1,109 research outputs found
Renormalization Group Flow of the Holst Action
The renormalization group (RG) properties of quantum gravity are explored,
using the vielbein and the spin connection as the fundamental field variables.
The scale dependent effective action is required to be invariant both under
space time diffeomorphisms and local frame rotations. The nonperturbative RG
equation is solved explicitly on the truncated theory space defined by a three
parameter family of Holst-type actions which involve a running Immirzi
parameter. We find evidence for the existence of an asymptotically safe
fundamental theory, probably inequivalent to metric quantum gravity constructed
in the same way.Comment: 5 pages, 1 figur
Hamiltonian and physical Hilbert space in polymer quantum mechanics
In this paper, a version of polymer quantum mechanics, which is inspired by
loop quantum gravity, is considered and shown to be equivalent, in a precise
sense, to the standard, experimentally tested, Schroedinger quantum mechanics.
The kinematical cornerstone of our framework is the so called polymer
representation of the Heisenberg-Weyl (H-W) algebra, which is the starting
point of the construction. The dynamics is constructed as a continuum limit of
effective theories characterized by a scale, and requires a renormalization of
the inner product. The result is a physical Hilbert space in which the
continuum Hamiltonian can be represented and that is unitarily equivalent to
the Schroedinger representation of quantum mechanics. As a concrete
implementation of our formalism, the simple harmonic oscillator is fully
developed.Comment: 19 pages, 2 figures. Comments and references added. Version to be
published in CQ
Fractal space-times under the microscope: A Renormalization Group view on Monte Carlo data
The emergence of fractal features in the microscopic structure of space-time
is a common theme in many approaches to quantum gravity. In this work we carry
out a detailed renormalization group study of the spectral dimension and
walk dimension associated with the effective space-times of
asymptotically safe Quantum Einstein Gravity (QEG). We discover three scaling
regimes where these generalized dimensions are approximately constant for an
extended range of length scales: a classical regime where , a
semi-classical regime where , and the UV-fixed point
regime where . On the length scales covered by
three-dimensional Monte Carlo simulations, the resulting spectral dimension is
shown to be in very good agreement with the data. This comparison also provides
a natural explanation for the apparent puzzle between the short distance
behavior of the spectral dimension reported from Causal Dynamical
Triangulations (CDT), Euclidean Dynamical Triangulations (EDT), and Asymptotic
Safety.Comment: 26 pages, 6 figure
Scale Radii and Aggregation Histories of Dark Haloes
Relaxed dark-matter haloes are found to exhibit the same universal density
profiles regardless of whether they form in hierarchical cosmologies or via
spherical collapse. Likewise, the shape parameters of haloes formed
hierarchically do not seem to depend on the epoch in which the last major
merger took place. Both findings suggest that the density profile of haloes
does not depend on their aggregation history. Yet, this possibility is
apparently at odds with some correlations involving the scale radius r_s found
in numerical simulations. Here we prove that the scale radius of relaxed,
non-rotating, spherically symmetric haloes endowed with the universal density
profile is determined exclusively by the current values of four independent,
though correlated, quantities: mass, energy and their respective instantaneous
accretion rates. Under this premise and taking into account the inside-out
growth of haloes during the accretion phase between major mergers, we build a
simple physical model for the evolution of r_s along the main branch of halo
merger trees that reproduces all the empirical trends shown by this parameter
in N-body simulations. This confirms the conclusion that the empirical
correlations involving r_s do not actually imply the dependence of this
parameter on the halo aggregation history. The present results give strong
support to the explanation put forward in a recent paper by Manrique et al.
(2003) for the origin of the halo universal density profile.Comment: 13 pages, 8 figures, accepted for publication in MNRA
Observable consequences of quantum gravity: Can light fermions exist?
Any theory of quantum gravity must ultimately be connected to observations.
This demand is difficult to be met due to the high energies at which we expect
the quantum nature of gravity to become manifest. Here we study, how viable
quantum gravity proposals can be restricted by investigating the interplay of
gravitational and matter degrees of freedom. Specifically we demand that a
valid quantum theory of gravity must allow for the existence of light (compared
to the Planck scale) fermions, since we observe these in our universe. Within
the effective theory framework, we can thus show that UV completions for
gravity are restricted, regardless of the details of the microscopic theory.
Specialising to asymptotically safe quantum gravity, we find indications that
universes with light fermions are favoured within this UV completion for
gravity.Comment: 4 pages, based on a talk given at Loops '11, Madrid, to appear in
Journal of Physics: Conference Series (JPCS
Quantum Interference in Single Molecule Electronic Systems
We present a general analytical formula and an ab initio study of quantum
interference in multi-branch molecules. Ab initio calculations are used to
investigate quantum interference in a benzene-1,2-dithiolate (BDT) molecule
sandwiched between gold electrodes and through oligoynes of various lengths. We
show that when a point charge is located in the plane of a BDT molecule and its
position varied, the electrical conductance exhibits a clear interference
effect, whereas when the charge approaches a BDT molecule along a line normal
to the plane of the molecule and passing through the centre of the phenyl ring,
interference effects are negligible. In the case of olygoynes, quantum
interference leads to the appearance of a critical energy , at which the
electron transmission coefficient of chains with even or odd numbers of
atoms is independent of length. To illustrate the underlying physics, we derive
a general analytical formula for electron transport through multi-branch
structures and demonstrate the versatility of the formula by comparing it with
the above ab-initio simulations. We also employ the analytical formula to
investigate the current inside the molecule and demonstrate that large counter
currents can occur within a ring-like molecule such as BDT, when the point
charge is located in the plane of the molecule. The formula can be used to
describe quantum interference and Fano resonances in structures with branches
containing arbitrary elastic scattering regions connected to nodal sites.Comment: 12 pages, 11 figure
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