Multidimensional quantum tunnelling is an important tool that is used in many areas of physics and chemistry. Sub-barrier fusion reactions of heavy-ions are governed by quantum tunnelling. However, the complexity of the structures of heavy-ions does not allow us to use simple one-dimensional tunnelling equations to and the tunnelling probabilities. Instead of this one should consider all the degrees of freedom which affect the phenomenon and accordingly the intrinsic structure or the deformation of the nuclei must be taken into account in the modelling of heavy-ion fusion. These extra degrees of freedom result in a coupling potential term in the Schrodinger equation of the fusing system. In this thesis 16O + 238 U system is considered. Only the rotational deformation of Uranium is assumed and the coupling potential term is calculated for this system by using two diffrent potential types, namely the Woods-Saxon potential and the double folding potential. Using this term in the Schrodinger equation fusion probability and theoretical cross section are calculated. A discussion that addresses then necessity of multidimensional formulation is given. Besides this point the effects of the choice of the potential type are shown.

We investigate the simulations of the the Schrödinger equation using the onedimensional quantum lattice Boltzmann (QLB) scheme and the irregular behaviour of solution. We isolate error due to approximation of the Schrödinger solution with the non-relativistic limit of the Dirac equation and numerical error in solving the Dirac equation. Detailed analysis of the original scheme showed it to be first order accurate. By discretizing the Dirac equation consistently on both sides we derive a second order accurate QLB scheme with the same evolution algorithm as the original and requiring only a one-time unitary transformation of the initial conditions and final output. We show that initializing the scheme in a way that is consistent with the non-relativistic limit supresses the oscillations around the Schrödinger solution. However, we find the QLB scheme better suited to simulation of relativistic quantum systems governed by the Dirac equation and apply it to the Klein paradox. We reproduce the quantum tunnelling results of previous research and show second order convergence to the theoretical wave packet transmission probability. After identifying and correcting the error in the multidimensional extension of the original QLB scheme that produced asymmetric solutions, we expand our second order QLB scheme to multiple dimensions. Next we use the QLB scheme to simulate Klein tunnelling of massless charge carriers in graphene, compare with theoretical solutions and study the dependence of charge transmission on the incidence angle, wave packet and potential barrier shape. To do this we derive a representation of the Dirac-like equation governing charge carriers in graphene for the one-dimensional QLB scheme, and derive a two-dimensional second order graphene QLB scheme for more accurate simulation of wave packets. We demonstrate charge confinement in a graphene device using a configuration of multiple smooth potential barriers, thereby achieving a high ratio of on/off current with potential application in graphene field effect transistors for logic devices. To allow simulation in magnetic or pseudo-magnetic fields created by deformation of graphene, we expand the scheme to include vector potentials. In addition, we derive QLB schemes for bilayer graphene and the non-linear Dirac equation governing Bose-Einstein condensates in hexagonal optical lattices.

Ce travail de thèse décrit (i) la synthèse de complexes hétérométalliques d’ions 3d et 4f à partir de précuseurs de Mn, Fe et Co, de sels de lanthanides et de ligands organiques et (ii) l'étude de leurs structures et propriétés. 41 complexes polynucléaires ont été synthétisés dans le cadre de ce travail. Les structures moléculaires de tous les composés ont été déterminées par diffraction des rayons X. Les propriétés magnétiques de 22 complexes ont été étudiées, dont quatre montrent une relaxation lente de leur aimantation considérée comme la signature d’un comportement de molécule-aimant. L'activité catalytique du complexe {Mn4Dy6Li2} calciné a aussi été étudiée et s'est avérée efficace pour l'oxydation du monoxyde de carbone. L'étude systématique de complexes isostructuraux de lanthanides a montré que l'incorporation d’ions 4f peut introduire de l’anisotropie magnétique et que l’ion DyIII est généralement le meilleur candidat pour le ciblage de molécules-aimants hétérométalliques 3d- 4f. / This dissertation describes the syntheses of 3d-4f-metal complexes starting from preformed compounds of Mn, Fe and Co, lanthanide salts and organic ligands and also the investigation of their structures and properties. 41 new polynuclear heterometallic metal complexes were synthesised in the course of this work with different interesting properties. The structures of all obtained compounds have been confirmed using X-ray diffraction. The magnetic properties of 22 complexes were studied, of which four show frequency dependent out-of-phase signals as expected for SMMs. The catalytic activity of calcinated {Mn4Dy6Li2} was investigated and proved effective for the oxidation of CO. It was established, that the use of precursors leads to new families of compounds. Moreover the study of isostructural compounds across the lanthanide series showed 1) that the incorporation of 4f ions introduces magnetic anisotropy and 2) DyIII is usually the best candidate for targeting 3d-4f-SMMs.

In this thesis, superconducting nanostructures for quantum detection of electromagnetic radiation are studied. In this regard, electrodynamics of topological excitations in 1D superconducting nanowires and 2D superconducting nanostrips is investigated. Topological excitations in superconducting nanowires and nanostrips lead to crucial deviation from the bulk properties. In 1D superconductors, topological excitations are phase slippages of the order parameter in which the magnitude of the order parameter locally drops to zero and the phase jumps by integer multiple of 2\pi. We investigate the effect of high-frequency field on 1D superconducting nanowires and derive the complex conductivity. Our study reveals that the rate of the quantum phase slips (QPSs) is exponentially enhanced under high-frequency irradiation. Based on this finding, we propose an energy-resolving terahertz radiation detector using superconducting nanowires. In superconducting nanostrips, topological fluctuations are the magnetic vortices. The motion of magnetic vortices result in dissipative processes that limit the efficiency of devices using superconducting nanostrips. It will be shown that in a multi-layer structure, the potential barrier for vortices to penetrate inside the structure is elevated. This results in significant reduction in dissipative process. In superconducting nanowire single photon detectors (SNSPDs), vortex motion results in dark counts and reduction of the critical current which results in low efficiency in these detectors. Based on this finding, we show that a multi-layer SNSPD is capable of approaching characteristics of an ideal single photon detector in terms of the dark count and quantum efficiency. It is shown that in a multi-layer SNSPD the photon coupling efficiency is dramatically enhanced due to the increase in the optical path of the incident photon.

The subject of study of this thesis is the Kerr-Newman-(anti-)de Sitter space- time, a rotating and charged exact black-hole solution of the Einstein-Maxwell equations with a non-zero cosmological constant. In the first part of the thesis we examine admissible extremal configurations, present the corresponding Penrose diagrams, and investigate the effects of frame-dragging. In the second part, we follow the motion of charged particles via the Lagrangian formalism, focusing on the equatorial plane and the axis where we arrived at some analytic results con- cerning the trajectories. Static particles, effective potentials and - in the case of the equatorial plane - stationary circular orbits are examined. We also perform numerical simulations of particle motion to be able to check our analytic results and also to foster our intuition regarding the behaviour of the test particles. The last part concerns quantum tunnelling of particles through the space-time's hori- zons, specifically the null geodesic method. The main goal of these computations is to obtain horizon temperatures, in which we succeed up to a constant multi- plicative factor. We discuss various pitfalls of the method and stake out a possible approach when applying it to the extreme horizons present in KN(a)dS. 1

This work deals with the theoretical foundations of electron emission into vacuum, various types of emissions, focused on the cold-emission and Schottky emission and the principle of quantum tunneling. The next part deals with the technical implementation of electron sources with a detailed study of the methodology of laboratory production of cathodes by electrochemical etching and construction of electron microscopes, using field-emission sources. This work also contains methods for measuring, processing and evaluation of electrical characteristics of emission sources.