1,176 research outputs found
Spontaneous symmetry breaking and the limit
We point out a basic ambiguity in the limit of the connected
propagator in a spontaneously broken phase. This may represent an indication
that the conventional singlet Higgs boson, rather than being a purely massive
field, might have a gap-less branch. This would dominate the energy spectrum
for and give rise to a very weak, long-range force. The
natural interpretation is in terms of density fluctuations of the `Higgs
condensate': in the region of very long wavelengths, infinitely larger than the
Fermi scale, it cannot be treated as a purely classical c-number field.Comment: 17 pages, LaTex, small changes and some comments adde
Probing Fuzzballs with Particles, Waves and Strings
We probe D1D5 micro-state geometries with massless particles, waves and
strings. To this end, we study geodetic motion, Klein-Gordon equation and
string scattering in the resulting gravitational background. Due to the reduced
rotational symmetry, even in the simple case of a circular fuzzball, the system
cannot be integrated elementarily. Yet, for motion in the plane of the string
profile or in the orthogonal plane to it, one can compute the deflection angle
or the phase shift and identify the critical impact parameter, at which even a
massless probe is captured by the fuzzball if its internal momentum is properly
tuned. We find agreement among the three approaches, thus giving further
support to the fuzzball proposal at the dynamical level.Comment: 35 pages. Extended and improved discussions on the integrability of
the geodetic equations and on the critical impact parameter
First lattice evidence for a non-trivial renormalization of the Higgs condensate
General arguments related to ``triviality'' predict that, in the broken phase
of theory, the condensate re-scales by a factor
$Z_{\phi}$ different from the conventional wavefunction-renormalization factor,
$Z_{prop}$. Using a lattice simulation in the Ising limit we measure
$Z_{\phi}=m^2 \chi$ from the physical mass and susceptibility and $Z_{prop}$
from the residue of the shifted-field propagator. We find that the two $Z$'s
differ, with the difference increasing rapidly as the continuum limit is
approached. Since $Z_{\phi}$ affects the relation of to the Fermi
constant it can sizeably affect the present bounds on the Higgs mass.Comment: 10 pages, 3 figures, 1 table, Latex2
Constructive Heuristics for the Minimum Labelling Spanning Tree Problem: a preliminary comparison
This report studies constructive heuristics for the minimum labelling spanning tree
(MLST) problem. The purpose is to find a spanning tree that uses edges that are as similar as
possible. Given an undirected labeled connected graph (i.e., with a label or color for each edge),
the minimum labeling spanning tree problem seeks a spanning tree whose edges have the smallest
possible number of distinct labels. The model can represent many real-world problems in
telecommunication networks, electric networks, and multimodal transportation networks, among
others, and the problem has been shown to be NP-complete even for complete graphs. A primary
heuristic, named the maximum vertex covering algorithm has been proposed. Several versions of
this constructive heuristic have been proposed to improve its efficiency. Here we describe the
problem, review the literature and compare some variants of this algorithm
Recommended from our members
Metaheuristic approaches for the quartet method of hierarchical clustering
Given a set of objects and their pairwise distances, we wish to determine a visual representation of the data. We use the quartet paradigm to compute a hierarchy of clusters of the objects. The method is based on an NP-hard graph optimization problem called the Minimum Quartet Tree Cost problem. This paper presents and compares several metaheuristic approaches to approximate the optimal hierarchy. The performance of the algorithms is tested through extensive computational experiments and it is shown that the Reduced Variable Neighbourhood Search metaheuristic is the most effective approach to the problem, obtaining high quality solutions in short computational running times
Breakdown of a conservation law in incommensurate systems
We show that invariance properties of the Lagrangian of an incommensurate
system, as described by the Frenkel Kontorova model, imply the existence of a
generalized angular momentum which is an integral of motion if the system
remains floating. The behavior of this quantity can therefore monitor the
character of the system as floating (when it is conserved) or locked (when it
is not). We find that, during the dynamics, the non-linear couplings of our
model cause parametric phonon excitations which lead to the appearance of
Umklapp terms and to a sudden deviation of the generalized momentum from a
constant value, signalling a dynamical transition from a floating to a pinned
state. We point out that this transition is related but does not coincide with
the onset of sliding friction which can take place when the system is still
floating.Comment: 7 pages, 6 figures, typed with RevTex, submitted to Phys. Rev. E
Replaced 27-03-2001: changes to text, minor revision of figure
Recommended from our members
Solving the minimum labelling spanning tree problem using hybrid local search
Given a connected, undirected graph whose edges are labelled (or coloured), the minimum
labelling spanning tree (MLST) problem seeks a spanning tree whose edges have the smallest
number of distinct labels (or colours). In recent work, the MLST problem has been shown
to be NP-hard and some effective heuristics (Modified Genetic Algorithm (MGA) and Pilot
Method (PILOT)) have been proposed and analyzed. A hybrid local search method, that we
call Group-Swap Variable Neighbourhood Search (GS-VNS), is proposed in this paper. It is
obtained by combining two classic metaheuristics: Variable Neighbourhood Search (VNS) and
Simulated Annealing (SA). Computational experiments show that GS-VNS outperforms MGA
and PILOT. Furthermore, a comparison with the results provided by an exact approach shows
that we may quickly obtain optimal or near-optimal solutions with the proposed heuristic
Discrete Particle Swarm Optimization for the minimum labelling Steiner tree problem
Particle Swarm Optimization is an evolutionary method inspired by the
social behaviour of individuals inside swarms in nature. Solutions of the problem are
modelled as members of the swarm which fly in the solution space. The evolution is
obtained from the continuous movement of the particles that constitute the swarm
submitted to the effect of the inertia and the attraction of the members who lead the
swarm. This work focuses on a recent Discrete Particle Swarm Optimization for combinatorial optimization, called Jumping Particle Swarm Optimization. Its effectiveness is
illustrated on the minimum labelling Steiner tree problem: given an undirected labelled
connected graph, the aim is to find a spanning tree covering a given subset of nodes,
whose edges have the smallest number of distinct labels
Physical mechanisms generating spontaneous symmetry breaking and a hierarchy of scales
We discuss the phase transition in 3+1 dimensional lambda Phi^4 theory from a
very physical perspective. The particles of the symmetric phase (`phions')
interact via a hard-core repulsion and an induced, long-range -1/r^3
attraction. If the phion mass is sufficiently small, the lowest-energy state is
not the `empty' state with no phions, but is a state with a non-zero density of
phions Bose-Einstein condensed in the zero-momentum mode. The condensate
corresponds to the spontaneous-symmetry-breaking vacuum with neq 0 and
its excitations ("phonons" in atomic-physics language) correspond to Higgs
particles. The phase transition happens when the phion's physical mass m is
still positive; it does not wait until m^2 passes through zero and becomes
negative. However, at and near the phase transition, m is much, much less than
the Higgs mass M_h. This interesting physics coexists with `triviality;' all
scattering amplitudes vanish in the continuum limit, but the vacuum condensate
becomes infinitely dense. The ratio m/M_h, which goes to zero in the continuum
limit, can be viewed as a measure of non-locality in the regularized theory. An
intricate hierarchy of length scales naturally arises. We speculate about the
possible implications of these ideas for gravity and inflation.Comment: 27 pages plus 2 files of figure
- …