17,558 research outputs found
Black Holes as Quantum Gravity Condensates
We model spherically symmetric black holes within the group field theory
formalism for quantum gravity via generalised condensate states, involving sums
over arbitrarily refined graphs (dual to 3d triangulations). The construction
relies heavily on both the combinatorial tools of random tensor models and the
quantum geometric data of loop quantum gravity, both part of the group field
theory formalism. Armed with the detailed microscopic structure, we compute the
entropy associated with the black hole horizon, which turns out to be
equivalently the Boltzmann entropy of its microscopic degrees of freedom and
the entanglement entropy between the inside and outside regions. We recover the
area law under very general conditions, as well as the Bekenstein-Hawking
formula. The result is also shown to be generically independent of any specific
value of the Immirzi parameter.Comment: 22 page
Quantum ESPRESSO: a modular and open-source software project for quantum simulations of materials
Quantum ESPRESSO is an integrated suite of computer codes for
electronic-structure calculations and materials modeling, based on
density-functional theory, plane waves, and pseudopotentials (norm-conserving,
ultrasoft, and projector-augmented wave). Quantum ESPRESSO stands for "opEn
Source Package for Research in Electronic Structure, Simulation, and
Optimization". It is freely available to researchers around the world under the
terms of the GNU General Public License. Quantum ESPRESSO builds upon
newly-restructured electronic-structure codes that have been developed and
tested by some of the original authors of novel electronic-structure algorithms
and applied in the last twenty years by some of the leading materials modeling
groups worldwide. Innovation and efficiency are still its main focus, with
special attention paid to massively-parallel architectures, and a great effort
being devoted to user friendliness. Quantum ESPRESSO is evolving towards a
distribution of independent and inter-operable codes in the spirit of an
open-source project, where researchers active in the field of
electronic-structure calculations are encouraged to participate in the project
by contributing their own codes or by implementing their own ideas into
existing codes.Comment: 36 pages, 5 figures, resubmitted to J.Phys.: Condens. Matte
Fluctuation Statistics in Networks: a Stochastic Path Integral Approach
We investigate the statistics of fluctuations in a classical stochastic
network of nodes joined by connectors. The nodes carry generalized charge that
may be randomly transferred from one node to another. Our goal is to find the
time evolution of the probability distribution of charges in the network. The
building blocks of our theoretical approach are (1) known probability
distributions for the connector currents, (2) physical constraints such as
local charge conservation, and (3) a time-scale separation between the slow
charge dynamics of the nodes and the fast current fluctuations of the
connectors. We derive a stochastic path integral representation of the
evolution operator for the slow charges. Once the probability distributions on
the discrete network have been studied, the continuum limit is taken to obtain
a statistical field theory. We find a correspondence between the diffusive
field theory and a Langevin equation with Gaussian noise sources, leading
nevertheless to non-trivial fluctuation statistics. To complete our theory, we
demonstrate that the cascade diagrammatics, recently introduced by Nagaev,
naturally follows from the stochastic path integral. We extend the
diagrammatics to calculate current correlation functions for an arbitrary
network. One primary application of this formalism is that of full counting
statistics (FCS). We stress however, that the formalism is suitable for general
classical stochastic problems as an alternative to the traditional master
equation or Doi-Peliti technique. The formalism is illustrated with several
examples: both instantaneous and time averaged charge fluctuation statistics in
a mesoscopic chaotic cavity, as well as the FCS and new results for a
generalized diffusive wire.Comment: Final version accepted in J. Math. Phys. Discussion of conservation
laws, Refs., 1 Fig., and minor extensions added. 23 pages, 9 figs.,
double-column forma
Linear response for spiking neuronal networks with unbounded memory
We establish a general linear response relation for spiking neuronal
networks, based on chains with unbounded memory. This relation allows us to
predict the influence of a weak amplitude time-dependent external stimuli on
spatio-temporal spike correlations, from the spontaneous statistics (without
stimulus) in a general context where the memory in spike dynamics can extend
arbitrarily far in the past. Using this approach, we show how linear response
is explicitly related to neuronal dynamics with an example, the gIF model,
introduced by M. Rudolph and A. Destexhe. This example illustrates the
collective effect of the stimuli, intrinsic neuronal dynamics, and network
connectivity on spike statistics. We illustrate our results with numerical
simulations.Comment: 60 pages, 8 figure
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