Studying and using light or "photons" to image and then to
control and transmit molecular information is among the most
challenging and significant research fields to emerge in recent
years. One of the fastest growing areas involves research in the
temporal imaging of quantum phenomena, ranging from molecular
dynamics in the femto (10-15s) time regime for atomic motion to the
atto (10-18s) time scale of electron motion. In fact, the
attosecond "revolution" is now recognized as one of the most
important recent breakthroughs and innovations in the science of
the 21st century. A major participant in the development of
ultrafast femto and attosecond temporal imaging of molecular
quantum phenomena has been theory and numerical simulation of the
nonlinear, non-perturbative response of atoms and molecules to
ultrashort laser pulses. Therefore, imaging quantum dynamics is a
new frontier of science requiring advanced mathematical approaches
for analyzing and solving spatial and temporal multidimensional
partial differential equations such as Time-Dependent Schroedinger
Equations (TDSE) andTime-Dependent Dirac equations (TDDEs for
relativistic phenomena). These equations are also coupled to the
photons in Maxwell's equations for collective propagation effects.
Inversion of the experimental imaging data of quantum dynamics
presents new mathematical challenges in the imaging of quantum wave
coherences on subatomic (subnanometer) spatial dimensions and
multiple timescales from atto to femto and even nanoseconds.In
"Quantum Dynamic Imaging: Theoretical and Numerical Methods,"
leading researchers discuss these exciting state-of-the-art
developments and theirimplications for R&D in view of the
promise of quantum dynamic imagingscience as the essential tool for
controlling matter at the molecular level."
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