An improved version of the perturbation theory has been proposed. Expressions for the wave functions and energies of both degenerate and nondegenerate cases are derived. This method provides a simple way to treat problems involving more than one potential in the Hamiltonian and the case when the perturbations are comparable with or larger than the unperturbed Hamiltonian. We use this method to ...

We study two questions associated with rational approximation of a function f(z) near the origin z-0: continuity of the Pad approximation operator, and convergence of Chebyshev to Pad ap-proximants as the domain of approximation shrinks to a point. Both become delicate in the case of degenerate approximations, i.e. approximations whose numerator and denominator are deficient in degree. In this ...

We outline a method based on successive canonical transformations which yields a product expansion for the evolution operator of a general (possibly non-Hermitian) Hamiltonian. For a class of such Hamiltonians this expansion involves a finite number of terms, and our method gives the exact solution of the corresponding timedependent Schrödinger equation. We apply this method to study the dynami...

The formulation of phase conjugation via nondegenerate four-wave mixing in a homogeneously broadened resonant medium is genetalized to include saturating pump waves. An ultrahigh-Q optical fdter is predicted, showing both gain and a bandwidth less than the homogeneous linewidth of the atom. The dependence of the filter function on the ac Stark effect and on the use of asymmetric pump wave inten...

Two predictor-corrector methods of order m = Ω(logn) are proposed for solving sufficient linear complementarity problems. The methods produce a sequence of iterates in the N− ∞ neighborhood of the central path. The first method requires an explicit upper bound κ of the handicap of the problem while the second method does not. Both methods have O((1 + κ)1+1/m √ nL) iteration complexity. They are...

In this Letter, telecom-band degenerate-frequency photon pairs are generated in a specific mode of a silicon microring cavity by the nondegenerate spontaneous four-wave mixing (SFWM) process, under two continuous-wave pumps at resonance wavelength of two different cavity modes. The ratio of coincidence to accidental coincidence is up to 100 under a time bin width of 5 ns, showing their characte...

In this paper we find closed forms of the generating function ∞ ∑ k=0 U r nx , for powers of any non-degenerate second-order recurrence sequence, Un+1 = aUn+bUn−1, a +4b 6= 0, completing a study began by Carlitz [1] and Riordan [4] in 1962. Moreover, we generalize a theorem of Horadam [3] on partial sums involving such sequences. Also, we find closed forms for weighted (by binomial coefficients...

Nondegenerate azimuthal morphology-dependent resonances are observed for a distorted, fluorescently labeled polystyrene microsphere levitated in a quadrupole ion trap. Modeling the individual resonances by using perturbation theory allows a determination of quadrupole and octupole distortion parameters. The particle’s shape changes slowly over the course of the measurement and eventually become...

We have investigated a double-island single-electron transistor ~DISET! coupled to a floating metal double-dot ~DD!. Low-temperature transport measurements were used to map out the charge configurations of both the DISET and the DD. A suppression of the current through the DISET was observed whenever the charge configurations of the DISET and the DD were energetically codegenerate. This effect ...

We show theoretically that concurrent interactions in a second-order nonlinear medium placed inside an optical resonator can generate multipartite entanglement between the resonator modes. We show that there is a mathematical connection between this system and van Loock and Braunstein’s proposal for entangling N continuous quantum optical variables by interfering with the outputs of N degenerat...