Magnetotransport in inhomogeneous magnetic fields

Quantum transport in inhomogeneous magnetic fields is investigated numerically in two-dimensional systems using the equation of motion method. In particular, the diffusion of electrons in random magnetic fields in the presence of additional weak uniform magnetic fields is examined. It is found that the conductivity is strongly suppressed by the additional uniform magnetic field and saturates when the uniform magnetic field becomes on the order of the fluctuation of the random magnetic field. The value of the conductivity at this saturation is found to be insensitive to the magnitude of the fluctuation of the random field. The effect of random potential on the magnetoconductance is also discussed.Comment: 5 pages, 5 figure

Analysis technique for exceptional points in open quantum systems and QPT analogy for the appearance of irreversibility

We propose an analysis technique for the exceptional points (EPs) occurring in the discrete spectrum of open quantum systems (OQS), using a semi-infinite chain coupled to an endpoint impurity as a prototype. We outline our method to locate the EPs in OQS, further obtaining an eigenvalue expansion in the vicinity of the EPs that gives rise to characteristic exponents. We also report the precise number of EPs occurring in an OQS with a continuum described by a quadratic dispersion curve. In particular, the number of EPs occurring in a bare discrete Hamiltonian of dimension $n_\textrm{D}$ is given by $n_\textrm{D} (n_\textrm{D} - 1)$; if this discrete Hamiltonian is then coupled to continuum (or continua) to form an OQS, the interaction with the continuum generally produces an enlarged discrete solution space that includes a greater number of EPs, specifically $2^{n_\textrm{C}} (n_\textrm{C} + n_\textrm{D}) [2^{n_\textrm{C}} (n_\textrm{C} + n_\textrm{D}) - 1]$, in which $n_\textrm{C}$ is the number of (non-degenerate) continua to which the discrete sector is attached. Finally, we offer a heuristic quantum phase transition analogy for the emergence of the resonance (giving rise to irreversibility via exponential decay) in which the decay width plays the role of the order parameter; the associated critical exponent is then determined by the above eigenvalue expansion.Comment: 16 pages, 7 figure

Regular black holes in quadratic gravity

The first-order correction of the perturbative solution of the coupled equations of the quadratic gravity and nonlinear electrodynamics is constructed, with the zeroth-order solution coinciding with the ones given by Ay\'on-Beato and Garc{\'\i}a and by Bronnikov. It is shown that a simple generalization of the Bronnikov's electromagnetic Lagrangian leads to the solution expressible in terms of the polylogarithm functions. The solution is parametrized by two integration constants and depends on two free parameters. By the boundary conditions the integration constants are related to the charge and total mass of the system as seen by a distant observer, whereas the free parameters are adjusted to make the resultant line element regular at the center. It is argued that various curvature invariants are also regular there that strongly suggests the regularity of the spacetime. Despite the complexity of the problem the obtained solution can be studied analytically. The location of the event horizon of the black hole, its asymptotics and temperature are calculated. Special emphasis is put on the extremal configuration

Charged cosmic strings interacting with gravitational and electromagnetic waves

Under a particular choice of the Ernst potential, we solve analytically the Einstein-Maxwell equations to derive a new exact solution depending on five parameters: the mass, the angular-momentum (per unit mass), the electromagnetic-field strength, k, the parameter-p and the Kerr-NUT parameter, l. This (Petrov Type D) solution is cylindrically-symmetric and represents the curved background around a charged, rotating cosmic string, surrounded by gravitational and electromagnetic waves, under the influence of the Kerr-NUT parameter. A C-energy study in the radiation zone suggests that both the incoming and the outgoing radiation is gravitational, strongly focused around the null direction and preserving its profile. In this case, the absence of the k-parameter from the C-energy implies that, away from the linear defect the electromagnetic field is too weak to contribute to the energy-content of the cylindrically-symmetric space-time under consideration. In order to explain this result, we have evaluated the Weyl and the Maxwell scalars near the axis of the linear defect and at the spatial infinity. Accordingly, we have found that the electromagnetic field is concentrated (mainly) in the vicinity of the axis, while falling-off prominently at large radial distances. However, as long as k differs from unity, the non-zero Kerr-NUT parameter enhances those scalars, both near the axis and at the spatial infinity, introducing some sort of gravitomagnetic contribution.Comment: 18 pages, Springer_Latex, accepted for publication in General Relativity and Gravitatio

GUTs in Curved Spacetime: Running Gravitational Constants, Newtonian Potential and the Quantum Corrected Gravitational Equations

