Resonance and threshold phenomena 

In quantum mechanics, the eigenstates of a binding (i.e. negative) and local (i.e. vanishing at the asymptotes at infinity) potential are generally divided to bound-states with negative eigen-energies (that exponentially vanish at the asymptotes), and continuum states with positive eigen-energies (that do not vanish at the asymptotes). In certain conditions however, quantum systems can support other types of states as well. These include resonances of various types (that might be metastable, with complex eigen-energies, exhibiting a mixed localized/delocalized nature), and bound states in the continuum (which are positive-energy localized continuum states). Quantum systems might also support threshold states that appear at exactly zero energy when a state in the system transitions between bound and continuum (e.g. while the potential is being infinitesimally deformed). Threshold states are not mathematically limited to a particular long-range behavior, and can be so-called ‘half-bound’, or exhibit other dispersion relations. When a system supports irregular threshold states it can lead to anomalous quantum scattering at the threshold. The extent of this phenomena and its origin are largely unexplained.

We are interested in the mathematical physical origins of anomalous quantum scattering from threshold states, and in developing set-ups that allow their observation (either in optics or other systems). We are interested in the role threshold states might play in nonlinear optics, electron capture, and light propagation in waveguide arrays.

We are also interested in resonance phenomena in HHG (e.g. giant resonances in atomic systems, or shape resonances in molecules), trying to explain physical effects with ab-initio calculations, especially searching for many-body correlated phenomena on attosecond timescales.