arXiv subjects

Torben Swart

Publications and source records attributed to Torben Swart.

2 recordsLinked to original sources

arXiv2008

Global L2-Boundedness Theorems for Semiclassical Fourier Integral Operators with Complex Phase

In this work, a class of semiclassical Fourier Integral Operators (FIOs) with complex phase associated to some canonical transformation of the phase space $T^*\R^d$ is constructed. Upon some general boundedness assumptions on the symbol and the canonical transformation, their continuity (as operators) from the Schwartz class into itself and from $L^2$ into itself are proven.

math-ph↗

arXiv2007

A Mathematical Justification for the Herman-Kluk Propagator

A class of Fourier Integral Operators which converge to the unitary group of the Schroedinger equation in semiclassical limit $\eps\to 0$ is constructed. The convergence is in the uniform operator norm and allows for an error bound of order $O(\eps^{1-ρ})$ for Ehrenfest timescales, where $ρ$ can be made arbitrary small. For the shorter times of order O(1), the error can be improved to arbitrary order in $\eps$. In the chemical literature the approximation is known as the Herman-Kluk propagator.

math-ph↗