We investigate the global classical solutions of the non-relativistic Vlasov-D arwin system with generalized variables(VDG)in three dimensions.We first prove the global existence and uniqueness for small initial data ...We investigate the global classical solutions of the non-relativistic Vlasov-D arwin system with generalized variables(VDG)in three dimensions.We first prove the global existence and uniqueness for small initial data and derive the decay estimates of the Darwin potentials.Then,we show in this framework that the solutions converge in a pointwise sense to solutions of the classical Vlasov-Poisson system(VP)at the asymptotic rate of 1/c2 as the speed of light c tends to infinity for all time.Moreover,we obtain rigorously an asymptotic estimate of the difference between the two systems.展开更多
We prove a concentration result of a Bloch eigenstate in a periodic channel under a constant gauge, In the semi-classical limit h → 0 these eigenstates concentrate near a maximizer of the scalar potential of the asso...We prove a concentration result of a Bloch eigenstate in a periodic channel under a constant gauge, In the semi-classical limit h → 0 these eigenstates concentrate near a maximizer of the scalar potential of the associated Schr6dinger operator, provided the constant gauge converges to a critical value from above. This is in contrast with the ground states which concentrate for any gauge in this limit near a minimizer of the scalar potential.展开更多
The exact classical limits for the coefficient of variation c for the normal distribution are derived. The hand-calculating approximated classical limits for c having high accuracy are given to meet practical engineer...The exact classical limits for the coefficient of variation c for the normal distribution are derived. The hand-calculating approximated classical limits for c having high accuracy are given to meet practical engineering needs. Using Odeh and Owen's computational method and Brent's algorithm, the tables for the r-upper exact classical limits of coefficient of variation for normal distribution are calculated for the different confidence coefficient y, the sample size n=1(1)30,40,60,120, the sample coefficient of variation c=0.01(0.01)0.20. It is shown that if n<8,c<0.20, then the V -upper exact classical limits cu for c are slightly higher than the exact fiducial limits cu,F for c if. n>8, c<0.02,then cu-cu,f<5x10-6展开更多
The classical limit of the quantum mechanical Kepler problem is derived by using a simple mathematical procedure recently proposed. The method is based both on Bohr’s correspondence principle and the local averages o...The classical limit of the quantum mechanical Kepler problem is derived by using a simple mathematical procedure recently proposed. The method is based both on Bohr’s correspondence principle and the local averages of the quantum probability distribution. We illustrate in a clear fashion the difference between Planck’s limit and Bohr’s correspondence principle. We discuss the confinement effect in macroscopic systems.展开更多
The different roles and natures of spacetime appearing in a quantum field theory and in classical physics are analyzed implying that a quantum theory of gravitation is not necessarily a quantum theory of curved spacet...The different roles and natures of spacetime appearing in a quantum field theory and in classical physics are analyzed implying that a quantum theory of gravitation is not necessarily a quantum theory of curved spacetime. Developing an alternative approach to quantum gravity starts with the postulate that inertial energy-momentum and gravitational energy-momentum need not be the same for virtual quantum states. Separating their roles naturally leads to the quantum gauge field theory of volume-preserving diffeomorphisms of an inner four-dimensional space. The classical limit of this theory coupled to a quantized scalar field is derived for an on-shell particle where inertial energy-momentum and gravitational energy-momentum coincide. In that process the symmetry under volume-preserving diffeomorphisms disappears and a new symmetry group emerges: the group of coordinate transformations of four-dimensional spacetime and with it General Relativity coupled to a classical relativistic point particle.展开更多
Quantum dispersions of various sets of dynamical variables of an open Bose-Hubbard system in a classical limit are studied. To this end, an open system is described in terms of stochastic evolution of its quantum pure...Quantum dispersions of various sets of dynamical variables of an open Bose-Hubbard system in a classical limit are studied. To this end, an open system is described in terms of stochastic evolution of its quantum pure states. It is shown that the class of variables that display classical behaviour crucially depends on the type of noise. This is relevant in the mean-field approximation of open Bose-Hubbard dynamics.展开更多
This article develops a new method, named M-Bayesian credible limit method, to estimate reliability parameter. In the article, the M-Bayesian credible limit method of failure rate is derived for zero-failure data from...This article develops a new method, named M-Bayesian credible limit method, to estimate reliability parameter. In the article, the M-Bayesian credible limit method of failure rate is derived for zero-failure data from products with exponential distribution. Relations between M-Bayesian credible limit and other classical confidence limits are discussed. Finally, the new method is applied to a real zero-failure data set, and as can be seen, it is both efficient and easy to operate.展开更多
We review the semiclassical method proposed in [1], a generalization of this method for n-dimensional system is presented. Using the cited method, we present an analytical method of obtain the semiclassical Husimi Fun...We review the semiclassical method proposed in [1], a generalization of this method for n-dimensional system is presented. Using the cited method, we present an analytical method of obtain the semiclassical Husimi Function. The validity of the method is tested using Harmonic Oscillator, Morse Potential and Dikie’s Model as example, we found a good accuracy in the classical limit.展开更多
基金supported by the National Natural ScienceFoundation of China(11871024)the Fundamental Research Program of Shanxi Province(202103021223182)。
文摘We investigate the global classical solutions of the non-relativistic Vlasov-D arwin system with generalized variables(VDG)in three dimensions.We first prove the global existence and uniqueness for small initial data and derive the decay estimates of the Darwin potentials.Then,we show in this framework that the solutions converge in a pointwise sense to solutions of the classical Vlasov-Poisson system(VP)at the asymptotic rate of 1/c2 as the speed of light c tends to infinity for all time.Moreover,we obtain rigorously an asymptotic estimate of the difference between the two systems.
