Numerical study of the coupled time-dependent Gross-Pitaevskii equation: Application to Bose-Einstein condensation

The Bose-Einstein condensate of several types of trapped bosons at ultralow temperature was described using the coupled time dependent Gross-Pitaevskii equation. Both the stationary and time evolution problems were analyzed using this approach. The ground state stationary wave functions were found to be sharply peaked near the origin for attractive interatomic interaction for larger nonlinearity while for a repulsive interatomic interaction the wave function extends over a larger region of space.

Temperature-dependent Raman study of thermal parameters in CdS quantum dots

We report on the strong temperature-dependent thermal expansion, alpha(D), in CdS quantum dots (QDs) embedded in a glass template. We have performed a systematic study by using the temperature-dependent first-order Raman spectra, in CdS bulk and in dot samples, in order to assess the size dependence of alpha(D), and where the role of the compressive strain provoked by the glass host matrix on the dot response is discussed. We report the Gruneisen mode parameters and the anharmonic coupling constants for small CdS dots with mean radius R similar to 2.0 nm. We found that gamma parameters change, with respect to the bulk CdS, in a range between 20 and 50%, while the anharmonicity contribution from two-phonon decay channel becomes the most important process to the temperature-shift properties.

Inverse problems in classical and quantum physics

The subject of this thesis is in the area of Applied Mathematics known as Inverse Problems. Inverse problems are those where a set of measured data is analysed in order to get as much information as possible on a model which is assumed to represent a system in the real world. We study two inverse problems in the fields of classical and quantum physics: QCD condensates from tau-decay data and the inverse conductivity problem. Despite a concentrated effort by physicists extending over many years, an understanding of QCD from first principles continues to be elusive. Fortunately, data continues to appear which provide a rather direct probe of the inner workings of the strong interactions. We use a functional method which allows us to extract within rather general assumptions phenomenological parameters of QCD (the condensates) from a comparison of the time-like experimental data with asymptotic space-like results from theory. The price to be paid for the generality of assumptions is relatively large errors in the values of the extracted parameters. Although we do not claim that our method is superior to other approaches, we hope that our results lend additional confidence to the numerical results obtained with the help of methods based on QCD sum rules. EIT is a technology developed to image the electrical conductivity distribution of a conductive medium. The technique works by performing simultaneous measurements of direct or alternating electric currents and voltages on the boundary of an object. These are the data used by an image reconstruction algorithm to determine the electrical conductivity distribution within the object. In this thesis, two approaches of EIT image reconstruction are proposed. The first is based on reformulating the inverse problem in terms of integral equations. This method uses only a single set of measurements for the reconstruction. The second approach is an algorithm based on linearisation which uses more then one set of measurements. A promising result is that one can qualitatively reconstruct the conductivity inside the cross-section of a human chest. Even though the human volunteer is neither two-dimensional nor circular, such reconstructions can be useful in medical applications: monitoring for lung problems such as accumulating fluid or a collapsed lung and noninvasive monitoring of heart function and blood flow.

Theoretical and numerical analysis of large-scale heat transfer problems with temperature-dependent pore-fluid densities

Purpose - In many scientific and engineering fields, large-scale heat transfer problems with temperature-dependent pore-fluid densities are commonly encountered. For example, heat transfer from the mantle into the upper crust of the Earth is a typical problem of them. The main purpose of this paper is to develop and present a new combined methodology to solve large-scale heat transfer problems with temperature-dependent pore-fluid densities in the lithosphere and crust scales. Design/methodology/approach - The theoretical approach is used to determine the thickness and the related thermal boundary conditions of the continental crust on the lithospheric scale, so that some important information can be provided accurately for establishing a numerical model of the crustal scale. The numerical approach is then used to simulate the detailed structures and complicated geometries of the continental crust on the crustal scale. The main advantage in using the proposed combination method of the theoretical and numerical approaches is that if the thermal distribution in the crust is of the primary interest, the use of a reasonable numerical model on the crustal scale can result in a significant reduction in computer efforts. Findings - From the ore body formation and mineralization points of view, the present analytical and numerical solutions have demonstrated that the conductive-and-advective lithosphere with variable pore-fluid density is the most favorite lithosphere because it may result in the thinnest lithosphere so that the temperature at the near surface of the crust can be hot enough to generate the shallow ore deposits there. The upward throughflow (i.e. mantle mass flux) can have a significant effect on the thermal structure within the lithosphere. In addition, the emplacement of hot materials from the mantle may further reduce the thickness of the lithosphere. Originality/value - The present analytical solutions can be used to: validate numerical methods for solving large-scale heat transfer problems; provide correct thermal boundary conditions for numerically solving ore body formation and mineralization problems on the crustal scale; and investigate the fundamental issues related to thermal distributions within the lithosphere. The proposed finite element analysis can be effectively used to consider the geometrical and material complexities of large-scale heat transfer problems with temperature-dependent fluid densities.

