The main area of our research is the quantum dynamics of many-body systems. While classical Molecular Dynamics can be computed for condensed phase systems with thousands of atoms, the time-dependent Schrödinger equation can be solved exactly only for small systems containing four or less atoms. We develop effective numerical methods that calculate quantum mechanical time evolution based on the semi-classical representation of a wavefunction by classical trajectories.

One important application of this research is in the rapidly growing field of ultra-fast spectroscopy in condensed phase. While the experimentalists can measure more and more detailed time-resolved signals the interpretation of the results in terms of molecular motions is often limited by our inability to compute the quantum dynamics of a system. Our goal is to go hand-in-hand with the modern experiments and to study such processes as solvation and charge transfer in liquids and dynamics of hydrogen bonds in water. At present the accurate calculations are possible for systems such as the one shown below.

Fig. 1. Calculated 2-D photon echo spectrum (top) of a chromophore undergoing solvation dynamics in a model liquid (bottom).

Among other applications is the dynamics of chaotic systems such as the highly excited (Rydberg) electrons in atoms. We are also interested in a semi-classical description of the Bose systems such as liquid helium. In this case, the goal is to understand the microscopic mechanisms that lead to the fascinating properties of superfluid helium.