7,908 research outputs found
Cadabra: reference guide and tutorial
Cadabra is a computer algebra system for the manipulation of tensorial mathematical expressions such as they occur in “field theory problems”. It is aimed at, but not necessarily restricted to, high-energy physicists. It is constructed as a simple tree-manipulating core, a large collection of standalone algorithmic modules which act on the expression tree, and a set of modules responsible for output of nodes in the tree. All of these parts are written in C++. The input and output formats closely follow TEX, which in many cases means that cadabra is much simpler to use than other similar programs. It intentionally does not contain its own programming language; instead, new functionality is added by writing new modules in C++
Quantum states in a magnetic anti-dot
We study a new system in which electrons in two dimensions are confined by a
non homogeneous magnetic field. The system consists of a heterostructure with
on top of it a superconducting disk. We show that in this system electrons can
be confined into a dot region. This magnetic anti-dot has the interesting
property that the filling of the dot is a discrete function of the magnetic
field. The circulating electron current inside and outside the anti-dot can be
in opposite direction for certain bound states. And those states exhibit a
diamagnetic to paramagnetic transition with increasing magnetic field. The
absorption spectrum consists of many peaks, some of which violate Kohn's
theorem, and which is due to the coupling of the center of mass motion with the
other degrees of freedom.Comment: 6 pages, 12 ps figure
Positively charged magneto-excitons in a semiconductor quantum well
A variational calculation of the lower singlet and triplet states of
positively charged excitons (trions) confined to a single quantum well and in
the presence of a perpendicular magnetic field is presented. We study the
dependence of the energy levels and of the binding energy on the well width and
on the magnetic field strength. Our results are compared with the available
experimental data and show a good qualitative and quantitative agreement. A
singlet-triplet crossing is found which for a 200 \AA wide GaAs is predicted to
occur for B = 15 T.Comment: 5 figs. Submitted to PR
Higher Derivative Corrections to Eleven Dimensional Supergravity via Local Supersymmetry
In this paper we derive higher derivative corrections to the eleven
dimensional supergravity by applying the Noether method with respect to the N=1
local supersymmetry. An ansatz for the higher derivative effective action,
which includes quartic terms of the Riemann tensor, is parametrized by 132
parameters. Then we show that by the requirement of the local supersymmetry,
the higher derivative effective action is essentially described by two
parameters. The bosonic parts of these two superinvariants completely match
with the known results obtained by the perturbative calculations in the type
IIA superstring theory. Since the calculations are long and systematic, we
build the computer programming to check the cancellation of the variations
under the local supersymmetry. This is an extended version of our previous
paper hep-th/0508204.Comment: 67 pages, no figure, references added, typos correcte
Magneto-exciton in planar type II quantum dots
We study an exciton in a type II quantum dot, where the electron is confined
in the dot, but the hole is located in the barrier material. The exciton
properties are studied as a function of a perpendicular magnetic field using a
Hartree-fock mesh calculation. Our model system consists of a planar quantum
disk. Angular momentum (l) transitions are predicted with increasing magnetic
field. We also study the transition from a type I to a type II quantum dot
which is induced by changing the confinement potential of the hole. For
sufficiently large magnetic fields a re-entrant behaviour is found from
to and back to , which results in a transition
from type II to type I.Comment: 6 pages, 12 figure
Wigner crystallization in quantum electron bilayers
The phase diagram of quantum electron bilayers in zero magnetic field is
obtained using density functional theory. For large electron densities the
system is in the liquid phase, while for smaller densities the liquid may
freeze (Wigner crystallization) into four different crystalline phases; the
lattice symmetry and the critical density depend on the the inter-layer
distance. The phase boundaries between different Wigner crystals consist of
both first and second order transitions, depending on the phases involved, and
join the freezing curve at three different triple points.Comment: To appear in Europhys. Lett. (11 pages in REVTEX + 2 figures in
postscript
Induced order and reentrant melting in classical two-dimensional binary clusters
A binary system of classical charged particles interacting through a dipole
repulsive potential and confined in a two-dimensional hardwall trap is studied
by Brownian dynamics simulations. We found that the presence of small particles
\emph{stabilizes} the angular order of the system as a consequence of radial
fluctuations of the small particles. There is an optimum in the increased
rigidity of the cluster as function of the number of small particles. The small
(i.e. defect) particles melt at a lower temperature compared to the big
particles and exhibit a \emph{reentrant} behavior in its radial order that is
induced by the intershell rotation of the big particles.Comment: 7 pages, 3 figure
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