Theoretical modeling of ionospheric electrodynamics including induction effects

This thesis deals with theoretical modeling of the electrodynamics of auroral ionospheres. In the five research articles forming the main part of the thesis we have concentrated on two main themes: Development of new data-analysis techniques and study of inductive phenomena in the ionospheric electrodynamics. The introductory part of the thesis provides a background for these new results and places them in the wider context of ionospheric research. In this thesis we have developed a new tool (called 1D SECS) for analysing ground based magnetic measurements from a 1-dimensional magnetometer chain (usually aligned in the North-South direction) and a new method for obtaining ionospheric electric field from combined ground based magnetic measurements and estimated ionospheric electric conductance. Both these methods are based on earlier work, but contain important new features: 1D SECS respects the spherical geometry of large scale ionospheric electrojet systems and due to an innovative way of implementing boundary conditions the new method for obtaining electric fields can be applied also at local scale studies. These new calculation methods have been tested using both simulated and real data. The tests indicate that the new methods are more reliable than the previous techniques. Inductive phenomena are intimately related to temporal changes in electric currents. As the large scale ionospheric current systems change relatively slowly, in time scales of several minutes or hours, inductive effects are usually assumed to be negligible. However, during the past ten years, it has been realised that induction can play an important part in some ionospheric phenomena. In this thesis we have studied the role of inductive electric fields and currents in ionospheric electrodynamics. We have formulated the induction problem so that only ionospheric electric parameters are used in the calculations. This is in contrast to previous studies, which require knowledge of the magnetospheric-ionosphere coupling. We have applied our technique to several realistic models of typical auroral phenomena. The results indicate that inductive electric fields and currents are locally important during the most dynamical phenomena (like the westward travelling surge, WTS). In these situations induction may locally contribute up to 20-30% of the total ionospheric electric field and currents. Inductive phenomena do also change the field-aligned currents flowing between the ionosphere and magnetosphere, thus modifying the coupling between the two regions.

Implications of Bohmian quantum ontology for psychopathology

This article discusses the prospects of quantum psychiatry from a Bohmian point of view, which provides an ontological interpretation of quantum theory, and extends such ontology to include mind. At first, we discuss the more general relevance of quantum theory to psychopathology. The basic idea is that because quantum theory emphasizes the role of wholeness, it might be relevant to psychopathology, where breakdown of unity in the mental domain is a key feature. We then discuss the role of information in psychopathology, and consider the connections with quantum theory in this area. In particular, we discuss David Bohm’s notion of active information, which arises in the ontological interpretation of quantum theory, and is suggested to play a fundamental role as the bridge between mind and matter. Some such bridge is needed if we are to understand how subtle mental properties are able to influence more manifest physical properties in the brain (all the way to the molecular and possibly microtubular level), and how changes in those possibly quantum‐level physical processes are able to influence higher cognitive functions. We also consider the implications of the notion of active information for psychopathology. The prospects of implementing the Bohmian scheme in neuroquantal terms are then briefly considered. Finally, we discuss some possible therapeutic implications of Bohm’s approach to information and the relation of mind and matter.

Implications of Bohmian quantum ontology for psychopathology

This article discusses the prospects of quantum psychiatry from a Bohmian point of view, which provides an ontological interpretation of quantum theory, and extends such ontology to include mind. At first, we discuss the more general relevance of quantum theory to psychopathology. The basic idea is that because quantum theory emphasizes the role of wholeness, it might be relevant to psychopathology, where breakdown of unity in the mental domain is a key feature. We then discuss the role of information in psychopathology, and consider the connections with quantum theory in this area. In particular, we discuss David Bohm’s notion of active information, which arises in the ontological interpretation of quantum theory, and is suggested to play a fundamental role as the bridge between mind and matter. Some such bridge is needed if we are to understand how subtle mental properties are able to influence more manifest physical properties in the brain (all the way to the molecular and possibly microtubular level), and how changes in those possibly quantum‐level physical processes are able to influence higher cognitive functions. We also consider the implications of the notion of active information for psychopathology. The prospects of implementing the Bohmian scheme in neuroquantal terms are then briefly considered. Finally, we discuss some possible therapeutic implications of Bohm’s approach to information and the relation of mind and matter.

AC transport at holographic quantum hall transitions

We compute AC electrical transport at quantum Hall critical points, as modeled by intersecting branes and gauge/gravity duality. We compare our results with a previous field theory computation by Sachdev, and find unexpectedly good agreement. We also give general results for DC Hall and longitudinal conductivities valid for a wide class of quantum Hall transitions, as well as (semi)analytical results for AC quantities in special limits. Our results exhibit a surprising degree of universality; for example, we find that the high frequency behavior, including subleading behavior, is identical for our entire class of theories.

