Preparing a quantum system in a pure state is ultimately limited by the nature of the system's evolution in the presence of its environment and by the initial state of the environment itself. We show that, when the system and environment are initially uncorrelated and arbitrary joint unitary dynamics is allowed, the system may be purified up to a certain (possibly arbitrarily small) threshold i...

This thesis consists of four papers that concern error estimates for the BornOppenheimer molecular dynamics, and adaptive algorithms for the Car-Parrinello and Ehrenfest molecular dynamics. In Paper I, we study error estimates for the Born-Oppenheimer molecular dynamics with nearly crossing potential surfaces. The paper first proves an error estimate showing that the difference of the values of...

G protein-coupled receptors (GPCRs) are key players of cell signaling, thus representing important drug targets for the treatment of human diseases. Since inherent difficulties in receptor production and handling have precluded the application of many in vitro experiments, major questions about GPCR mechanisms and dynamics remain elusive to date. We recently used directed evolution in Escherich...

We consider qubit purification under simultaneous continuous measurement of the three non-commuting qubit operators σ(x), σ(y), σ(z). The purification dynamics is quantified by (i) the average purification rate and (ii) the mean time of reaching a given level of purity, 1-ε. Under ideal measurements (detector efficiency η=1), we show in the first case an asymptotic mean purification speed-up of...

Assembly of oppositely charged triblock copolyelectrolytes into phase-separated gels at low polymer concentrations (<1% by mass) has been observed in scattering experiments and molecular dynamics simulations. Here we show that in contrast to uncharged, amphiphilic block copolymers that form discrete micelles at low concentrations and enter a phase of strongly interacting micelles in a gradual m...

Small amounts of surfactant can drastically change bubble behavior. For example, a bubble in aqueous surfactant solution rises much slower than one in purified water. This phenomenon is explained by the so-called Marangoni effect caused by a nonuniform concentration distribution of surfactant along the bubble surface. In other words, a tangential shear stress appears on the bubble surface due t...

In this tutorial review, recent developments in modeling and experimental studies on nanofludics were reported. Nanofluidic studies were categorized into two groups depending on the characteristic length scale. When the size of the nanochannels and pores is 5-100 nm, electrostatic interactions are dominant, and ion and fluid flow can be analyzed by continuum dynamics. Various nanofluidic device...

The interplay between unitary dynamics and local quantum measurements results in unconventional non-unitary dynamical phases transitions. In this paper we investigate the of $(d+1)$-dimensional hybrid stabilizer circuits, for $d=1,2,3$. We characterize measurement-induced their transitions using large-scale numerical simulations focusing on entanglement measures, purification dynamics, wave-fun...