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We introduce a novel approach for a fully quantum description of coupled electron-ion systems from first principles. It combines the variational quantum Monte Carlo (QMC) solution of the electronic part with the path integral (PI) formalism…
In quantum electrodynamics, photon-photon scattering can be the result of the exchange of virtual electron-positron pairs. This gives rise to a non-trivial dispersion relation for a single photon moving on a background of electromagnetic…
The semiclassically scaled time-dependent multi-particle Schr\"odinger equation describes, inter alia, quantum dynamics of nuclei in a molecule. It poses the combined computational challenges of high oscillations and high dimensions. This…
The coherence properties of the classical waves are discussed in terms of the Cauchy problem for the wave equation, and of a discrete representation by an ensemble of Hamiltonian systems. Wave quanta are related to specific "action fields",…
We study the Wigner distributions for a physical electron, which reveal the multidimensional images of the electron. The physical electron is considered as a composite system of a bare electron and photon. The Wigner distributions for…
In this dissertation, I explore interactions between matter and propagating light. The electromagnetic field is modeled as a reservoir of quantum harmonic oscillators successively streaming past a quantum system. Each weak and fleeting…
Particles and fields are standard components in numerical simulations like transport simulations in nuclear physics and have very well understood dynamics. Still, a common problem is the interaction between particles and fields due to their…
At present, there are many methods of quantum entanglement of particles with an electromagnetic field. Most methods have a low probability of quantum entanglement and not an exact theoretical apparatus based on an approximate solution of…
We present a new formulation for the mean-field propagation part of the relativistic quantum molecular dynamics, simulating an $N$-body system of interacting Gaussian wave packets via Lorentz scalar and vector potentials. Covariant…
A method for characterising the wave-function of freely-propagating particles would provide a useful tool for developing quantum-information technologies with single electronic excitations. Previous continuous-variable quantum tomography…
We present a review of recent developments of simulations of the Vlasov-Maxwell system of equations using a Fourier transform method in velocity space. In this method, the distribution functions for electrons and ions are Fourier…
We investigate tensor-train approaches to the solution of the time-dependent Schr\"{o}dinger equation for chain-like quantum systems with on-site and nearest-neighbor interactions only. Using efficient low-rank tensor train representations,…
The general matrix representation of a beam splitter array is presented. Each beam splitter has a transmission/reflection coefficient that determines the behavior of these individual devices and, in consequence, the whole system response.…
The interaction of a propagating pulse of quantum radiation with a localized quantum system can be described by a cascaded master equation with a distinct initially populated input and a finally populated output field mode [Phys. Rev. Lett.…
A model is developed for a detailed investigation of the current flowing through a cylindrical nanosize MOSFET with a close gate electrode. The quantum mechanical features of the lateral charge transport are described by Wigner distribution…
This work presents a selective review of results concerning the mathematical interface between the classical and quantum aspects encountered in problems such as the nuclear mean-field dynamics or quantum Brownian motion. It is shown that…
The random matrix ensembles (RME) of quantum statistical Hamiltonian operators, e.g. Gaussian random matrix ensembles (GRME) and Ginibre random matrix ensembles (Ginibre RME), are applied to following quantum statistical systems: nuclear…
We investigate the effect of electronic correlations on the transmission phase of quantum coherent scatterers, considering quantum dots in the Coulomb blockade regime connected to two single-channel leads. We focus on transmission zeros and…
The assisted Schwinger effect, which is predicted to display non-perturbative quantum tunnelling, is expected to be produced in precision lab experiments with electron beams and intense lasers. Indeed, many novel effects predicted by a…
A planar Maxwell-Chern-Simons-Proca model endowed with a Lorentz-violating background is taken as framework to investigate the electron-electron interaction. The Dirac sector is introduced exhibiting a Yukawa and a minimal coupling with the…