2,575 research outputs found
Multiple Invaded Consolidating Materials
We study a multiple invasion model to simulate corrosion or intrusion
processes. Estimated values for the fractal dimension of the invaded region
reveal that the critical exponents vary as function of the generation number
, i.e., with the number of times the invasion process takes place. The
averaged mass of the invaded region decreases with a power-law as a
function of , , where the exponent . We
also find that the fractal dimension of the invaded cluster changes from
to . This result confirms that the
multiple invasion process follows a continuous transition from one universality
class (NTIP) to another (optimal path). In addition, we report extensive
numerical simulations that indicate that the mass distribution of avalanches
has a power-law behavior and we find that the exponent
governing the power-law changes continuously as a
function of the parameter . We propose a scaling law for the mass
distribution of avalanches for different number of generations .Comment: 8 pages and 16 figure
Self-consistent fragmented excited states of trapped condensates
Self-consistent excited states of condensates are solutions of the
Gross-Pitaevskii (GP) equation and have been amply discussed in the literature
and related to experiments. By introducing a more general mean-field which
includes the GP one as a special case, we find a new class of self-consistent
excited states. In these states macroscopic numbers of bosons reside in
different one-particle functions, i.e., the states are fragmented. Still, a
single chemical potential is associated with the condensate. A numerical
example is presented, illustrating that the energies of the new, fragmented,
states are much lower than those of the GP excited states, and that they are
stable to variations of the particle number and shape of the trap potential.Comment: (11 pages 2 figures, submitted to PRL
Skeleton and fractal scaling in complex networks
We find that the fractal scaling in a class of scale-free networks originates
from the underlying tree structure called skeleton, a special type of spanning
tree based on the edge betweenness centrality. The fractal skeleton has the
property of the critical branching tree. The original fractal networks are
viewed as a fractal skeleton dressed with local shortcuts. An in-silico model
with both the fractal scaling and the scale-invariance properties is also
constructed. The framework of fractal networks is useful in understanding the
utility and the redundancy in networked systems.Comment: 4 pages, 2 figures, final version published in PR
Testing equivalence of pure quantum states and graph states under SLOCC
A set of necessary and sufficient conditions are derived for the equivalence
of an arbitrary pure state and a graph state on n qubits under stochastic local
operations and classical communication (SLOCC), using the stabilizer formalism.
Because all stabilizer states are equivalent to a graph state by local unitary
transformations, these conditions constitute a classical algorithm for the
determination of SLOCC-equivalence of pure states and stabilizer states. This
algorithm provides a distinct advantage over the direct solution of the
SLOCC-equivalence condition for an unknown invertible local operator S, as it
usually allows for easy detection of states that are not SLOCC-equivalent to
graph states.Comment: 9 pages, to appear in International Journal of Quantum Information;
Minor typos corrected, updated references
Analytical results for a trapped, weakly-interacting Bose-Einstein condensate under rotation
We examine the problem of a repulsive, weakly-interacting and harmonically
trapped Bose-Einstein condensate under rotation. We derive a simple analytic
expression for the energy incorporating the interactions when the angular
momentum per particle is between zero and one and find that the interaction
energy decreases linearly as a function of the angular momentum in agreement
with previous numerical and limiting analytical studies.Comment: 3 pages, RevTe
Shape deformations and angular momentum transfer in trapped Bose-Einstein condensates
Angular momentum can be transferred to a trapped Bose-Einstein condensate by
distorting its shape with an external rotating field, provided the rotational
frequency is larger than a critical frequency fixed by the energy and angular
momentum of the excited states of the system. By using the Gross-Pitaevskii
equation and sum rules, we explore the dependence of such a critical frequency
on the multipolarity of the excitations and the asymmetry of the confining
potential. We also discuss its possible relevance for vortex nucleation in
rotating traps.Comment: 4 pages revtex, 2 figures include
Double-Slit Interferometry with a Bose-Einstein Condensate
A Bose-Einstein "double-slit" interferometer has been recently realized
experimentally by (Y. Shin et. al., Phys. Rev. Lett. 92 50405 (2004)). We
analyze the interferometric steps by solving numerically the time-dependent
Gross-Pitaevski equation in three-dimensional space. We focus on the
adiabaticity time scales of the problem and on the creation of spurious
collective excitations as a possible source of the strong dephasing observed
experimentally. The role of quantum fluctuations is discussed.Comment: 4 pages, 3 figure
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