Conformal fixed point, Cosmological Constant and Quintessence

We connect a possible solution for the ``cosmological constant problem'' to the existence of a (postulated) conformal fixed point in a fundamental theory. The resulting cosmology leads to quintessence, where the present acceleration of the expansion of the universe is linked to a crossover in the flow of coupling constants.Comment: More detailed discussion of quantum fluctuations,update with WMAP-data,4 pages,LaTe

Nonexistence of random gradient Gibbs measures in continuous interface models in d=2d=2

We consider statistical mechanics models of continuous spins in a disordered environment. These models have a natural interpretation as effective interface models. It is well known that without disorder there are no interface Gibbs measures in infinite volume in dimension $d=2$, while there are ``gradient Gibbs measures'' describing an infinite-volume distribution for the increments of the field, as was shown by Funaki and Spohn. In the present paper we show that adding a disorder term prohibits the existence of such gradient Gibbs measures for general interaction potentials in $d=2$. This nonexistence result generalizes the simple case of Gaussian fields where it follows from an explicit computation. In $d=3$ where random gradient Gibbs measures are expected to exist, our method provides a lower bound of the order of the inverse of the distance on the decay of correlations of Gibbs expectations w.r.t. the distribution of the random environment.Comment: Published in at http://dx.doi.org/10.1214/07-AAP446 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Grover's quantum searching algorithm is optimal

I improve the tight bound on quantum searching by Boyer et al. (quant-ph/9605034) to a matching bound, thus showing that for any probability of success Grovers quantum searching algorithm is optimal. E.g. for near certain success we have to query the oracle pi/4 sqrt{N} times, where N is the size of the search space. I also show that unfortunately quantum searching cannot be parallelized better than by assigning different parts of the search space to independent quantum computers. Earlier results left open the possibility of a more efficient parallelization.Comment: 13 pages, LaTeX, essentially published versio

Schroedinger Invariance from Lifshitz Isometries in Holography and Field Theory

We study non-relativistic field theory coupled to a torsional Newton-Cartan geometry both directly as well as holographically. The latter involves gravity on asymptotically locally Lifshitz space-times. We define an energy-momentum tensor and a mass current and study the relation between conserved currents and conformal Killing vectors for flat Newton-Cartan backgrounds. It is shown that flat NC space-time realizes two copies of the Lifshitz algebra that together form a Schroedinger algebra (without the central element). We show why the Schroedinger scalar model has both copies as symmetries and the Lifshitz scalar model only one. Finally we discuss the holographic dual of this phenomenon by showing that the bulk Lifshitz space-time realizes the same two copies of the Lifshitz algebra.Comment: 5 pages, modified abstract, clarifications added, typos fixed, refs update

Non-Equilibrium Time Evolution in Quantum Field Theory

The time development of equal-time correlation functions in quantum mechanics and quantum field theory is described by an exact evolution equation for generating functionals. This permits a comparison between classical and quantum evolution in non-equilibrium systems.Comment: 7 pages, LaTe

Mass freezing in growing neutrino quintessence

Growing neutrino quintessence solves the coincidence problem for dark energy by a growing cosmological value of the neutrino mass which emerges from a cosmon-neutrino interaction stronger than gravity. The cosmon-mediated attraction between neutrinos induces the formation of large scale neutrino lumps in a recent cosmological epoch. We argue that the non-linearities in the cosmon field equations stop the further increase of the neutrino mass within sufficiently dense and large lumps. As a result, we find the neutrino induced gravitational potential to be substantially reduced when compared to linear extrapolations. We furthermore demonstrate that inside a lump the possible time variation of fundamental constants is much smaller than their cosmological evolution. This feature may reconcile current geophysical bounds with claimed cosmological variations of the fine structure constant.Comment: 15 pages, 12 figures. Version published in PR