The development of integrated optical communication systems demands efficient on-chip multidimensional multiplexing to enhance transmission capacity and network robustness[1].Traditional micro-ring resonators(MRRs)hav...The development of integrated optical communication systems demands efficient on-chip multidimensional multiplexing to enhance transmission capacity and network robustness[1].Traditional micro-ring resonators(MRRs)have emerged as promising candidates for wavelength-division multiplexing due to their compact footprint and wavelength-dependent resonance.However,a critical limitation arises from the effective refractive index mismatch between transverse electric(TE)and transverse magnetic(TM)polarizations,which introduces complexities in polarization channel multiplexing[2].展开更多
In this paper, we use the theory of generalized Poisson bracket (GPB) to build the Poisson structure of three-dimensional 'frozen' systems Of Hamiltonian systems with slow time variable,and show that under pro...In this paper, we use the theory of generalized Poisson bracket (GPB) to build the Poisson structure of three-dimensional 'frozen' systems Of Hamiltonian systems with slow time variable,and show that under proper conditions, there exists an adiabatic invariant on every closed simply connected symplectic leaf for the time-dependent Hamiltonian systems. If the Hamiltonian H(p,q,τ) on these symplectic leaves are periodic with respect to τ and the frozen systems are in some sense strictly nonisochronous, then there are perpetual adiabatic invariants. To illustrate these results, we discuss the classical Lotka-Volterra equation with slowly periodic time-dependent coefficients modeling the interactions of three species.展开更多
文摘The development of integrated optical communication systems demands efficient on-chip multidimensional multiplexing to enhance transmission capacity and network robustness[1].Traditional micro-ring resonators(MRRs)have emerged as promising candidates for wavelength-division multiplexing due to their compact footprint and wavelength-dependent resonance.However,a critical limitation arises from the effective refractive index mismatch between transverse electric(TE)and transverse magnetic(TM)polarizations,which introduces complexities in polarization channel multiplexing[2].
文摘In this paper, we use the theory of generalized Poisson bracket (GPB) to build the Poisson structure of three-dimensional 'frozen' systems Of Hamiltonian systems with slow time variable,and show that under proper conditions, there exists an adiabatic invariant on every closed simply connected symplectic leaf for the time-dependent Hamiltonian systems. If the Hamiltonian H(p,q,τ) on these symplectic leaves are periodic with respect to τ and the frozen systems are in some sense strictly nonisochronous, then there are perpetual adiabatic invariants. To illustrate these results, we discuss the classical Lotka-Volterra equation with slowly periodic time-dependent coefficients modeling the interactions of three species.
