Dynamics of Many-Body Systems
Quantum many-body systems are at the core of current interest both in experimental as well as in theoretical physics, since a better understanding of these systems bears a large potential for technology and applications. Table-top sources of coherent X-ray light from strongly driven gases of atoms might become available in near future. Highly accurate gravimeters are being constructed using the coherence of matter waves. Petahertz electronics is at reach based on the driving of currents in dielectrics by femtosecond laser pulses. All these applications share that the underlying effects originate from or exploit non-equilibrium quantum matter. Many novel experimental tools are being developed that allow for unprecedented driving for example by strong and ultrashort laser pulses, by bichromatic fields, or by structured light, and are being used to explore new effects and applications.
Exact theoretical description not possible
At the same time, theoretical tools to describe these systems are lagging behind those available for systems at rest. In our research, we address exactly this discrepancy. We use and develop novel theoretical approaches to describe quantum systems out of equilibrium. Starting point of our investigations into non-equilibrium quantum matter is the many-body time-dependent Schrödinger equation. The complexity of this equation increases exponentially with the number of particles in the system. It thus cannot be solved numerically exactly except for the simplest systems consisting of just a few particles. A simple estimate shows that storing the wavefunction of, e.g. , the lithium atom with reasonable resolution would exceed the storage capacity of current supercomputers not to mention performing calculations with it. One way around is to avoid the wave function and use a reduced object such as the particle density. The time-dependent density functional theory, e.g., follows these lines by using the particle density as the fundamental object. However, it suffers from unknown energy functionals because quantum correlations cannot be easily taken into account. We have developed a time-dependent quantum many-body approach that uses the two-particle reduced density matrix instead. In this way all two-particle correlations are incorporated. Since all fundamental interactions can be regarded as pairwise interactions, two-body correlations are the most important ones. With the new method, we were able to solve a wide variety of problems ranging from the multi-electron dynamics of atoms driven by strong and ultrashort pulses to quench dynamics of ultracold atoms in optical lattices.