Stochastic TDDFT on a Lattice

Ultrafast laser technology has paved the way to study physical processes under unprece-dented conditions and lead to a major progress in telecommunications, chemistry, medical and bio-technologies. Nowadays, the laser pulses have reached attosecond (10–18 second) duration allowing for investigations of the electron dynamics in atoms, molecules and solids on their “natural” timescale. Availability of new reliable laser sources provides an opportunity to build ultrafast “cameras” that can film microscopic processes with unprecedented temporal resolution and hold promise for new applications in electronics, photonics and medical diagnostics.

Experimental achievements in ultrafast optics raise completely new challenges to theoretical and computational physicists, who aim for correct simulations of the observed phenomena, explanations of the underlying physics and implementations of reliable algorithms for obtaining the information from experimental data. Strong laser fields excite the electron plasma, where many-particle effects play a significant role. Also, all real systems are interacting with their sur-roundings. This generates system-environment correlations and leads to loss of quantum co-herence. Recent research of ultrafast phenomena has shown that their adequate numerical simulation requires inclusion of electron-electron interactions and coupling with environment beyond the conventionally used approximations, where scattering events are treated as instan-taneous. Unfortunately, the currently available methods are becoming unreliable, when they are applied to system of interacting electrons, because they involve hierarchies of many coupled differential equations, whose solution is computationally very expensive.

These challenges can be addressed with a novel approach, stochastic time-dependent density functional theory (STDDFT), where complicated many-body dynamics and the interac-tion with the environment are effectively mapped to a system of non-interacting quasiparticles. This theory was recently formulated, but only applied to simple atomic systems. However, there is a great demand for its application to attosecond processes in semiconductors and nanostructures.
The main goal of our research project is a theoretical description of ultrafast electron dynamics on the lattice in the framework of STDDFT and an implementation of this method for periodic systems ranging from bulk semiconductors to nanostructures. We expect that our work will provide a new, computationally effective method and open a new research direction in the theory of ultrafast phenomena and physics of open quantum systems.