634 research outputs found
Matrix permanent and quantum entanglement of permutation invariant states
We point out that a geometric measure of quantum entanglement is related to
the matrix permanent when restricted to permutation invariant states. This
connection allows us to interpret the permanent as an angle between vectors. By
employing a recently introduced permanent inequality by Carlen, Loss and Lieb,
we can prove explicit formulas of the geometric measure for permutation
invariant basis states in a simple way.Comment: 10 page
Rainbow matchings in Dirac bipartite graphs
This is the peer reviewed version of the following article: Coulson, M, Perarnau, G. Rainbow matchings in Dirac bipartite graphs. Random Struct Alg. 2019; 55: 271– 289., which has been published in final form at https://doi.org/10.1002/rsa.20835. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Use of Self-Archived VersionsWe show the existence of rainbow perfect matchings in µn-bounded edge colorings of Dirac bipartite graphs, for a sufficiently small µ¿>¿0. As an application of our results, we obtain several results on the existence of rainbow k-factors in Dirac graphs and rainbow spanning subgraphs of bounded maximum degree on graphs with large minimum degree
Link and subgraph likelihoods in random undirected networks with fixed and partially fixed degree sequence
The simplest null models for networks, used to distinguish significant
features of a particular network from {\it a priori} expected features, are
random ensembles with the degree sequence fixed by the specific network of
interest. These "fixed degree sequence" (FDS) ensembles are, however, famously
resistant to analytic attack. In this paper we introduce ensembles with
partially-fixed degree sequences (PFDS) and compare analytic results obtained
for them with Monte Carlo results for the FDS ensemble. These results include
link likelihoods, subgraph likelihoods, and degree correlations. We find that
local structural features in the FDS ensemble can be reasonably well estimated
by simultaneously fixing only the degrees of few nodes, in addition to the
total number of nodes and links. As test cases we use a food web, two protein
interaction networks (\textit{E. coli, S. cerevisiae}), the internet on the
autonomous system (AS) level, and the World Wide Web. Fixing just the degrees
of two nodes gives the mean neighbor degree as a function of node degree,
, in agreement with results explicitly obtained from rewiring. For
power law degree distributions, we derive the disassortativity analytically. In
the PFDS ensemble the partition function can be expanded diagrammatically. We
obtain an explicit expression for the link likelihood to lowest order, which
reduces in the limit of large, sparse undirected networks with links and
with to the simple formula . In a
similar limit, the probability for three nodes to be linked into a triangle
reduces to the factorized expression .Comment: 17 pages, includes 11 figures; first revision: shortened to 14 pages
(7 figures), added discussion of subgraph counts, deleted discussion of
directed network
Solution of the tunneling-percolation problem in the nanocomposite regime
We noted that the tunneling-percolation framework is quite well understood at
the extreme cases of percolation-like and hopping-like behaviors but that the
intermediate regime has not been previously discussed, in spite of its
relevance to the intensively studied electrical properties of nanocomposites.
Following that we study here the conductivity of dispersions of particle
fillers inside an insulating matrix by taking into account explicitly the
filler particle shapes and the inter-particle electron tunneling process. We
show that the main features of the filler dependencies of the nanocomposite
conductivity can be reproduced without introducing any \textit{a priori}
imposed cut-off in the inter-particle conductances, as usually done in the
percolation-like interpretation of these systems. Furthermore, we demonstrate
that our numerical results are fully reproduced by the critical path method,
which is generalized here in order to include the particle filler shapes. By
exploiting this method, we provide simple analytical formulas for the composite
conductivity valid for many regimes of interest. The validity of our
formulation is assessed by reinterpreting existing experimental results on
nanotube, nanofiber, nanosheet and nanosphere composites and by extracting the
characteristic tunneling decay length, which is found to be within the expected
range of its values. These results are concluded then to be not only useful for
the understanding of the intermediate regime but also for tailoring the
electrical properties of nanocomposites.Comment: 13 pages with 8 figures + 10 pages with 9 figures of supplementary
material (Appendix B
Tunneling-percolation origin of nonuniversality: theory and experiments
A vast class of disordered conducting-insulating compounds close to the
percolation threshold is characterized by nonuniversal values of transport
critical exponent t, in disagreement with the standard theory of percolation
which predicts t = 2.0 for all three dimensional systems. Various models have
been proposed in order to explain the origin of such universality breakdown.
Among them, the tunneling-percolation model calls into play tunneling processes
between conducting particles which, under some general circumstances, could
lead to transport exponents dependent of the mean tunneling distance a. The
validity of such theory could be tested by changing the parameter a by means of
an applied mechanical strain. We have applied this idea to universal and
nonuniversal RuO2-glass composites. We show that when t > 2 the measured
piezoresistive response \Gamma, i. e., the relative change of resistivity under
applied strain, diverges logarithmically at the percolation threshold, while
for t = 2, \Gamma does not show an appreciable dependence upon the RuO2 volume
fraction. These results are consistent with a mean tunneling dependence of the
nonuniversal transport exponent as predicted by the tunneling-percolation
model. The experimental results are compared with analytical and numerical
calculations on a random-resistor network model of tunneling-percolation.Comment: 13 pages, 12 figure
Decision and function problems based on boson sampling
Boson sampling is a mathematical problem that is strongly believed to be
intractable for classical computers, whereas passive linear interferometers can
produce samples efficiently. So far, the problem remains a computational
curiosity, and the possible usefulness of boson-sampling devices is mainly
limited to the proof of quantum supremacy. The purpose of this work is to
investigate whether boson sampling can be used as a resource of decision and
function problems that are computationally hard, and may thus have
cryptographic applications. After the definition of a rather general
theoretical framework for the design of such problems, we discuss their
solution by means of a brute-force numerical approach, as well as by means of
non-boson samplers. Moreover, we estimate the sample sizes required for their
solution by passive linear interferometers, and it is shown that they are
independent of the size of the Hilbert space.Comment: Close to the version published in PR
Assessment of factors influencing the occurrence and pathological picture of sarcoptic mange in red foxes (Vulpes vulpes)
Many-particle interference beyond many-boson and many-fermion statistics
Identical particles exhibit correlations even in the absence of
inter-particle interaction, due to the exchange (anti)symmetry of the
many-particle wavefunction. Two fermions obey the Pauli principle and
anti-bunch, whereas two bosons favor bunched, doubly occupied states. Here, we
show that the collective interference of three or more particles leads to a
much more diverse behavior than expected from the boson-fermion dichotomy known
from quantum statistical mechanics. The emerging complexity of many-particle
interference is tamed by a simple law for the strict suppression of events in
the Bell multiport beam splitter. The law shows that counting events are
governed by widely species-independent interference, such that bosons and
fermions can even exhibit identical interference signatures, while their
statistical character remains subordinate. Recent progress in the preparation
of tailored many-particle states of bosonic and fermionic atoms promises
experimental verification and applications in novel many-particle
interferometers.Comment: 12 pages, 5 figure
- …