Iterative solutions for low lying excited states of a class of SchrSdinger equation

The convergent iterative procedure for solving the groundstate Schr?dinger equation is extended to derive the excitation energy and the wavefunction of the low-lying excited states. The method is applied to the one-dimensional quartic potential problem. The results show that the iterative solution converges rapidly when the coupling g is not too small.     

Superconductivity in PdAlx hydrides

Hydrides of PdA$\text{l}$_x alloys prepared by electron beam co-evaporation and subsequent implantation of hydrogen ions are found to exhibit anomalous changes in the superconducting transition temperature with increasing A$\text{l}$ content. At large hydrogen concentrations, H/Pd ～ 1, the addition of aluminum increases T_c only slightly (from 8.1 to 8.6°K for 7 at. % A$\text{l}$), and then yields an abrupt decrease in T_c at 10% A$\text{l}$. This behavior is in sharp contrast to PdAg_xH_y alloys which exhibit an enhanced T_c ～ 16°K at relatively low silver content.     

Eigenvalues of collective emission in multi-slice slab configurations

We compute the eigenmodes of collective emission from multi-slice slab configurations, using the transfer matrix formalism. We elucidate within this formalism the phenomena of “Invisible Gaps” in multiple-slice configuration and of “Precocious Superradiance” in periodic structures previously observed in numerical solutions of Maxwell-Bloch equations.     

Effects of including the counterrotating term and virtual photons on the eigenfunctions and eigenvalues of a scalar photon collective emission theory

We find eigenmodes of an integral equation describing N 2-level atoms interacting with a scalar field, one atom being initially excited. Neglect of virtual field quanta would replace the correct kernel by its real part. This has serious consequences both for small and large samples.     

A new proof for the convergent iterative solution of the degenerate quantum double-well potential and its generalization

We present a new and simpler proof for the convergent iterative solution of the one-dimensional degenerate double-well potential. This new proof depends on a general theorem, called the hierarchy theorem, that shows the successive stages in the iteration to form a monotonically increasing sequence of approximations to the energy and to the wavefunction at any point x. This important property makes possible a much simpler proof of convergence than the one given before in the literature. The hierarchy theorem proven in this paper is applicable to a much wider class of potentials which includes the quartic potential.     

Nonvanishing theorems for L-functions of modular forms and their derivatives

Inventiones mathematicae -     

Theta function transformation formulas and the Weil representation

A short proof is given that the theta functional is invariant under the Weil representation, and the explicit determination of the eighth root of unity which arises is also shown. Namely, the action of the Weil representation on the theta functional is described as the limit of integration against a specialization of the symplectic theta function as the symplectic variable approaches a cusp. The invariance is then a consequence of the automorphic nature of this theta function, coupled with the fact that in the limit it acts as the reproducing kernel for a certain lattice. Using results of Stark and Styer, this also allows one to determine the root of unity involved.