This paper studies a class of impulsive neutral stochastic partial differential equations in real Hilbert spaces.The main goal here is to consider the Trotter-Kato approximations of mild solutions of such equations in...This paper studies a class of impulsive neutral stochastic partial differential equations in real Hilbert spaces.The main goal here is to consider the Trotter-Kato approximations of mild solutions of such equations in the pth-mean(p≥2).As an application,a classical limit theorem on the dependence of such equations on a parameter is obtained.The novelty of this paper is that the combination of this approximating system and such equations has not been considered before.展开更多
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
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
Because of the use of different limiting procedures, there are two conflict conclusions on wave function. One is that a wave function can describe a single particle and the other is that it can only describe an ensemb...Because of the use of different limiting procedures, there are two conflict conclusions on wave function. One is that a wave function can describe a single particle and the other is that it can only describe an ensemble in the classical limit. In this paper the limiting procedures have been compared. We put the synthesized limit n→∞, (?)→0 but keep E(n,(?)) to be the actual measured value of energy. Under this limit condition, we can not only prove that a wave function can only describe an ensemble, but also can make clear the dynamical behavior of the particles of the ensemble. Calculations show that the reason why quantum mechanics cannot describe a particle is not because of the motion equation but because of the definition of state for the particle.展开更多
By comparison between equations of motion of geometrical optics and that of classical statistical mechanics, this paper finds that there should be an analogy between geometrical optics and classical statistical mechan...By comparison between equations of motion of geometrical optics and that of classical statistical mechanics, this paper finds that there should be an analogy between geometrical optics and classical statistical mechanics instead of geometrical mechanics and classical mechanics. Furthermore, by comparison between the classical limit of quantum mechanics and classical statistical mechanics, it finds that classical limit of quantum mechanics is classical statistical mechanics not classical mechanics, hence it demonstrates that quantum mechanics is a natural generalization of classical statistical mechanics instead of classical mechanics. Thence quantum mechanics in its true appearance is a wave statistical mechanics instead of a wave mechanics.展开更多
基金Supported by the National Natural Science Foundation of China(Grant No.12171361)the Humanity and Social Science Youth foundation of Ministry of Education(Grant No.20YJC790174)。
文摘This paper studies a class of impulsive neutral stochastic partial differential equations in real Hilbert spaces.The main goal here is to consider the Trotter-Kato approximations of mild solutions of such equations in the pth-mean(p≥2).As an application,a classical limit theorem on the dependence of such equations on a parameter is obtained.The novelty of this paper is that the combination of this approximating system and such equations has not been considered before.
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.
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the National Natural Science Foundation of China
文摘Because of the use of different limiting procedures, there are two conflict conclusions on wave function. One is that a wave function can describe a single particle and the other is that it can only describe an ensemble in the classical limit. In this paper the limiting procedures have been compared. We put the synthesized limit n→∞, (?)→0 but keep E(n,(?)) to be the actual measured value of energy. Under this limit condition, we can not only prove that a wave function can only describe an ensemble, but also can make clear the dynamical behavior of the particles of the ensemble. Calculations show that the reason why quantum mechanics cannot describe a particle is not because of the motion equation but because of the definition of state for the particle.
文摘By comparison between equations of motion of geometrical optics and that of classical statistical mechanics, this paper finds that there should be an analogy between geometrical optics and classical statistical mechanics instead of geometrical mechanics and classical mechanics. Furthermore, by comparison between the classical limit of quantum mechanics and classical statistical mechanics, it finds that classical limit of quantum mechanics is classical statistical mechanics not classical mechanics, hence it demonstrates that quantum mechanics is a natural generalization of classical statistical mechanics instead of classical mechanics. Thence quantum mechanics in its true appearance is a wave statistical mechanics instead of a wave mechanics.
