Fairmont Queen Elizabeth (Montreal), December 7 - 10, 2012
In principle, it is straightforward to compute the vibrational spectrum of a molecule without neglecting
coupling and anharmonicity: one must calculate eigenvalues and eigenvectors of a matrix representing the Hamiltonian in an
appropriate basis. In practice, this is difficult because the matrix is very large. To obviate the $N^2 $
memory and $N^3$ CPU costs of standard diagonalisation methods, it is now common to use iterative algorithms
(e.g. Lanczos, Davidson, Filter Diagonalisation) for computing eigenvalues and eigenvectors.
It is easy to efficiently implement iterative algorithms when a direct product basis is used.
However, for a molecule with more then four atoms, a direct product basis set is large and (although
iterative algorithms eliminate the need to store the matrix)
minimising the number of basis functions required to obtain converged eigenvalues
would be advantageous. Can this be done without jeopardizing the efficiency of the matrix-vector products
required by all iterative algorithms?
One way to reduce the number of basis functions is to discard unimportant functions from a direct product basis.
In this talk I shall present new basis-size reduction ideas of this type that are compatible with efficient matrix-vector products.
Things have changed first in the 1980s, with the related concept of "Tunnelling Time", i.e. how to measure "the time it takes a particle to tunnel through a potential barrier"? It turns out that no consensus has been reached yet on how to define such tunnelling times. It is in the 2010s, with the advent of sources of coherent radiation delivering "attosecond" (1 as = 10-18 s) pulses, that one has investigated photoionization in the time domain. At a fundamental level, this has opened the possibility to "clock" the response of a quantum system to the annihilation (absorption) of one photon.
We shall address some issues raised by this new generation of measurements and we shall present a theoretical analysis of recent experiments. These have evidenced the existence of attosecond time delays between the emission times of electrons ejected from different sub-shells in atoms, upon the absorption of one photon , .
 M. Schultze et al. "Delay in Photoemission", Science 328 1658-1662 (2010).
 K. Klünder et al. "Probing Single-Photon Ionization on the Attosecond Time Scale",
Phys. Rev. Lett. 106, 143002 (2011).