20,116 research outputs found
A unified approach to exact solutions of time-dependent Lie-algebraic quantum systems
By using the Lewis-Riesenfeld theory and the invariant-related unitary
transformation formulation, the exact solutions of the {\it time-dependent}
Schr\"{o}dinger equations which govern the various Lie-algebraic quantum
systems in atomic physics, quantum optics, nuclear physics and laser physics
are obtained. It is shown that the {\it explicit} solutions may also be
obtained by working in a sub-Hilbert-space corresponding to a particular
eigenvalue of the conserved generator ({\it i. e.}, the {\it time-independent}
invariant) for some quantum systems without quasi-algebraic structures. The
global and topological properties of geometric phases and their adiabatic limit
in time-dependent quantum systems/models are briefly discussed.Comment: 11 pages, Latex. accepted by Euro. Phys. J.
Conversions between barycentric, RKFUN, and Newton representations of rational interpolants
We derive explicit formulas for converting between rational interpolants in
barycentric, rational Krylov (RKFUN), and Newton form. We show applications of
these conversions when working with rational approximants produced by the AAA
algorithm [Y. Nakatsukasa, O. S\`ete, L. N. Trefethen, arXiv preprint
1612.00337, 2016] within the Rational Krylov Toolbox and for the solution of
nonlinear eigenvalue problems
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