The running coupling constants (in particular, the gravitational one) are studied in asymptotically free GUTs and in finite GUTs in curved spacetime, with explicit examples. The running gravitational coupling is used to calculate the leading quantum GUT corrections to the Newtonian potential, which turn out to be of logarithmic form in asymptotically free GUTs. A comparison with the effective theory for the conformal factor ---where leading quantum corrections to the Newtonian potential are again logarithmic--- is made. A totally asymptotically free $O(N)$ GUT with quantum higher derivative gravity is then constructed, using the technique of introducing renormalization group (RG) potentials in the space of couplings. RG equations for the cosmological and gravitational couplings in this theory are derived, and solved numerically, showing the influence of higher-derivative quantum gravity on the Newtonian potential. The RG-improved effective gravitational Lagrangian for asymptotically free massive GUTs is calculated in the strong (almost constant) curvature regime, and the non-singular De Sitter solution to the quantum corrected gravitational equations is subsequently discussed. Finally, possible extensions of the results here obtained are briefly outlined.Comment: LaTeX, 27 pages, 2 uu-figure

Green function techniques in the treatment of quantum transport at the molecular scale

The theoretical investigation of charge (and spin) transport at nanometer length scales requires the use of advanced and powerful techniques able to deal with the dynamical properties of the relevant physical systems, to explicitly include out-of-equilibrium situations typical for electrical/heat transport as well as to take into account interaction effects in a systematic way. Equilibrium Green function techniques and their extension to non-equilibrium situations via the Keldysh formalism build one of the pillars of current state-of-the-art approaches to quantum transport which have been implemented in both model Hamiltonian formulations and first-principle methodologies. We offer a tutorial overview of the applications of Green functions to deal with some fundamental aspects of charge transport at the nanoscale, mainly focusing on applications to model Hamiltonian formulations.Comment: Tutorial review, LaTeX, 129 pages, 41 figures, 300 references, submitted to Springer series "Lecture Notes in Physics

Phylogenetic and developmental studies into the evolution of an insect novelty.

The insects possess one of the most instantly recognisable bodyplans. This thesis addresses the evolution of one characteristic feature of the insects: the intercalary segment of the head. This small, appendageless segment is the homologue of the ancestral crustacean second antennal segment and its evolution underlies the loss of the second pair of antennae in the insect head. There is little consensus between different methods of phylogenetic reconstruction as to which crustacean group the insects are most closely related to. This question is addressed by compiling a multigene dataset and running a number of Bayesian phylogenetic analyses to investigate the effects of analysing the data under different models of evolution. In addition, Bayes factor hypothesis tests addressing the position of the insects within the Pancrustacea are described. The rest of the thesis addresses the developmental changes underlying the evolution of the intercalary segment. Almost everything that is known about the development of this segment in the insects comes from Drosophila. However, it is not clear exactly what constitutes the segment in the fly embryo. Specifically, it is unclear whether a pair of lobes behind the Drosophila stomodeum – the hypopharyngeal lobes – belong to the intercalary or mandibular segment. Using a detailed comparison of expression patterns between Drosophila and the red flour beetle Tribolium, the segmental affinity of these lobes is resolved. Finally, a screen to identify potential candidate genes for patterning the intercalary segment is described. The screen makes use of the Berkley Drosophila Genome Project expression pattern database to identify genes expressed in the segment of the fly. Having identified orthologues of the genes in Tribolium using the genome sequence on BeetleBase, their expression patterns are examined in the beetle. Genes with conserved expression are deemed good candidates for a more widespread role in patterning the segment.

Theoretical calculation of Tc for lead

Using our ab initio band structure results, we calculate the transition temperature of Pb according to the Gaspari-Gyorffy theory. The calculated value is half the experimental one. The discrepancy is attributed to the rigid muffin tin approximation. A simple method with no adjustable parameters is developed to account for this approximation. The new transition temperature is in excellent agreement with experiment.Nous calculons la température de transition supraconductrice du Pb avec la théorie de Gaspari et Gyorffy, en utilisant nos calculs ab initio de structure de bande. La valeur calculée ainsi est la moitié de la valeur expérimentale. Cet écart est attribué à l'approximation du potentiel muffin tin rigide. Pour tenir compte de cette approximation nous présentons une méthode simple, sans paramètre ajustable. La nouvelle valeur calculée de la température de transition est en accord excellent avec la valeur expérimentale

Ab initio bandstructure of lead

The self-consistent semi-relativistic APW method has been employed to calculate the bandstructure of lead and its electronic density of states from first principles. The results of the calculation agree with optical and specific heat data to within 30 and 1% respectively. Calculated frequencies for the second band hole surface agree with experimental Fermi surface results to within 4%. An application of the bandstructure results to the study of the electron-phonon interaction and superconductivity is made including the variation of these properties upon alloying lead with bismuth. These results are also in good agreement with experiment and demonstrate the increase of the superconducting transition temperature for the Pb-Bi alloys

Ab initio bandstructure of lead

The self-consistent semi-relativistic APW method has been employed to calculate the bandstructure of lead and its electronic density of states from first principles. The results of the calculation agree with optical and specific heat data to within 30 and 1% respectively. Calculated frequencies for the second band hole surface agree with experimental Fermi surface results to within 4%. An application of the bandstructure results to the study of the electron-phonon interaction and superconductivity is made including the variation of these properties upon alloying lead with bismuth. These results are also in good agreement with experiment and demonstrate the increase of the superconducting transition temperature for the Pb-Bi alloys