20,340 research outputs found
On the propagation of semiclassical Wigner functions
We establish the difference between the propagation of semiclassical Wigner
functions and classical Liouville propagation. First we re-discuss the
semiclassical limit for the propagator of Wigner functions, which on its own
leads to their classical propagation. Then, via stationary phase evaluation of
the full integral evolution equation, using the semiclassical expressions of
Wigner functions, we provide the correct geometrical prescription for their
semiclassical propagation. This is determined by the classical trajectories of
the tips of the chords defined by the initial semiclassical Wigner function and
centered on their arguments, in contrast to the Liouville propagation which is
determined by the classical trajectories of the arguments themselves.Comment: 9 pages, 1 figure. To appear in J. Phys. A. This version matches the
one set to print and differs from the previous one (07 Nov 2001) by the
addition of two references, a few extra words of explanation and an augmented
figure captio
Convergence of the Crank-Nicolson-Galerkin finite element method for a class of nonlocal parabolic systems with moving boundaries
The aim of this paper is to establish the convergence and error bounds to the
fully discrete solution for a class of nonlinear systems of reaction-diffusion
nonlocal type with moving boundaries, using a linearized
Crank-Nicolson-Galerkin finite element method with polynomial approximations of
any degree. A coordinate transformation which fixes the boundaries is used.
Some numerical tests to compare our Matlab code with some existing moving
finite elements methods are investigated
Experimental quantum computing without entanglement
Entanglement is widely believed to lie at the heart of the advantages offered
by a quantum computer. This belief is supported by the discovery that a
noiseless (pure) state quantum computer must generate a large amount of
entanglement in order to offer any speed up over a classical computer. However,
deterministic quantum computation with one pure qubit (DQC1), which employs
noisy (mixed) states, is an efficient model that generates at most a marginal
amount of entanglement. Although this model cannot implement any arbitrary
algorithm it can efficiently solve a range of problems of significant
importance to the scientific community. Here we experimentally implement a
first-order case of a key DQC1 algorithm and explicitly characterise the
non-classical correlations generated. Our results show that while there is no
entanglement the algorithm does give rise to other non-classical correlations,
which we quantify using the quantum discord - a stronger measure of
non-classical correlations that includes entanglement as a subset. Our results
suggest that discord could replace entanglement as a necessary resource for a
quantum computational speed-up. Furthermore, DQC1 is far less resource
intensive than universal quantum computing and our implementation in a scalable
architecture highlights the model as a practical short-term goal.Comment: 5 pages, 4 figure
Structural and insulator-to-metal phase transition at 50 GPa in GdMnO3
We present a study of the effect of very high pressure on the orthorhombic
perovskite GdMnO3 by Raman spectroscopy and synchrotron x-ray diffraction up to
53.2 GPa. The experimental results yield a structural and insulator-to-metal
phase transition close to 50 GPa, from an orthorhombic to a metrically cubic
structure. The phase transition is of first order with a pressure hysteresis of
about 6 GPa. The observed behavior under very high pressure might well be a
general feature in rare-earth manganites.Comment: 4 pages, 3 figures and 2 table
Microbiological analysis of Portugal northern coastal beach sands
Poster apresentado no XIV Congresso Nacional de Bioquímica, Vilamoura, Portugal, 2004
Critical Behavior of a Three-State Potts Model on a Voronoi Lattice
We use the single-histogram technique to study the critical behavior of the
three-state Potts model on a (random) Voronoi-Delaunay lattice with size
ranging from 250 to 8000 sites. We consider the effect of an exponential decay
of the interactions with the distance,, with , and
observe that this system seems to have critical exponents and
which are different from the respective exponents of the three-state Potts
model on a regular square lattice. However, the ratio remains
essentially the same. We find numerical evidences (although not conclusive, due
to the small range of system size) that the specific heat on this random system
behaves as a power-law for and as a logarithmic divergence for
and Comment: 3 pages, 5 figure
The Word Problem for Omega-Terms over the Trotter-Weil Hierarchy
For two given -terms and , the word problem for
-terms over a variety asks whether
in all monoids in . We show that the
word problem for -terms over each level of the Trotter-Weil Hierarchy
is decidable. More precisely, for every fixed variety in the Trotter-Weil
Hierarchy, our approach yields an algorithm in nondeterministic logarithmic
space (NL). In addition, we provide deterministic polynomial time algorithms
which are more efficient than straightforward translations of the
NL-algorithms. As an application of our results, we show that separability by
the so-called corners of the Trotter-Weil Hierarchy is witnessed by
-terms (this property is also known as -reducibility). In
particular, the separation problem for the corners of the Trotter-Weil
Hierarchy is decidable
Periodic orbit bifurcations and scattering time delay fluctuations
We study fluctuations of the Wigner time delay for open (scattering) systems
which exhibit mixed dynamics in the classical limit. It is shown that in the
semiclassical limit the time delay fluctuations have a distribution that
differs markedly from those which describe fully chaotic (or strongly
disordered) systems: their moments have a power law dependence on a
semiclassical parameter, with exponents that are rational fractions. These
exponents are obtained from bifurcating periodic orbits trapped in the system.
They are universal in situations where sufficiently long orbits contribute. We
illustrate the influence of bifurcations on the time delay numerically using an
open quantum map.Comment: 9 pages, 3 figures, contribution to QMC200
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