文摘We prove a concentration result of a Bloch eigenstate in a periodic channel under a constant gauge, In the semi-classical limit h → 0 these eigenstates concentrate near a maximizer of the scalar potential of the associated Schr6dinger operator, provided the constant gauge converges to a critical value from above. This is in contrast with the ground states which concentrate for any gauge in this limit near a minimizer of the scalar potential.
文摘The exact classical limits for the coefficient of variation c for the normal distribution are derived. The hand-calculating approximated classical limits for c having high accuracy are given to meet practical engineering needs. Using Odeh and Owen's computational method and Brent's algorithm, the tables for the r-upper exact classical limits of coefficient of variation for normal distribution are calculated for the different confidence coefficient y, the sample size n=1(1)30,40,60,120, the sample coefficient of variation c=0.01(0.01)0.20. It is shown that if n<8,c<0.20, then the V -upper exact classical limits cu for c are slightly higher than the exact fiducial limits cu,F for c if. n>8, c<0.02,then cu-cu,f<5x10-6
文摘The classical limit of the quantum mechanical Kepler problem is derived by using a simple mathematical procedure recently proposed. The method is based both on Bohr’s correspondence principle and the local averages of the quantum probability distribution. We illustrate in a clear fashion the difference between Planck’s limit and Bohr’s correspondence principle. We discuss the confinement effect in macroscopic systems.
文摘The different roles and natures of spacetime appearing in a quantum field theory and in classical physics are analyzed implying that a quantum theory of gravitation is not necessarily a quantum theory of curved spacetime. Developing an alternative approach to quantum gravity starts with the postulate that inertial energy-momentum and gravitational energy-momentum need not be the same for virtual quantum states. Separating their roles naturally leads to the quantum gauge field theory of volume-preserving diffeomorphisms of an inner four-dimensional space. The classical limit of this theory coupled to a quantized scalar field is derived for an on-shell particle where inertial energy-momentum and gravitational energy-momentum coincide. In that process the symmetry under volume-preserving diffeomorphisms disappears and a new symmetry group emerges: the group of coordinate transformations of four-dimensional spacetime and with it General Relativity coupled to a classical relativistic point particle.
基金supported in part by the Ministry of Education and Science of the Republic of Serbia (Grant No. ON171017)
文摘Quantum dispersions of various sets of dynamical variables of an open Bose-Hubbard system in a classical limit are studied. To this end, an open system is described in terms of stochastic evolution of its quantum pure states. It is shown that the class of variables that display classical behaviour crucially depends on the type of noise. This is relevant in the mean-field approximation of open Bose-Hubbard dynamics.
基金This work was supported partly by the Fujian Province Natural Science Foundation of Chinapartly by the Fujian University of Technology of China
文摘This article develops a new method, named M-Bayesian credible limit method, to estimate reliability parameter. In the article, the M-Bayesian credible limit method of failure rate is derived for zero-failure data from products with exponential distribution. Relations between M-Bayesian credible limit and other classical confidence limits are discussed. Finally, the new method is applied to a real zero-failure data set, and as can be seen, it is both efficient and easy to operate.
文摘We review the semiclassical method proposed in [1], a generalization of this method for n-dimensional system is presented. Using the cited method, we present an analytical method of obtain the semiclassical Husimi Function. The validity of the method is tested using Harmonic Oscillator, Morse Potential and Dikie’s Model as example, we found a good accuracy in the classical limit.
