23 research outputs found
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 is given by ; 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 , in which
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 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