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) and Time-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 their implications for R&D in
view of the promise of quantum dynamic imaging science as the essential
tool for controlling matter at the molecular level.
