From its beginning in the early 20th century, quantum theory has become progressively more important especially due to its contributions to the development of technologies. Quantum mechanics is crucial for current technology such as semiconductors, and also holds promise for future technologies such as superconductors and quantum computing. Despite of the success of quantum theory, its applications have been mostly limited to equilibrium or static systems due to 1. lack of experimental controllability of non-equilibrium quantum systems 2. lack of theoretical frameworks to understand non-equilibrium dynamics. Consequently, physicists have not yet discovered too many interesting phenomena in non-equilibrium quantum systems from both theoretical and experimental point of view and thus, non-equilibrium quantum physics did not attract too much attentions. / Physics

Ο κύριος σκοπός της παρούσας εργασίας είναι να συγκεντρωθούν συγκεκριμένες θεωρήσεις που χρησιμοποιούν τον φορμαλισμό των συνεπών ιστοριών σε βασικά προβλήματα της κβαντικής θεωρίας και κβαντικής κοσμολογίας. Ο φορμαλισμός αυτός είναι πολλά υποσχόμενος για τον τομέα της κανονικής κβαντικής βαρύτητας. Ο λόγος που θα κάνουμε αυτή την ανασκόπηση είναι για να δώσουμε μία ενοποιημένη εικόνα στα ζητήματα αυτά και να μπορέσουμε να τα συγκρίνουμε. Συγκεκριμένα, το πρώτο μέρος αφορά δύο διαφορετικές προσεγγίσεις για το πρόβλημα του χρόνου άφιξης στην κβαντομηχανική, εκ των οποίων και οι δύο χρησιμοποιούν φορμαλισμό ιστοριών. Η πρώτη έγινε από τους Halliwell και Yearsly (2009) και η δεύτερη από τους Anastopoulo και Saviddou (2012). Από την σύγκριση αυτών καταλήγουμε στο συμπέρασμα ότι και οι δύο δίνουν μία αδρομερή μορφή της εξίσωσης του Kijowski. Το δεύτερο μέρος αφορά την κβαντική κοσμολογία. Σε αυτό αρχικά παρουσιάζεται μία προσέγγιση με συνεπείς ιστορίες για την πυκνότητα πιθανότητας στην κβαντική κοσμολογία η οποία έγινε από τον Halliwell (2009). Στην συνέχεια παρουσιάζεται μία προσέγγιση με ιστορίες για μοντέλα μίνι-υπερχώρου από τους Anastopoulo and Savidou (2005). Σε αυτή κατασκευάζονται μοντέλα μίνι-υπερχώρου με όρους προβολικών τελεστών ιστοριών (HPO). Η σπουδαιότητα αυτού του φορμαλισμού έγκειται στο γεγονός ότι η γενική σχετικότητα σε αυτή την μορφή ικανοποιεί και τους χωροχρονικούς διαφορομορφισμούς και την άλγεβρα Dirac, με αποτέλεσμα να είναι εύκολα κβαντίσιμη. / The major purpose of this study is to consecrate specific approaches to some problems of quantum theory and quantum cosmology, in terms of decoherence histories formalism which is a very promising formalism for the canonical quantum gravity theories. The reason is to give a unified picture to these issues in order to be possible to compare them. Specifically, the first part contains two different approaches to the time of arrival in quantum mechanics, both of these use a histories formalism. The first is from Halliwell and Yearsly (2009) and the second from Anastopoulos and Saviddou (2012). By comparing them we deduce that both of them first gives a coarse-grain form of the Kijowski' s probability distribution. The second part concerns quantum cosmology. In this, we presented a decoherent histories approach to quantum cosmological probabilities, in which was used a complex potential, from Halliwell (2009). After that we present a histories approach to minisuperspace models by Anastopoulos and Savidou (2005). In this, minisuperspace models is written in terms of histories projector operator (HPO) formalism. The spectacular of this is that in that form general relativity satisfies both spacetime diffeomorfisms and Dirac algebra, which is very important because it is easier to be quantized.

In this thesis a kinetic theory for spin-1/2 particles is given a brief overview, focusing on the derivation of an evolution equation for the quasiprobability distribution function used in the theory to describe certain types of quantum plasma. The current theory is expanded upon by exploring conservation laws. A local conservation law for momentum is derived using two different expressions for electromagnetic momentum, given by Abraham and Minkowski respectively. There has been some controversy over which of these expressions should be used; in the case considered here the expression given by Minkowski seems to be more suitable. Based on the conservation law for momentum, a conservation law for angular momentum is also derived.