Temperature-dependent internal quantum efficiency of blue high-brightness light-emitting diodes

Internal quantum efficiency (IQE) of a blue high-brightness InGaN/GaN light-emitting diode (LED) was evaluated from the external quantum efficiency measured as a function of current at various temperatures ranged between 13 and 440 K. Processing the data with a novel evaluation procedure based on the ABC-model, we have determined the temperature-dependent IQE of the LED structure and light extraction efficiency of the LED chip. Separate evaluation of these parameters is helpful for further optimization of the heterostructure and chip designs. The data obtained enable making a guess on the temperature dependence of the radiative and Auger recombination coefficients, which may be important for identification of dominant mechanisms responsible for the efficiency droop in III-nitride LEDs. Thermal degradation of the LED performance in terms of the emission efficiency is also considered.

Fast iterative solvers for time-dependent PDE-constrained optimization problems

Otto-von-Guericke-Universität Magdeburg, Fakultät für Mathematik, Kumulative Habilitation, 2016

Flow shop scheduling problems under machine-dependent precedence constraints

Abstract not available

Measure-valued mass evolution problems with flux boundary conditions and solution-dependent velocities

In this paper we prove well-posedness for a measure-valued continuity equation with solution-dependent velocity and flux boundary conditions, posed on a bounded one-dimensional domain. We generalize the results of an earlier paper [J. Differential Equations, 259 (2015), pp. 10681097] to settings where the dynamics are driven by interactions. In a forward-Euler-like approach, we construct a time-discretized version of the original problem and employ those results as a building block within each subinterval. A limit solution is obtained as the mesh size of the time discretization goes to zero. Moreover, the limit is independent of the specific way of partitioning the time interval [0, T]. This paper is partially based on results presented in Chapter 5 of [Evolution Equations for Systems Governed by Social Interactions, Ph.D. thesis, Eindhoven University of Technology, 2015], while a number of issues that were still open there are now resolved.

The quantum time-dependent harmonic oscillator

La presente tesi si propone di mostrare che l’oscillatore armonico quantistico dipendente dal tempo è un sistema risolvibile in maniera esatta. La trattazione è articolata in tre capitoli: nel primo viene richiamata la teoria dell’oscillatore armonico quantistico indipendente dal tempo, al fine di recuperare i concetti e le metodologie che sono comuni anche alla sua controparte dipendente dal tempo. Nel secondo capitolo viene fornita una breve introduzione alla teoria degli operatori invarianti dipendenti dal tempo, di cui ci interessa la loro relazione con le soluzioni dell’equazione di Schrödinger. Infine, nel terzo capitolo viene presentato il problema dell’oscillatore armonico quantistico dipendente dal tempo e discussa la sua soluzione esatta. In aggiunta se ne individuano gli stati coerenti.

Analyzing the n→π* Electronic Transition of Formaldehyde in Water. A Sequential Monte Carlo/Time-Dependent Density Functional Theory

The n→π* absorption transition of formaldehyde in water is analyzed using combined and sequential classical Monte Carlo (MC) simulations and quantum mechanics (QM) calculations. MC simulations generate the liquid solute-solvent structures for subsequent QM calculations. Using time-dependent density functional theory in a localized set of gaussian basis functions (TD-DFT/6-311++G(d,p)) calculations are made on statistically relevant configurations to obtain the average solvatochromic shift. All results presented here use the electrostatic embedding of the solvent. The statistically converged average result obtained of 2300 cm-1 is compared to previous theoretical results available. Analysis is made of the effective dipole moment of the hydrogen-bonded shell and how it could be held responsible for the polarization of the solvent molecules in the outer solvation shells.

