arXiv subjects

Caroline Lasser

Publications and source records attributed to Caroline Lasser.

39 records · Page 3Linked to original sources

arXiv2014

Hagedorn wavepackets in time-frequency and phase space

The Hermite functions are an orthonormalbasis of the space of square integrable functions with favourable approximation properties. Allowing for a flexible localization in position and momentum, the Hagedorn wavepackets generalize the Hermite functions also to several dimensions. Using Hagedorn's raising and lowering operators, we derive explicit formulas and recurrence relations for the Wigner and FBI transform of the wavepackets and show their relation to the Laguerre polyomials.

math-ph↗

arXiv2013

Propagation of Quantum Expectations with Husimi Functions

We analyse the dynamics of expectation values of quantum observables for the time-dependent semiclassical Schrödinger equation. To benefit from the positivity of Husimi functions, we switch between observables obtained from Weyl and Anti-Wick quantization. We develop and prove a second order Egorov type propagation theorem with Husimi functions by establishing transition and commutator rules for Weyl and Anti-Wick operators. We provide a discretized version of our theorem and present numerical experiments for Schrödinger equations in dimensions two and six that validate our results.

math.NA↗

arXiv2012

Wigner Measure Propagation and Conical Singularity for General Initial Data

We study the evolution of Wigner measures of a family of solutions of a Schrödinger equation with a scalar potential displaying a conical singularity. Under a genericity assumption, classical trajectories exist and are unique, thus the question of the propagation of Wigner measures along these trajectories becomes relevant. We prove the propagation for general initial data.

math.AP↗