The calculation results of the R-branch transition emission spectra of(0–0) band of the A21 → X21 transition system of Sb Na molecule are presented in this paper. These R-branch high-lying transitional emission spec...The calculation results of the R-branch transition emission spectra of(0–0) band of the A21 → X21 transition system of Sb Na molecule are presented in this paper. These R-branch high-lying transitional emission spectral lines are predicted by using the difference converging method(DCM). Our results show excellent agreement between DCM spectral lines and the experimental values, and the deviations are controlled within 0.0224 cm-1. What is more, based on the principle of over-determined linear equations, the prediction error is quantified in this work, which provides reliable theoretical support for our predicted DCM calculations. This work provides a lot of useful information for understanding the microstructure of Sb Na molecule.展开更多
We initiate an approach to simultaneously treat numerators and denominators of Green’s functions arising from quasi-periodic Schrödinger operators,which in particular allows us to study completely resonant phase...We initiate an approach to simultaneously treat numerators and denominators of Green’s functions arising from quasi-periodic Schrödinger operators,which in particular allows us to study completely resonant phases of the almost Mathieu operator.Let(H_(λ,α,θ)u)(n)=u(n+1)+u(n−1)+2λcos 2π(θ+nα)u(n)be the almost Mathieu operator on l^(2)(Z),where λ,α,θ∈R.Let β(α)=lim sup k→∞−ln||kα||R/Z/|k|.We prove that for anyθwith 2θ∈αZ+Z,H_(λ,α,θ) satisfies Anderson localization if|λ|>e2β(α).This confirms a conjecture of Avila and Jitomirskaya(Ann Math(2)170(1):303–342,2009)and a particular case of the second spectral transition line conjecture of Jitomirskaya(XIth International Congress of Mathematical Physics(Paris,1994),Int.Press,Cambridge,pp.373–382,1995).展开更多
基金Project supported by the Sichuan Education Department Project,China(Grant No.17ZA0369)the Fund for Sichuan Distinguished Scientists of China(Grant Nos.2019JDJQ0050 and 2019JDJQ0051)+2 种基金the National Natural Science Foundation of China(Grant Nos.61722507 and 11904295)the State Key Laboratory Open Fund of Quantum Optics and Quantum Optics DevicesLaser Spectroscopy Laboratory,China(Grant Nos.KF201811 and KF2020003)。
文摘The calculation results of the R-branch transition emission spectra of(0–0) band of the A21 → X21 transition system of Sb Na molecule are presented in this paper. These R-branch high-lying transitional emission spectral lines are predicted by using the difference converging method(DCM). Our results show excellent agreement between DCM spectral lines and the experimental values, and the deviations are controlled within 0.0224 cm-1. What is more, based on the principle of over-determined linear equations, the prediction error is quantified in this work, which provides reliable theoretical support for our predicted DCM calculations. This work provides a lot of useful information for understanding the microstructure of Sb Na molecule.
基金supported in part by NSF DMS-2000345,DMS-2052572 and DMS-2246031.
文摘We initiate an approach to simultaneously treat numerators and denominators of Green’s functions arising from quasi-periodic Schrödinger operators,which in particular allows us to study completely resonant phases of the almost Mathieu operator.Let(H_(λ,α,θ)u)(n)=u(n+1)+u(n−1)+2λcos 2π(θ+nα)u(n)be the almost Mathieu operator on l^(2)(Z),where λ,α,θ∈R.Let β(α)=lim sup k→∞−ln||kα||R/Z/|k|.We prove that for anyθwith 2θ∈αZ+Z,H_(λ,α,θ) satisfies Anderson localization if|λ|>e2β(α).This confirms a conjecture of Avila and Jitomirskaya(Ann Math(2)170(1):303–342,2009)and a particular case of the second spectral transition line conjecture of Jitomirskaya(XIth International Congress of Mathematical Physics(Paris,1994),Int.Press,Cambridge,pp.373–382,1995).
