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Fully numerical mesh solutions of 2D and 3D quantum equations of Schroedinger and Hartree-Fock type allow us to work with wavefunctions which possess a very flexible geometry. This flexibility is especially important for calculations of…
This thesis report deals with the 1D Hubbard model and the quantum objects that diagonalize the normal ordered Hubbard hamiltonian, among those the so called PseudoFermions (PFs). These PFs have no residual energy interactions, are eta-spin…
Energy functionals of the Green's function can simultaneously provide spectral and thermodynamic properties of interacting electrons' systems. Though powerful in principle, these formulations need to deal with dynamical…
We present a method for accurately computing transition probabilities in one-dimensional photoionization problems. Our approach involves solving the time-dependent Schr\"odinger equation and projecting its solution onto scattering states…
We develop a formalism based on a time-dependent wave-function ansatz to study correlations of photons emitted from a collection of two-level quantum emitters. We show how to simulate the system dynamics and evaluate the intensity of the…
A time-dependent vibrational electronic coupled-cluster (VECC) approach is proposed to simulate photoelectron/ UV-VIS absorption spectra, as well as time-dependent properties for non-adiabatic vibronic models, going beyond the…
The quantum behavior of charge carriers in semiconductor structures is often described in terms of the effective mass Schr\"{o}dinger equation, neglecting the rapid fluctuations of the wave function on the scale of the atomic lattice. For…
The paper deals with the ground and the first excited state of the polaron in the one dimensional Holstein model. Various variational methods are used to investigate both the weak coupling and strong coupling case, as well as the crossover…
Excluding the very shallow potential minimum of the electronic ground state, all bound electronic states of He$_2$ have Rydberg character. Their potential-energy functions are similar to those of the He$_2^+$ states to which the Rydberg…
This paper reexamines the results of Cummings in which the quantum mechanical two-level-system (TLS) interacts with the electromagnetic field with various initial distributions and extends that work for both resonant and non-resonant to…
We present an experimental test of the use of stress engineered optics incorporated into a Shack-Hartmann wavefront sensor in such a way that the shape of the point spread function (PSF) provides polarization information while the…
The Holstein model, which describes purely local coupling of an itinerant excitation (electron, hole, exciton) with zero-dimensional (dispersionless) phonons, represents the paradigm for short-range excitation-phonon interactions. It is…
Variational calculations of excited electronic states are carried out by finding saddle points on the surface that describes how the energy of the system varies as a function of the electronic degrees of freedom. This approach has several…
Volkov states are exact solutions of the Dirac equation in the presence of an arbitrary plane wave. Volkov states, as well as free photon states, are not stable in the presence of the background plane-wave field but "decay" as…
The article presents the result of an extended in silico experiment on computational vibrational spectroscopy of graphene molecules performed using the virtual vibrational spectrometer UHF VVS, previously proposed in the first part of the…
A low-dimensional model (LDM) for turbulent Rayleigh-Benard convection in a Cartesian cell with square domain, based on the Galerkin projection of the Boussinesq equations onto a finite set of empirical eigenfunctions, is presented. The…
The pointwise space-time behavior of the Green's function of the one-dimensional Vlasov-Maxwell-Boltzmann (VMB) system is studied in this paper. It is shown that the Green's function consists of the macroscopic diffusive waves and Huygens…
We study the Landau level spectrum of bulk graphene monolayers beyond the Dirac Hamiltonian with linear dispersion. We consider an effective Wannier-like tight-binding model obtained from ab initio calculations, that includes long-range…
A single incompressible, inviscid, irrotational fluid medium bounded by a free surface and varying bottom is considered. The Hamiltonian of the system is expressed in terms of the so-called Dirichlet-Neumann operators. The equations for the…
We introduce a generic approach to study interaction effects in diffusive or chaotic quantum dots in the Coulomb blockade regime. The randomness of the single-particle wave functions induces randomness in the two-body interaction matrix…