3,564 research outputs found
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
Quantum Einstein Gravity
We give a pedagogical introduction to the basic ideas and concepts of the
Asymptotic Safety program in Quantum Einstein Gravity. Using the continuum
approach based upon the effective average action, we summarize the state of the
art of the field with a particular focus on the evidence supporting the
existence of the non-trivial renormalization group fixed point at the heart of
the construction. As an application, the multifractal structure of the emerging
space-times is discussed in detail. In particular, we compare the continuum
prediction for their spectral dimension with Monte Carlo data from the Causal
Dynamical Triangulation approach.Comment: 87 pages, 13 figures, review article prepared for the New Journal of
Physics focus issue on Quantum Einstein Gravit
Renormalization group improved gravitational actions: a Brans-Dicke approach
A new framework for exploiting information about the renormalization group
(RG) behavior of gravity in a dynamical context is discussed. The
Einstein-Hilbert action is RG-improved by replacing Newton's constant and the
cosmological constant by scalar functions in the corresponding Lagrangian
density. The position dependence of and is governed by a RG
equation together with an appropriate identification of RG scales with points
in spacetime. The dynamics of the fields and does not admit a
Lagrangian description in general. Within the Lagrangian formalism for the
gravitational field they have the status of externally prescribed
``background'' fields. The metric satisfies an effective Einstein equation
similar to that of Brans-Dicke theory. Its consistency imposes severe
constraints on allowed backgrounds. In the new RG-framework, and
carry energy and momentum. It is tested in the setting of homogeneous-isotropic
cosmology and is compared to alternative approaches where the fields and
do not carry gravitating 4-momentum. The fixed point regime of the
underlying RG flow is studied in detail.Comment: LaTeX, 72 pages, no figure
Non-adiabatic Effects in the Dissociation of Oxygen Molecules at the Al(111) Surface
The measured low initial sticking probability of oxygen molecules at the
Al(111) surface that had puzzled the field for many years was recently
explained in a non-adiabatic picture invoking spin-selection rules [J. Behler
et al., Phys. Rev. Lett. 94, 036104 (2005)]. These selection rules tend to
conserve the initial spin-triplet character of the free O2 molecule during the
molecule's approach to the surface. A new locally-constrained
density-functional theory approach gave access to the corresponding
potential-energy surface (PES) seen by such an impinging spin-triplet molecule
and indicated barriers to dissociation which reduce the sticking probability.
Here, we further substantiate this non-adiabatic picture by providing a
detailed account of the employed approach. Building on the previous work, we
focus in particular on inaccuracies in present-day exchange-correlation
functionals. Our analysis shows that small quantitative differences in the
spin-triplet constrained PES obtained with different gradient-corrected
functionals have a noticeable effect on the lowest kinetic energy part of the
resulting sticking curve.Comment: 17 pages including 11 figures; related publications can be found at
http://www.fhi-berlin.mpg.de/th/th.htm
Sequential and co-tunneling behavior in the temperature-dependent thermopower of few-electron quantum dots
We have studied the temperature dependent thermopower of gate-defined,
lateral quantum dots in the Coulomb blockade regime using an electron heating
technique. The line shape of the thermopower oscillations depends strongly on
the contributing tunneling processes. Between 1.5 K and 40 mK a crossover from
a pure sawtooth- to an intermitted sawtooth-like line shape is observed. The
latter is attributed to the increasing dominance of cotunneling processes in
the Coulomb blockade regime at low temperatures.Comment: 4 pages, 4 figures, submitted to Phys. Rev.
Detailed Radio Spectra of Selected Compact Sources in the Nucleus of M82
We have determined detailed radio spectra for 26 compact sources in the
starburst nucleus of M82, between 74 and 1.3 cm. Seventeen show low-frequency
turnovers. One other has a thermal emission spectrum, and we identify it as an
HII region. The low frequency turnovers are due to absorption by the
interstellar gas in M82. New information on the AGN candidate 44.01+595, shows
it to have a non-thermal falling powerlaw spectrum at the highest frequencies,
and that it is strongly absorbed below 2 GHz. We derive large magnetic fields
in the supernova remnants, of order 1-2 milliGauss, hence large pressures in
the sources suggest that the brightest ones are either expanding or are
strongly confined by a dense interstellar medium. From the largest source in
our sample, we derive a supernova rate of 0.016 SN/yr.Comment: 19 pages, 7 tables, 29 figures, LaTeX, requires AAS macros v. 4.0. To
appear in ApJ July 20, 199
Fractals at T=Tc due to instanton-like configurations
We investigate the geometry of the critical fluctuations for a general system
undergoing a thermal second order phase transition. Adopting a generalized
effective action for the local description of the fluctuations of the order
parameter at the critical point () we show that instanton-like
configurations, corresponding to the minima of the effective action functional,
build up clusters with fractal geometry characterizing locally the critical
fluctuations. The connection between the corresponding (local) fractal
dimension and the critical exponents is derived. Possible extension of the
local geometry of the system to a global picture is also discussed.Comment: To appear in Physical Review Letter
Renormalization Group Flow in Scalar-Tensor Theories. II
We study the UV behaviour of actions including integer powers of scalar
curvature and even powers of scalar fields with Functional Renormalization
Group techniques. We find UV fixed points where the gravitational couplings
have non-trivial values while the matter ones are Gaussian. We prove several
properties of the linearized flow at such a fixed point in arbitrary dimensions
in the one-loop approximation and find recursive relations among the critical
exponents. We illustrate these results in explicit calculations in for
actions including up to four powers of scalar curvature and two powers of the
scalar field. In this setting we notice that the same recursive properties
among the critical exponents, which were proven at one-loop order, still hold,
in such a way that the UV critical surface is found to be five dimensional. We
then search for the same type of fixed point in a scalar theory with minimal
coupling to gravity in including up to eight powers of scalar curvature.
Assuming that the recursive properties of the critical exponents still hold,
one would conclude that the UV critical surface of these theories is five
dimensional.Comment: 14 pages. v.2: Minor changes, some references adde
Correction to the Casimir force due to the anomalous skin effect
The surface impedance approach is discussed in connection with the precise
calculation of the Casimir force between metallic plates. It allows to take
into account the nonlocal connection between the current density and electric
field inside of metals. In general, a material has to be described by two
impedances and corresponding to two
different polarization states. In contrast with the approximate Leontovich
impedance they depend not only on frequency but also on the wave
vector along the plate . In this paper only the nonlocal effects happening
at frequencies (plasma frequency) are analyzed. We refer to
all of them as the anomalous skin effect. The impedances are calculated for the
propagating and evanescent fields in the Boltzmann approximation. It is found
that significantly deviates from the local impedance as a result of the
Thomas-Fermi screening. The nonlocal correction to the Casimir force is
calculated at zero temperature. This correction is small but observable at
small separations between bodies. The same theory can be used to find more
significant nonlocal contribution at due to the plasmon
excitation.Comment: 29 pages. To appear in Phys. Rev.
Nonperturbative Evolution Equation for Quantum Gravity
A scale--dependent effective action for gravity is introduced and an exact
nonperturbative evolution equation is derived which governs its renormalization
group flow. It is invariant under general coordinate transformations and
satisfies modified BRS Ward--Identities. The evolution equation is solved for a
simple truncation of the space of actions. In 2+epsilon dimensions,
nonperturbative corrections to the beta--function of Newton's constant are
derived and its dependence on the cosmological constant is investigated. In 4
dimensions, Einstein gravity is found to be ``antiscreening'', i.e., Newton's
constant increases at large distances.Comment: 35 pages, late
- …