This thesis is concerned with employing the statistics of charge transfer in a conductor as a tool for quantum measurement. The physical systems studied are electronic devices made by nanoscale manufacturing techniques. In this context quantum measurement appears not as a postulate, but as physical process. In this thesis I am considering a quantum system, in particular a qubit or a nanomechanical resonator, interacting with a tunnel junction. The effect of coupling a quantum system to a tunnel junction is twofold: The state of the quantum system will be changed and there will be information about the quantum system in the statistics of charge transfer of the tunnel junction. As the first example a quantum measurement process of a qubit is considered. A common description of the system and charge dynamics is found by introducing a new quantity, the charge specific density matrix. By deriving and solving a Markovian master equation for this quantity the measurement process is analyzed. The measurement is shown to be a dynamical process, where correlations between the initial state of the qubit and the number of charges transferred in the tunnel junction arise on a typical timescale, the measurement time. As another example of a quantum system a nanomechanical oscillator is considered. It is found, that the biased tunnel junction, acting as a non-equilibrium environment to the oscillator, increases the temperature of the oscillator from its thermal equilibrium value. The current in the junction is modulated by the interaction with the oscillator, but the influence vanishes for bias voltages smaller than the oscillator frequency. For an asymmetric junction and non-vanishing oscillator momentum a current is shown to flow through the junction even at zero bias. The current noise spectrum induced by the oscillator in the tunnel junction consists of a noise floor and a peaked structure with peaks at zero frequency, the oscillator frequency and double the oscillator frequency. The peak heights are dependent on the coupling strength between oscillator and junction, the occupation number of the oscillator, the bias voltage and the junction temperature. I show how the peak height can be used as a measure of the oscillator temperature, demonstrating that the noise of a tunnel junction can be used for electronic thermometry of a nanomechanical oscillator.

Bose-Einstein condensates of dilute gases provide a rich and versatile platform to study both single-particle and many-body quantum phenomena. This thesis describes several experiments using a Bose-Einstein condensate of Rb-87 as a model system to study novel matter-wave effects that traditionally arise in vastly different systems, yet are difficult to access. We study the scattering of a particle from a repulsive potential barrier in the non-asymptotic regime, for which the collision dynamics are on-going. Using a Bose-Einstein condensate interacting with a sharp repulsive potential, two distinct transient scattering effects are observed: one due to the momentary deceleration of particles atop the barrier, and one due to the abrupt discontinuity in phase written on the wavepacket in position-space, akin to quantum reflection. Both effects lead to a redistribution of momenta, resulting in a rich interference pattern that may be used to reconstruct the single-particle wavefunction. In a second experiment, we study the response of a particle in a periodic potential to an applied force. By abruptly applying an external force to a Bose-Einstein condensate in a one-dimensional optical lattice, we show that the initial response of a particle in a periodic potential is in fact characterized by the bare mass, and only over timescales long compared to that of interband dynamics is the usual effective mass an appropriate description. This breakdown of the effective mass description on fast timescales is difficult to observe in traditional solid state systems due to their large bandgaps and fast timescale of interband dynamics. Both these experiments make use of the condensate's long coherence length, and the ability to shape and modulate the external potential on timescales fast compared to the particle dynamics, allowing for observation of novel matter-wave effects.

Bose-Einstein condensates of dilute gases provide a rich and versatile platform to study both single-particle and many-body quantum phenomena. This thesis describes several experiments using a Bose-Einstein condensate of Rb-87 as a model system to study novel matter-wave effects that traditionally arise in vastly different systems, yet are difficult to access. We study the scattering of a particle from a repulsive potential barrier in the non-asymptotic regime, for which the collision dynamics are on-going. Using a Bose-Einstein condensate interacting with a sharp repulsive potential, two distinct transient scattering effects are observed: one due to the momentary deceleration of particles atop the barrier, and one due to the abrupt discontinuity in phase written on the wavepacket in position-space, akin to quantum reflection. Both effects lead to a redistribution of momenta, resulting in a rich interference pattern that may be used to reconstruct the single-particle wavefunction. In a second experiment, we study the response of a particle in a periodic potential to an applied force. By abruptly applying an external force to a Bose-Einstein condensate in a one-dimensional optical lattice, we show that the initial response of a particle in a periodic potential is in fact characterized by the bare mass, and only over timescales long compared to that of interband dynamics is the usual effective mass an appropriate description. This breakdown of the effective mass description on fast timescales is difficult to observe in traditional solid state systems due to their large bandgaps and fast timescale of interband dynamics. Both these experiments make use of the condensate's long coherence length, and the ability to shape and modulate the external potential on timescales fast compared to the particle dynamics, allowing for observation of novel matter-wave effects.