Electron dephasing scattering rate in two-dimensional GaAs/InGaAs heterostructures with embedded InAs quantum dots

We report a comprehensive study of weak-localization and electron-electron interaction effects in a GaAs/InGaAs two-dimensional electron system with nearby InAs quantum dots, using measurements of the electrical conductivity with and without magnetic field. Although both the effects introduce temperature dependent corrections to the zero magnetic field conductivity at low temperatures, the magnetic field dependence of conductivity is dominated by the weak-localization correction. We observed that the electron dephasing scattering rate tau(-1)(phi), obtained from the magnetoconductivity data, is enhanced by introducing quantum dots in the structure, as expected, and obeys a linear dependence on the temperature and elastic mean free path, which is against the Fermi-liquid model. (c) 2008 American Institute of Physics. [DOI: 10.1063/1.2996034]

Dynamic polarizability, Cauchy moments, and the optical absorption spectrum of liquid water: A sequential molecular dynamics/quantum mechanical approach

The dynamic polarizability and optical absorption spectrum of liquid water in the 6-15 eV energy range are investigated by a sequential molecular dynamics (MD)/quantum mechanical approach. The MD simulations are based on a polarizable model for liquid water. Calculation of electronic properties relies on time-dependent density functional and equation-of-motion coupled-cluster theories. Results for the dynamic polarizability, Cauchy moments, S(-2), S(-4), S(-6), and dielectric properties of liquid water are reported. The theoretical predictions for the optical absorption spectrum of liquid water are in good agreement with experimental information.

Quantum reflection: The invisible quantum barrier

We construct an invisible quantum barrier which represents the phenomenon of quantum reflection using available data on atom-wall and Bose-Einstein-condensate-wall reflection. We use the Abel equation to invert the data. The resulting invisible quantum barrier is double valued in both axes. We study this invisible barrier in the case of atom and Bose-Einstein condensate (BEC) reflection from a solid silicon surface. A time-dependent, one-spatial-dimension Gross-Pitaevskii equation is solved for the BEC case. We found that the BEC behaves very similarly to the single atom except for size effects, which manifest themselves in a maximum in the reflectivity at small distances from the wall. The effect of the atom-atom interaction on the BEC reflection and correspondingly on the invisible barrier is found to be appreciable at low velocities and comparable to the finite-size effect. The trapping of an ultracold atom or BEC between two walls is discussed.

A Goldstone theorem in thermal relativistic quantum field theory

We prove a Goldstone theorem in thermal relativistic quantum field theory, which relates spontaneous symmetry breaking to the rate of spacelike decay of the two-point function. The critical rate of fall-off coincides with that of the massless free scalar field theory. Related results and open problems are briefly discussed. (C) 2011 American Institute of Physics. [doi:10.1063/1.3526961]

Gradient-dependent density functionals of the Perdew-Burke-Ernzerhof type for atoms, molecules, and solids

One of the standard generalized-gradient approximations (GGAs) in use in modern electronic-structure theory [Perdew-Burke-Ernzerhof (PBE) GGA] and a recently proposed modification designed specifically for solids (PBEsol) are identified as particular members of a family of functionals taking their parameters from different properties of homogeneous or inhomogeneous electron liquids. Three further members of this family are constructed and tested, together with the original PBE and PBEsol, for atoms, molecules, and solids. We find that PBE, in spite of its popularity in solid-state physics and quantum chemistry, is not always the best performing member of the family and that PBEsol, in spite of having been constructed specifically for solids, is not the best for solids. The performance of GGAs for finite systems is found to sensitively depend on the choice of constraints stemming from infinite systems. Guidelines both for users and for developers of density functionals emerge from this work.