1,992 research outputs found
Low-Lying Excitations from the Yrast Line of Weakly Interacting Trapped Bosons
Through an extensive numerical study, we find that the low-lying,
quasi-degenerate eigenenergies of weakly-interacting trapped N bosons with
total angular momentum L are given in case of small L/N and sufficiently small
L by E = L hbar omega + g[N(N-L/2-1)+1.59 n(n-1)/2], where omega is the
frequency of the trapping potential and g is the strength of the repulsive
contact interaction; the last term arises from the pairwise repulsive
interaction among n octupole excitations and describes the lowest-lying
excitation spectra from the Yrast line. In this case, the quadrupole modes do
not interact with themselves and, together with the octupole modes, exhaust the
low-lying spectra which are separated from others by N-linear energy gaps.Comment: 5 pages, RevTeX, 2 figures, revised version, submitted to PR
Fractional time random walk subdiffusion and anomalous transport with finite mean residence times: faster, not slower
Continuous time random walk (CTRW) subdiffusion along with the associated
fractional Fokker-Planck equation (FFPE) is traditionally based on the premise
of random clock with divergent mean period. This work considers an alternative
CTRW and FFPE description which is featured by finite mean residence times
(MRTs) in any spatial domain of finite size. Transient subdiffusive transport
can occur on a very large time scale which can greatly exceed mean
residence time in any trap, , and even not being related to
it. Asymptotically, on a macroscale transport becomes normal for .
However, mesoscopic transport is anomalous. Differently from viscoelastic
subdiffusion no long-range anti-correlations among position increments are
required. Moreover, our study makes it obvious that the transient subdiffusion
and transport are faster than one expects from their normal asymptotic limit on
a macroscale. This observation has profound implications for anomalous
mesoscopic transport processes in biological cells because of macroscopic
viscosity of cytoplasm is finite
Roughening of Fracture Surfaces: the Role of Plastic Deformations
Post mortem analysis of fracture surfaces of ductile and brittle materials on
the m-mm and the nm scales respectively, reveal self affine graphs with an
anomalous scaling exponent . Attempts to use elasticity
theory to explain this result failed, yielding exponent up
to logarithms. We show that when the cracks propagate via plastic void
formations in front of the tip, followed by void coalescence, the voids
positions are positively correlated to yield exponents higher than 0.5.Comment: 4 pages, 6 figure
A Dichotomy Theorem for Homomorphism Polynomials
In the present paper we show a dichotomy theorem for the complexity of
polynomial evaluation. We associate to each graph H a polynomial that encodes
all graphs of a fixed size homomorphic to H. We show that this family is
computable by arithmetic circuits in constant depth if H has a loop or no edge
and that it is hard otherwise (i.e., complete for VNP, the arithmetic class
related to #P). We also demonstrate the hardness over the rational field of cut
eliminator, a polynomial defined by B\"urgisser which is known to be neither VP
nor VNP-complete in the field of two elements, if VP is not equal to VNP (VP is
the class of polynomials computable by arithmetic circuit of polynomial size)
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
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
Distinguishing fractional and white noise in one and two dimensions
We discuss the link between uncorrelated noise and Hurst exponent for one and
two-dimensional interfaces. We show that long range correlations cannot be
observed using one-dimensional cuts through two-dimensional self-affine
surfaces whose height distributions are characterized by a Hurst exponent lower
than -1/2. In this domain, fractional and white noise are not distinguishable.
A method analysing the correlations in two dimensions is necessary. For Hurst
exponents larger than -1/2, a crossover regime leads to a systematic over
estimate of the Hurst exponent.Comment: 3 pages RevTeX, 4 Postscript figure
Scale-free network topology and multifractality in weighted planar stochastic lattice
We propose a weighted planar stochastic lattice (WPSL) formed by the random
sequential partition of a plane into contiguous and non-overlapping blocks and
find that it evolves following several non-trivial conservation laws, namely
is independent of time , where
and are the length and width of the th block. Its dual on the
other hand, obtained by replacing each block with a node at its center and
common border between blocks with an edge joining the two vertices, emerges as
a network with a power-law degree distribution where
revealing scale-free coordination number disorder since
also describes the fraction of blocks having neighbours. To quantify the
size disorder, we show that if the th block is populated with then its distribution in the WPSL exhibits multifractality.Comment: 7 pages, 8 figures, To appear in New Journal of Physics (NJP
Is subdiffusional transport slower than normal?
We consider anomalous non-Markovian transport of Brownian particles in
viscoelastic fluid-like media with very large but finite macroscopic viscosity
under the influence of a constant force field F. The viscoelastic properties of
the medium are characterized by a power-law viscoelastic memory kernel which
ultra slow decays in time on the time scale \tau of strong viscoelastic
correlations. The subdiffusive transport regime emerges transiently for t<\tau.
However, the transport becomes asymptotically normal for t>>\tau. It is shown
that even though transiently the mean displacement and the variance both scale
sublinearly, i.e. anomalously slow, in time, ~ F t^\alpha,
~ t^\alpha, 0<\alpha<1, the mean displacement at each instant
of time is nevertheless always larger than one obtained for normal transport in
a purely viscous medium with the same macroscopic viscosity obtained in the
Markovian approximation. This can have profound implications for the
subdiffusive transport in biological cells as the notion of "ultra-slowness"
can be misleading in the context of anomalous diffusion-limited transport and
reaction processes occurring on nano- and mesoscales
Rotation of an atomic Bose-Einstein condensate with and without a quantized vortex
We theoretically examine the rotation of an atomic Bose-Einstein condensate
in an elliptical trap, both in the absence and presence of a quantized vortex.
Two methods of introducing the rotating potential are considered -
adiabatically increasing the rotation frequency at fixed ellipticity, and
adiabatically increasing the trap ellipticity at fixed rotation frequency.
Extensive simulations of the Gross-Pitaevskii equation are employed to map out
the points where the condensate becomes unstable and ultimately forms a vortex
lattice. We highlight the key features of having a quantized vortex in the
initial condensate. In particular, we find that the presence of the vortex
causes the instabilities to shift to lower or higher rotation frequencies,
depending on the direction of the vortex relative to the trap rotation.Comment: 15 pages, 8 figure
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