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 (1018 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 theoreti- cal 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 nanostruc- tures. The main goal of our research project is a theoretical description of ultrafast electron dy- namics 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.

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 duration allowing for investigations of the electron dynamics in atoms, molecules and solids on their "natural" timescale. 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 surroundings. This generates system-environment correlations and leads to loss of quantum coherence. 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 instantaneous. These challenges were addressed within the stochastic wavefunction and density-matrix approaches of the time-dependent density functional theory, where complicated many-body dynamics and the interaction with the environment are effectively mapped to a system of non-interacting quasiparticles. We implemented these approaches in the VASP code, which is one of the most widely used in both academia and industry. We developed of the non-Markovian theory of pure dephasing in semiconductors and dielectric excited by a few-femtosecond infrared pulse. Numerical simulations have shown that time-dependent rates allow for temporally high dephasing to successfully reproduce the main features of high-harmonics spectrum and avoid an overestimation of the charge carrier population after the pulse, which is a common problem of the Markov approximation. Furthermore, we theoretically analysed the mechanisms of giant Stokes shift in ternary I-III-VI quantum dots. We found that this phenomenon is explained by the recombination of a polaronic state formed by non-trapped electron and a trapped hole interacting with phonons.