2,844 research outputs found
Physical consequences of PNP and the DMRG-annealing conjecture
Computational complexity theory contains a corpus of theorems and conjectures
regarding the time a Turing machine will need to solve certain types of
problems as a function of the input size. Nature {\em need not} be a Turing
machine and, thus, these theorems do not apply directly to it. But {\em
classical simulations} of physical processes are programs running on Turing
machines and, as such, are subject to them. In this work, computational
complexity theory is applied to classical simulations of systems performing an
adiabatic quantum computation (AQC), based on an annealed extension of the
density matrix renormalization group (DMRG). We conjecture that the
computational time required for those classical simulations is controlled
solely by the {\em maximal entanglement} found during the process. Thus, lower
bounds on the growth of entanglement with the system size can be provided. In
some cases, quantum phase transitions can be predicted to take place in certain
inhomogeneous systems. Concretely, physical conclusions are drawn from the
assumption that the complexity classes {\bf P} and {\bf NP} differ. As a
by-product, an alternative measure of entanglement is proposed which, via
Chebyshev's inequality, allows to establish strict bounds on the required
computational time.Comment: Accepted for publication in JSTA
Compelled to do the right thing
We use a model of opinion formation to study the consequences of some
mechanisms attempting to enforce the right behaviour in a society. We start
from a model where the possible choices are not equivalent (such is the case
when the agents decide to comply or not with a law) and where an imitation
mechanism allow the agents to change their behaviour based on the influence of
a group of partners. In addition, we consider the existence of two social
constraints: a) an external authority, called monitor, that imposes the correct
behaviour with infinite persuasion and b) an educated group of agents that act
upon their fellows but never change their own opinion, i.e., they exhibit
infinite adamancy. We determine the minimum number of monitors to induce an
effective change in the behaviour of the social group, and the size of the
educated group that produces the same effect. Also, we compare the results for
the cases of random social interactions and agents placed on a network. We have
verified that a small number of monitors are enough to change the behaviour of
the society. This also happens with a relatively small educated group in the
case of random interactions.Comment: 8 pages, 9 figures, submitted to EPJ
Distortion of Globular Clusters by Galactic Bulges
One of the external fields that influences the population of globular
clusters is that due to galactic bulges. In extreme situations, perigalactic
distances pc, globular clusters could suffer total disruption in
a single passage. A more common scenario is that for cluster orbits with pc. We investigate the effects of tidal forces from a bulge on the
shape of globular clusters for this type of encounters. We find distortions
characterized by ``twisting isophotes'' and consider the potential for
observability of this effect. In the Milky Way, a typical globular cluster must
pass within several hundred pc of the center to experience substantial
distortion, and it is possible that this has happened recently to one or two
present day clusters. We estimate that this distortion could be observed even
for globulars in dense fields toward the bulge. In more extreme environments
such as giant ellipticals or merger products with newly formed globulars, this
effect could be more common, extending out to orbits that pass within 1 kpc of
the bulge center. This would lead to a substantial shift in the eccentricity
distribution of globulars in those galaxies.Comment: 12 pages, 8 figure
Perturbations of the Kerr spacetime in horizon penetrating coordinates
We derive the Teukolsky equation for perturbations of a Kerr spacetime when
the spacetime metric is written in either ingoing or outgoing Kerr-Schild form.
We also write explicit formulae for setting up the initial data for the
Teukolsky equation in the time domain in terms of a three metric and an
extrinsic curvature. The motivation of this work is to have in place a
formalism to study the evolution in the ``close limit'' of two recently
proposed solutions to the initial value problem in general relativity that are
based on Kerr-Schild slicings. A perturbative formalism in horizon penetrating
coordinates is also very desirable in connection with numerical relativity
simulations using black hole ``excision''.Comment: 8 pages, RevTex, 2 figures, final version to appear in CQ
Why, when, and how fast innovations are adopted
When the full stock of a new product is quickly sold in a few days or weeks,
one has the impression that new technologies develop and conquer the market in
a very easy way. This may be true for some new technologies, for example the
cell phone, but not for others, like the blue-ray. Novelty, usefulness,
advertising, price, and fashion are the driving forces behind the adoption of a
new product. But, what are the key factors that lead to adopt a new technology?
In this paper we propose and investigate a simple model for the adoption of an
innovation which depends mainly on three elements: the appeal of the novelty,
the inertia or resistance to adopt it, and the interaction with other agents.
Social interactions are taken into account in two ways: by imitation and by
differentiation, i.e., some agents will be inclined to adopt an innovation if
many people do the same, but other will act in the opposite direction, trying
to differentiate from the "herd". We determine the conditions for a successful
implantation of the new technology, by considering the strength of advertising
and the effect of social interactions. We find a balance between the
advertising and the number of anti-herding agents that may block the adoption
of a new product. We also compare the effect of social interactions, when
agents take into account the behavior of the whole society or just a part of
it. In a nutshell, the present model reproduces qualitatively the available
data on adoption of innovation.Comment: 11 pages, 13 figures (with subfigures), full paper (EPJB 2012) on
innovation adoption mode
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