3,733 research outputs found
A perturbative approach to Dirac observables and their space-time algebra
We introduce a general approximation scheme in order to calculate gauge
invariant observables in the canonical formulation of general relativity. Using
this scheme we will show how the observables and the dynamics of field theories
on a fixed background or equivalently the observables of the linearized theory
can be understood as an approximation to the observables in full general
relativity. Gauge invariant corrections can be calculated up to an arbitrary
high order and we will explicitly calculate the first non--trivial correction.
Furthermore we will make a first investigation into the Poisson algebra between
observables corresponding to fields at different space--time points and
consider the locality properties of the observables.Comment: 23 page
Formation and Size-Dependence of Vortex Shells in Mesoscopic Superconducting Niobium Disks
Recent experiments [I.V. Grigorieva et al., Phys. Rev. Lett. 96, 077005
(2006)] on visualization of vortices using the Bitter decoration technique
revealed vortex shells in mesoscopic superconducting Nb disks containing up to
L=40 vortices. Some of the found configurations did not agree with those
predicted theoretically. We show here that this discrepancy can be traced back
to the larger disks with radii R ~ 1 to 2.5\mu m, i.e., R ~ 50-100\xi(0) used
in the experiment, while in previous theoretical studies vortex states with
vorticity L < 40 were analyzed for smaller disks with R ~ 5-20\xi(0). The
present analysis is done for thin disks (mesoscopic regime) and for thick
(macroscopic) disks where the London screening is taken into account. We found
that the radius of the superconducting disk has a pronounced influence on the
vortex configuration in contrast to, e.g., the case of parabolic confined
charged particles. The missing vortex configurations and the region of their
stability are found, which are in agreement with those observed in the
experiment.Comment: 12 pages, 1 table, 12 figure
Magnetoresistance of a 2-dimensional electron gas in a random magnetic field
We report magnetoresistance measurements on a two-dimensional electron gas
(2DEG) made from a high mobility GaAs/AlGaAs heterostructure, where the
externally applied magnetic field was expelled from regions of the
semiconductor by means of superconducting lead grains randomly distributed on
the surface of the sample. A theoretical explanation in excellent agreement
with the experiment is given within the framework of the semiclassical
Boltzmann equation.Comment: REVTEX 3.0, 11 pages, 3 Postscript figures appended. The manuscript
can also be obtained from our World Wide Web server:
http://roemer.fys.ku.dk/randmag.ht
A Comparative Study of Laplacians and Schroedinger-Lichnerowicz-Weitzenboeck Identities in Riemannian and Antisymplectic Geometry
We introduce an antisymplectic Dirac operator and antisymplectic gamma
matrices. We explore similarities between, on one hand, the
Schroedinger-Lichnerowicz formula for spinor bundles in Riemannian spin
geometry, which contains a zeroth-order term proportional to the Levi-Civita
scalar curvature, and, on the other hand, the nilpotent, Grassmann-odd,
second-order \Delta operator in antisymplectic geometry, which in general has a
zeroth-order term proportional to the odd scalar curvature of an arbitrary
antisymplectic and torsionfree connection that is compatible with the measure
density. Finally, we discuss the close relationship with the two-loop scalar
curvature term in the quantum Hamiltonian for a particle in a curved Riemannian
space.Comment: 55 pages, LaTeX. v2: Subsection 3.10 expanded. v3: Reference added.
