Differences of the time periods in two independent quantum systems are examined on a semiclassical level. The systems are the electron in the hydrogen atom and a free-electron particle moving in a one-dimensional pote...Differences of the time periods in two independent quantum systems are examined on a semiclassical level. The systems are the electron in the hydrogen atom and a free-electron particle moving in a one-dimensional potential box, respectively. It is demonstrated that in both systems the relativistic correction to the time interval can be expressed as a multiple of the same quantum of time. The size of the quantum is proportional to the ratio of the Planck’s constant and the rest energy of the electron particle.展开更多
In this paper, we study the Poisson stability(in particular, stationarity, periodicity, quasiperiodicity, Bohr almost periodicity, almost automorphy, recurrence in the sense of Birkhoff, Levitan almost periodicity, ps...In this paper, we study the Poisson stability(in particular, stationarity, periodicity, quasiperiodicity, Bohr almost periodicity, almost automorphy, recurrence in the sense of Birkhoff, Levitan almost periodicity, pseudo periodicity, almost recurrence in the sense of Bebutov, pseudo recurrence, Poisson stability) of motions for monotone nonautonomous dynamical systems and of solutions for some classes of monotone nonautonomous evolution equations(ODEs, FDEs and parabolic PDEs). As a byproduct, some of our results indicate that all the trajectories of monotone systems converge to the above mentioned Poisson stable trajectories under some suitable conditions, which is interesting in its own right for monotone dynamics.展开更多
In this paper,we use a unified framework to study Poisson stable(including stationary,periodic,quasi-periodic,almost periodic,almost automorphic,Birkhoff recurrent,almost recurrent in the sense of Bebutov,Levitan almo...In this paper,we use a unified framework to study Poisson stable(including stationary,periodic,quasi-periodic,almost periodic,almost automorphic,Birkhoff recurrent,almost recurrent in the sense of Bebutov,Levitan almost periodic,pseudo-periodic,pseudo-recurrent and Poisson stable)solutions for semilinear stochastic differential equations driven by infinite dimensional L′evy noise with large jumps.Under suitable conditions on drift,diffusion and jump coefficients,we prove that there exist solutions which inherit the Poisson stability of coefficients.Further we show that these solutions are globally asymptotically stable in square-mean sense.Finally,we illustrate our theoretical results by several examples.展开更多
文摘Differences of the time periods in two independent quantum systems are examined on a semiclassical level. The systems are the electron in the hydrogen atom and a free-electron particle moving in a one-dimensional potential box, respectively. It is demonstrated that in both systems the relativistic correction to the time interval can be expressed as a multiple of the same quantum of time. The size of the quantum is proportional to the ratio of the Planck’s constant and the rest energy of the electron particle.
基金supported by National Natural Science Foundation of China (Grant Nos. 11271151 and 11522104)the Startup and Xinghai Jieqing Funds from Dalian University of Technology
文摘In this paper, we study the Poisson stability(in particular, stationarity, periodicity, quasiperiodicity, Bohr almost periodicity, almost automorphy, recurrence in the sense of Birkhoff, Levitan almost periodicity, pseudo periodicity, almost recurrence in the sense of Bebutov, pseudo recurrence, Poisson stability) of motions for monotone nonautonomous dynamical systems and of solutions for some classes of monotone nonautonomous evolution equations(ODEs, FDEs and parabolic PDEs). As a byproduct, some of our results indicate that all the trajectories of monotone systems converge to the above mentioned Poisson stable trajectories under some suitable conditions, which is interesting in its own right for monotone dynamics.
基金Supported by NSFC(Grant Nos.11522104,11871132 and 11925102)Xinghai Jieqing and DUT19TD14 funds from Dalian University of Technology。
文摘In this paper,we use a unified framework to study Poisson stable(including stationary,periodic,quasi-periodic,almost periodic,almost automorphic,Birkhoff recurrent,almost recurrent in the sense of Bebutov,Levitan almost periodic,pseudo-periodic,pseudo-recurrent and Poisson stable)solutions for semilinear stochastic differential equations driven by infinite dimensional L′evy noise with large jumps.Under suitable conditions on drift,diffusion and jump coefficients,we prove that there exist solutions which inherit the Poisson stability of coefficients.Further we show that these solutions are globally asymptotically stable in square-mean sense.Finally,we illustrate our theoretical results by several examples.