The Atiyah-Singer index theorem, the Euler number, and the Hirzebruch signature are derived via the supersymmetric path integral. Concisely, the supersymmetric path integral is a combination of a bosonic and a femionic path integral. The action in the supersymmetric path integral includes here bosonic, fermionic- and isospin fields (backgroundfields), where the cross terms in the Lagrangian are nicely eliminated due to scaling of the fields and using techniques from spontaneous breaking of supersymmetry (that give rise to a mechanism, analogous to the Higgs-mechanism, but here regarding the so called superparticles instead).  Thus, the supersymmetric path integral is a product of three pathintegrals over the three given fields, respectively, that can be evaluated exactly by means of Gaussian integrals. The closely related Witten index is a measure of the failure of spontaneous breaking of supersymmetry. In addition, the basic concepts of supersymmetry breaking are reviewed.

No description available.

Computational quantum mechanics in the frame work of density functional theory (DFT) was used to investigate the effect of chemical impurities on high field conduction in polyethylene (PE). The impurity states in the band gap caused by common chemical impurities were characterized in terms of their “depth”, i.e. energy relative to their relevant band edge (valence band or conduction band), and in terms of the extent to which their wavefunctions were localized to a single polymer chain or extended across chains. It was found that impurity states can affect high field phenomena by providing “traps” for carriers, the depths of which were computed from first principle in agreement with estimates in literature. Since the square of the wavefunction is proportional to the spatial electron probability density, transfer of charge between chains requires wavefunctions which are extended across chains. Impurity states which are extended between chains can facilitate the inherently limited interchain charge transfer in PE, as the DFT study of iodine doped PE revealed. The introduction of iodine into PE increases conductivity by several orders of magnitude, increases hole mobility to a much greater extent than electron mobility, and decreases the activation energy of conduction from about 1 eV to about 0.8 eV. These characteristics were explained in terms of the impurity states introduced by iodine and wavefunctions of those states. Understanding the effect of iodine on conduction in PE provided a basis for understanding the effect of common chemical impurities on conduction therein. In particular, carbonyl and vinyl impurities create states which should promote hole mobility in a manner very similar to that caused by iodine. It was demonstrated that in the context of high field conduction in PE, besides the traditional focus on the depth of impurity states, it is important to study the spatial features of the states wavefunctions which are neither discussed nor accounted for in present models.

Computational quantum mechanics in the frame work of density functional theory (DFT) was used to investigate the effect of chemical impurities on high field conduction in polyethylene (PE). The impurity states in the band gap caused by common chemical impurities were characterized in terms of their “depth”, i.e. energy relative to their relevant band edge (valence band or conduction band), and in terms of the extent to which their wavefunctions were localized to a single polymer chain or extended across chains. It was found that impurity states can affect high field phenomena by providing “traps” for carriers, the depths of which were computed from first principle in agreement with estimates in literature. Since the square of the wavefunction is proportional to the spatial electron probability density, transfer of charge between chains requires wavefunctions which are extended across chains. Impurity states which are extended between chains can facilitate the inherently limited interchain charge transfer in PE, as the DFT study of iodine doped PE revealed. The introduction of iodine into PE increases conductivity by several orders of magnitude, increases hole mobility to a much greater extent than electron mobility, and decreases the activation energy of conduction from about 1 eV to about 0.8 eV. These characteristics were explained in terms of the impurity states introduced by iodine and wavefunctions of those states. Understanding the effect of iodine on conduction in PE provided a basis for understanding the effect of common chemical impurities on conduction therein. In particular, carbonyl and vinyl impurities create states which should promote hole mobility in a manner very similar to that caused by iodine. It was demonstrated that in the context of high field conduction in PE, besides the traditional focus on the depth of impurity states, it is important to study the spatial features of the states wavefunctions which are neither discussed nor accounted for in present models.