solving the Dirac equation has played an important role in many areas of fundamental physics.In this work,we present the Dirac equation solver DiracSVT,which solves the Dirac equation with scalar,vector,and tensor nuclear potentials in spherical coordinate space.The shooting method was used with a Runge–Kutta 4 integration scheme.The potentials are parameterized in a Woods–Saxon form,which reproduce well the known single-particle states around all doubly magic nuclei and can be applied to study the shell evolution of exotic nuclei.The code can be easily extended to the study of other systems,including atomic,hadron,and molecular physics.
文摘In this paper,we solve the Dirac equation under spin symmetry limit for attractive radial potential including a Coulomb-like tensor interaction.By using the parametric generalization of the Nikiforov-Uvarov method,the energy eigenvalues equation and the corresponding wave functions have been obtained in closed forms.Some numerical results are given too.
基金supported by Hibah Peneliti Utama(PUT UNS)2014DIKTI(Grant No.165a/UN27.11/PN2013)
文摘The bound state solutions of Dirac equations for a trigonometric Scarf potential with a new tensor potential under spin and pseudospin symmetry limits are investigated using Romanovski polynomials. The proposed new tensor potential is inspired by superpotential form in supersymmetric （SUSY） quantum mechanics. The Dirac equations with trigonometric Scarf potential coupled by a new tensor potential for the pseudospin and spin symmetries reduce to Schrtdinger-type equations with a shape invariant potential since the proposed new tensor potential is similar to the superpotential of trigonometric Scarf potential. The relativistic wave functions are exactly obtained in terms of Romanovski polynomials and the relativistic energy equations are also exactly obtained in the approximation scheme of centrifugal term. The new tensor potential removes the degeneracies both for pseudospin and spin symmetries.
基金supported by the Scientific and Technological Research Council of Turkey (TUBITAK)
文摘Approximate analytical solutions of the Dirac equation for Tietz-Hua （TH） potential including Coulomb-like tensor （CLT） potential with arbitrary spin-orbit quantum number K are obtained within the Pekeris approximation scheme to deal with the spin-orbit coupling terms K（K± 1）r^-2. Under the exact spin and pseudospin symmetric limitation, bound state energy eigenvalues and associated unnormalized two-component wave functions of the Dirac particle in the field of both attractive and repulsive TH potential with tensor potential are found using the parametric Nikiforov-Uvarov （NU） method. The cases of the Morse oscillator with tensor potential, the generalized Morse oscillator with tensor potential, and the non-relativistic limits have been investigated.
文摘We approximately solve the Dirac equation for attractive radial potential including a Coulomb-like tensor interaction under pseudospin and the spin symmetry limit for any arbitrary spin-orbit quantum number, by employing the supersymmetric （SUSY） quantum mechanics and supersymmetric shape invariance technique. We obtain the energy eigenvalue equation under the pseudospin and spin conditions. Some numerical results are compared with those obtained by the Nikiforove-Uvarov （NU） method.
基金Supported by the National Natural Science Foundation of China(Grant No.11201400)Basic and Frontier Technology Reseach Project of Henan Province(Grant No.142300410433)Project for Youth Teacher of Xinyang Normal University(Grant No.2014-QN-061)
文摘In this paper, we introduce the notion of EF-critical map with potential with respect to the functional EF,H（u）. By using the stress-energy tensor, we obtain some monotonicity formulas and vanishing results for these maps under conditions on H.
文摘Two fundamental hypotheses of special relativistic gravitational theory are: (1) the equivalence of gravitational mass and inertial mass, (2) the equation of the gravitational tensor potential in linear approximation. Main results: (1) the values of the planetary perihelion shill, and the angle of deflection of light are the same as those of general relativity. The value of the red shill is consistent with the experiment. One cannot use these experimental values to judge whether space-time is curved. (2) In GP-B experiment, the gyroscope will be acted on by the additional gravitational fields due to the Earth's spin (S) and the orbital motion of satellite (L). The average precession rates are , where β and δ are the gyroscope's polar angles, (S) and (G) designate values deduced from special and general relativity, respectively. The GP-B experiment is the first one to judge whether space-time is flat.
基金supported by EPSRC(EP/X010422/1 and EP/X011941/1)the Leverhulme Trust(RPG-2022-175).Via membership of the UK's HEC Materials Chemistry Consortium,which was funded by the EPSRC(EP/X035859/1),this work used the ARCHER2 UK National Supercomputing Service.
文摘The design and understanding of oxide-ion and proton transport in solid electrolytes are pivotal to the development of fuel cells that can operate at reduced temperatures of<600℃.Atomistic modelling and machine learning are playing evermore crucial roles in achieving this objective.In this study,using passive and active learning techniques,we develop moment tensor potentials(MTPs)for two promising ionic conductors,namely,Ba_(7)Nb_(4)MoO_(20)and Sr_(3)V_(2)O_(8).Our MTPs accurately reproduce ab initio molecular dynamics data and demonstrate strong agreement with density functional theory calculations for forces,energies and stresses.They successfully predict diffusion coefficients and conductivities for both oxide ions and protons,showing excellent agreement with experimental data and ab initio molecular dynamics results.Additionally,the MTPs accurately estimate migration barriers,thereby underscoring their robustness and transferability.Our findings highlight the potential of MTPs in significantly reducing computational costs while maintaining high accuracy,making them invaluable for simulating complex ion transport mechanisms and supporting the development of nextgeneration solid oxide fuel cells.
基金Supported by Grants-in-Aid of the Ministry of Education,Culture,Sports,Science and Technology of Japan (20340047,20105001,20105003)
文摘We report on new attempt to investigate baryon-baryon interactions in lattice QCD.From the Bethe-Salpeter （BS） wave function,we have successfully extracted the nucleon-nucleon （NN） potentials in quenched QCD simulations,which reproduce qualitative features of modern NN potentials.The method has been extended to obtain the tensor potential as well as the central potential and also applied to the hyperonnucleon （YN） interactions,in both quenched and full QCD.
