Search results for "renormalization group"

Structure of longitudinal chromomagnetic fields in high energy collisions

2014

We compute expectation values of spatial Wilson loops in the forward light cone of high-energy collisions. We consider ensembles of gauge field configurations generated from a classical Gaussian effective action as well as solutions of high-energy renormalization group evolution with fixed and running coupling. The initial fields correspond to a color field condensate exhibiting domain-like structure over distance scales of order the saturation scale. At later times universal scaling emerges at large distances for all ensembles, with a nontrivial critical exponent. Finally, we compare the results for the Wilson loop to the two-point correlator of magnetic fields.

Muon Anomaly from Lepton Vacuum Polarization and The Mellin--Barnes Representation

2008

We evaluate, analytically, a specific class of eighth--order and tenth--order QED contributions to the anomalous magnetic moment of the muon. They are generated by Feynman diagrams involving lowest order vacuum polarization insertions of leptons $l=e,\mu$, and $\tau$. The results are given in the form of analytic expansions in terms of the mass ratios $m_e/m_\mu$ and $m_\mu/m_\tau$. We compute as many terms as required by the error induced by the present experimental uncertainty on the lepton masses. We show how the Mellin--Barnes integral representation of Feynman parametric integrals allows for an easy analytic evaluation of as many terms as wanted in these expansions and how its underlyi…

Neutrino anarchy and renormalization group evolution

2015

The observed pattern of neutrino mixing angles is in good agreement with the hypothesis of neutrino anarchy, which posits that Nature has chosen the entries of the leptonic mixing matrix at random. In this paper we investigate how stable this conclusion is under renormalization group effects. Working in the simplest type-I seesaw model and two variants of the inverse seesaw model we study how the statistical distributions of the neutrino mixing parameters evolve between the Grand Unification scale and the electroweak scale. Especially in the inverse seesaw case we find significant distortions: mixing angles tend to be smaller after RG running, and the Dirac CP phase tends to be closer to ze…

2014

Here we investigate the connection between topological order and the geometric entanglement, as measured by the logarithm of the overlap between a given state and its closest product state of blocks. We do this for a variety of topologically-ordered systems such as the toric code, double semion, color code, and quantum double models. As happens for the entanglement entropy, we find that for sufficiently large block sizes the geometric entanglement is, up to possible sub-leading corrections, the sum of two contributions: a bulk contribution obeying a boundary law times the number of blocks, and a contribution quantifying the underlying pattern of long-range entanglement of the topologically-…

Dynamical coexistence in moderately polydisperse hard-sphere glasses

2020

We perform extensive numerical simulations of a paradigmatic model glass former, the hard-sphere fluid with 10% polydispersity. We sample from the ensemble of trajectories with fixed observation time, whereby single trajectories are generated by event-driven molecular dynamics. We show that these trajectories can be characterized in terms of the local structure, and we find a dynamical-structural (active-inactive) phase transition between two dynamical phases: one dominated by liquidlike trajectories with a low degree of local order and one dominated by glassylike trajectories with a high degree of local order. We show that both phases coexist and are separated by a spatiotemporal interface…

Low-temperature specific heat of orientational glasses

1992

This review summarizes specific heat data measured at low temperatures (T<1 K) on orientational glasses. Three species of mixed molecular crystals exhibiting orientational disorder are considered, namely (KBr)1−x (KCN) x , (NaCN)1−x (KCN) x (Rb)1−x (NH4) x H2PO4. For intermediate concentrations of the anisotropic components, glass-like excitations have been observed. It is demonstrated that with respect to thermal properties, orientational disorder leads to the same “universal” behaviours than for structural disorder, i.e. a specific heat which varies below 1 K and for times 10−4 s–10 s as:C p(T,t)∞T 1×ln(t). The variation of the glass-like anomaly with compositional disorder is also discus…

Kolmogorov-Arnold-Moser–Renormalization-Group Analysis of Stability in Hamiltonian Flows

1997

We study the stability and breakup of invariant tori in Hamiltonian flows using a combination of Kolmogorov-Arnold-Moser (KAM) theory and renormalization-group techniques. We implement the scheme numerically for a family of Hamiltonians quadratic in the actions to analyze the strong coupling regime. We show that the KAM iteration converges up to the critical coupling at which the torus breaks up. Adding a renormalization consisting of a rescaling of phase space and a shift of resonances allows us to determine the critical coupling with higher accuracy. We determine a nontrivial fixed point and its universality properties.

Ferroelastic transition in Kbr:Kcn studied by neutrons, x-rays and ultrasonic

1986

The ferroelastic phase transition of (KBr) 0 27 (KNC) 0.73 has been studied by X-ray diffraction, ultrasonics and inelastic neutron scattering. It is the first example of a cubic crystal where the elastic shear constant C 44 softens completely corresponding to the m = 2 universality class. C 44 and the Bragg intensities show a non-classical critical behaviour.

Ultraviolet Fixed Point and Generalized Flow Equation of Quantum Gravity

2001

A new exact renormalization group equation for the effective average action of Euclidean quantum gravity is constructed. It is formulated in terms of the component fields appearing in the transverse-traceless decomposition of the metric. It facilitates both the construction of an appropriate infrared cutoff and the projection of the renormalization group flow onto a large class of truncated parameter spaces. The Einstein-Hilbert truncation is investigated in detail and the fixed point structure of the resulting flow is analyzed. Both a Gaussian and a non-Gaussian fixed point are found. If the non-Gaussian fixed point is present in the exact theory, quantum Einstein gravity is likely to be r…

Smooth Feshbach map and operator-theoretic renormalization group methods

2003

Abstract A new variant of the isospectral Feshbach map defined on operators in Hilbert space is presented. It is constructed with the help of a smooth partition of unity, instead of projections, and is therefore called smooth Feshbach map . It is an effective tool in spectral and singular perturbation theory. As an illustration of its power, a novel operator-theoretic renormalization group method is described and applied to analyze a general class of Hamiltonians on Fock space. The main advantage of the new renormalization group method over its predecessors is its technical simplicity, which it owes to the use of the smooth Feshbach map.