v4: Published versio
Kerr-Schild spacetimes with (A)dS background
General properties of Kerr-Schild spacetimes with (A)dS background in
arbitrary dimension are studied. It is shown that the geodetic Kerr-Schild
vector k is a multiple WAND of the spacetime. Einstein Kerr-Schild spacetimes
with non-expanding k are shown to be of Weyl type N, while the expanding
spacetimes are of type II or D. It is shown that this class of spacetimes obeys
the optical constraint. This allows us to solve Sachs equation, determine
r-dependence of boost weight zero components of the Weyl tensor and discuss
curvature singularities.Comment: 17 pages, minor change
String loop corrections to the universal hypermultiplet
We study loop corrections to the universal dilaton supermultiplet for type
IIA strings compactified on Calabi-Yau threefolds. We show that the
corresponding quaternionic kinetic terms receive non-trivial one-loop
contributions proportional to the Euler number of the Calabi-Yau manifold,
while the higher-loop corrections can be absorbed by field redefinitions. The
corrected metric is no longer Kahler. Our analysis implies in particular that
the Calabi-Yau volume is renormalized by loop effects which are present even in
higher orders, while there are also one-loop corrections to the Bianchi
identities for the NS and RR field strengths.Comment: 30 pages, harvmac, 1 figure. v2: minor typos corrected. Version to
appear in Classical and Quantum Gravit
Off center centers in a quantum well in the presence of a perpendicular magnetic field: angular momentum transition and magnetic evaporation
We investigate the effect of the position of the donor in the quantum well on
the energy spectrum and the oscillator strength of the D- system in the
presence of a perpendicular magnetic field. As a function of the magnetic field
we find that when the D- centers are placed sufficiently off-center they
undergo singlet-triplet transitions which are similar to those found in
many-electron parabolic quantum dots. The main difference is that the number of
such transitions depends on the position of the donor and only a finite number
of such singlet-triplet transitions are found as function of the strength of
the magnetic field. For sufficiently large magnetic fields the two electron
system becomes unbound. For the near center D- system no singlet-triplet and no
unbinding of the D- is found with increasing magnetic field. A magnetic field
vs. donor position phase diagram is presented that depends on the width of the
quantum well.Comment: 16 pages, 17 figures. Accepted for publication in Phys. Rev.
Localized Wavefunctions and Magnetic Band Structure for Lateral Semiconductor Superlattices
In this paper we present calculations on the electronic band structure of a
two-dimensional lateral superlattice subject to a perpendicular magnetic field
by employing a projection operator technique based on the ray-group of
magnetotranslation operators. We construct a new basis of appropriately
symmetrized Bloch-like wavefunctions as linear combination of well-localized
magnetic-Wannier functions. The magnetic field was consistently included in the
Wannier functions defined in terms of free-electron eigenfunctions in the
presence of external magnetic field in the symmetric gauge. Using the above
basis, we calculate the magnetic energy spectrum of electrons in a lateral
superlattice with bi-directional weak electrostatic modulation. Both a square
lattice and a triangular one are considered as special cases. Our approach
based on group theory handles the cases of integer and rational magnetic fluxes
in a uniform way and the provided basis could be convenient for further both
analytic and numerical calculations.Comment: 19 pages, 5 figures. accepted to Int. J. Mod. Phys. B (April 2006
Magnetic field dependence of the energy of negatively charged excitons in semiconductor quantum wells
A variational calculation of the spin-singlet and spin-triplet state of a
negatively charged exciton (trion) confined to a single quantum well and in the
presence of a perpendicular magnetic field is presented. We calculated the
probability density and the pair correlation function of the singlet and
triplet trion states. The dependence of the energy levels and of the binding
energy on the well width and on the magnetic field strength was investigated.
We compared our results with the available experimental data on GaAs/AlGaAs
quantum wells and find that in the low magnetic field region (B<18 T) the
observed transition are those of the singlet and the dark triplet trion (with
angular momentum ), while for high magnetic fields (B>25 T) the dark
trion becomes optically inactive and possibly a transition to a bright triplet
trion (angular momentum ) state is observed.Comment: 9 pages, 10 figures submitted to Phys. Rev.
Exciton and negative trion dissociation by an external electric field in vertically coupled quantum dots
We study the Stark effect for an exciton confined in a pair of vertically
coupled quantum dots. A single-band approximation for the hole and a parabolic
lateral confinement potential are adopted which allows for the separation of
the lateral center-of-mass motion and consequently for an exact numerical
solution of the Schr\"odinger equation. We show that for intermediate tunnel
coupling the external electric field leads to the dissociation of the exciton
via an avoided crossing of bright and dark exciton energy levels which results
in an atypical form of the Stark shift. The electric-field-induced dissociation
of the negative trion is studied using the approximation of frozen lateral
degrees of freedom. It is shown that in a symmetric system of coupled dots the
trion is more stable against dissociation than the exciton. For an asymmetric
system of coupled dots the trion dissociation is accompanied by a positive
curvature of the recombination energy line as a function of the electric field.Comment: PRB - in prin
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