Coherent quantum Boltzmann equations from cQPA

We reformulate and extend our recently introduced quantum kinetic theory for interacting fermion and scalar fields. Our formalism is based on the coherent quasiparticle approximation (cQPA) where nonlocal coherence information is encoded in new spectral solutions at off-shell momenta. We derive explicit forms for the cQPA propagators in the homogeneous background and show that the collision integrals involving the new coherence propagators need to be resummed to all orders in gradient expansion. We perform this resummation and derive generalized momentum space Feynman rules including coherent propagators and modified vertex rules for a Yukawa interaction. As a result we are able to set up self-consistent quantum Boltzmann equations for both fermion and scalar fields. We present several examples of diagrammatic calculations and numerical applications including a simple toy model for coherent baryogenesis.

Gauge Field Theories, Quantum Space-Time and Some Applications

In this thesis, the possibility of extending the Quantization Condition of Dirac for Magnetic Monopoles to noncommutative space-time is investigated. The three publications that this thesis is based on are all in direct link to this investigation. Noncommutative solitons have been found within certain noncommutative field theories, but it is not known whether they possesses only topological charge or also magnetic charge. This is a consequence of that the noncommutative topological charge need not coincide with the noncommutative magnetic charge, although they are equivalent in the commutative context. The aim of this work is to begin to fill this gap of knowledge. The method of investigation is perturbative and leaves open the question of whether a nonperturbative source for the magnetic monopole can be constructed, although some aspects of such a generalization are indicated. The main result is that while the noncommutative Aharonov-Bohm effect can be formulated in a gauge invariant way, the quantization condition of Dirac is not satisfied in the case of a perturbative source for the point-like magnetic monopole.

Noncommutative Quantum Field Theory : Problem of Time and Some Applications

In this thesis the current status and some open problems of noncommutative quantum field theory are reviewed. The introduction aims to put these theories in their proper context as a part of the larger program to model the properties of quantized space-time. Throughout the thesis, special focus is put on the role of noncommutative time and how its nonlocal nature presents us with problems. Applications in scalar field theories as well as in gauge field theories are presented. The infinite nonlocality of space-time introduced by the noncommutative coordinate operators leads to interesting structure and new physics. High energy and low energy scales are mixed, causality and unitarity are threatened and in gauge theory the tools for model building are drastically reduced. As a case study in noncommutative gauge theory, the Dirac quantization condition of magnetic monopoles is examined with the conclusion that, at least in perturbation theory, it cannot be fulfilled in noncommutative space.

Computational Methods for Studies of Quantum Dots and Boson Condensates

This thesis presents ab initio studies of two kinds of physical systems, quantum dots and bosons, using two program packages of which the bosonic one has mainly been developed by the author. The implemented models, \emph{i.e.}, configuration interaction (CI) and coupled cluster (CC) take the correlated motion of the particles into account, and provide a hierarchy of computational schemes, on top of which the exact solution, within the limit of the single-particle basis set, is obtained. The theory underlying the models is presented in some detail, in order to provide insight into the approximations made and the circumstances under which they hold. Some of the computational methods are also highlighted. In the final sections the results are summarized. The CI and CC calculations on multiexciton complexes in self-assembled semiconductor quantum dots are presented and compared, along with radiative and non-radiative transition rates. Full CI calculations on quantum rings and double quantum rings are also presented. In the latter case, experimental and theoretical results from the literature are re-examined and an alternative explanation for the reported photoluminescence spectra is found. The boson program is first applied on a fictitious model system consisting of bosonic electrons in a central Coulomb field for which CI at the singles and doubles level is found to account for almost all of the correlation energy. Finally, the boson program is employed to study Bose-Einstein condensates confined in different anisotropic trap potentials. The effects of the anisotropy on the relative correlation energy is examined, as well as the effect of varying the interaction potential.}

Paradoxical reflection in quantum mechanics

This article concerns a phenomenon of elementary quantum mechanics that is quite counter-intuitive, very non-classical, and apparently not widely known: a quantum particle can get reflected at a downward potential step. In contrast, classical particles get reflected only at upward steps. The conditions for this effect are that the wave length is much greater than the width of the potential step and the kinetic energy of the particle is much smaller than the depth of the potential step. This phenomenon is suggested by non-normalizable solutions to the time-independent Schroedinger equation, and we present evidence, numerical and mathematical, that it is also indeed predicted by the time-dependent Schroedinger equation. Furthermore, this paradoxical reflection effect suggests, and we confirm mathematically, that a quantum particle can be trapped for a long time (though not forever) in a region surrounded by downward potential steps, that is, on a plateau.