狄拉克-库仑传播子的衍射

狄拉克-库仑传播子的奇异性

Singularities of Dirac-Coulomb propagators

本文研究含时库仑势下狄拉克场传播子与N点函数的奇异性，证明r≠0时狄拉克-库仑真空为哈达玛态，且任意两哈达玛态的相对电荷密度在r=0附近也可良好定义，推广了相关奇异性定理至含时势情形。

Existence of Propagators for Time Dependent Coulomb-like Potentials

We prove existence of propagators for a time dependent Schrödinger equation with a new class of softened Coulomb potentials, which we allow to be time dependent, in the context of time dependent density functional theory. We compute explicitly the Fourier transform of these new potentials, and provide an alternative proof for the Fourier transform of the Coulomb potential using distribution theory. Finally we show the new potentials are dilatation analytic, and so the spectrum of the corresponding Hamiltonian can be fully characterized.

Diffraction of the Aharonov-Bohm Hamiltonian

In this paper, we compute the diffractive wave propagator of the Aharonov-Bohm effect on $\mathbf{R}^2$ with a single solenoid using a technique of moving solenoid location. In addition, we compute the corresponding diffraction coefficient which is the principal symbol of the diffractive propagator. This paper gives the first proof of propagation of singularities of the Aharonov-Bohm Hamiltonian.

Wave propagation on Euclidean surfaces with conical singularities. I: Geometric diffraction

We investigate the singularities of the trace of the half-wave group, $\mathrm{Tr} \, e^{-it\sqrtΔ}$, on Euclidean surfaces with conical singularities $(X,g)$. We compute the leading-order singularity associated to periodic orbits with successive degenerate diffractions. This result extends the previous work of the third author \cite{Hil} and the two-dimensional case of the work of the first author and Wunsch \cite{ForWun} as well as the seminal result of Duistermaat and Guillemin \cite{DuiGui} in the smooth setting. As an intermediate step, we identify the wave propagators on $X$ as singular …