Self-tuning to the Hopf bifurcation in fluctuating systems

The problem of self-tuning a system to the Hopf bifurcation in the presence of noise and periodic external forcing is discussed. We find that the response of the system has a non-monotonic dependence on the noise-strength, and displays an amplified response which is more pronounced for weaker signals. The observed effect is to be distinguished from stochastic resonance. For the feedback we have studied, the unforced self-tuned Hopf oscillator in the presence of fluctuations exhibits sharp peaks in its spectrum. The implications of our general results are briefly discussed in the context of sound detection by the inner ear.Comment: 37 pages, 7 figures (8 figure files

Regularity Properties and Pathologies of Position-Space Renormalization-Group Transformations

We reconsider the conceptual foundations of the renormalization-group (RG) formalism, and prove some rigorous theorems on the regularity properties and possible pathologies of the RG map. Regarding regularity, we show that the RG map, defined on a suitable space of interactions (= formal Hamiltonians), is always single-valued and Lipschitz continuous on its domain of definition. This rules out a recently proposed scenario for the RG description of first-order phase transitions. On the pathological side, we make rigorous some arguments of Griffiths, Pearce and Israel, and prove in several cases that the renormalized measure is not a Gibbs measure for any reasonable interaction. This means that the RG map is ill-defined, and that the conventional RG description of first-order phase transitions is not universally valid. For decimation or Kadanoff transformations applied to the Ising model in dimension $d \ge 3$, these pathologies occur in a full neighborhood $\{ \beta > \beta_0 ,\, |h| < \epsilon(\beta) \}$ of the low-temperature part of the first-order phase-transition surface. For block-averaging transformations applied to the Ising model in dimension $d \ge 2$, the pathologies occur at low temperatures for arbitrary magnetic-field strength. Pathologies may also occur in the critical region for Ising models in dimension $d \ge 4$. We discuss in detail the distinction between Gibbsian and non-Gibbsian measures, and give a rather complete catalogue of the known examples. Finally, we discuss the heuristic and numerical evidence on RG pathologies in the light of our rigorous theorems.Comment: 273 pages including 14 figures, Postscript, See also ftp.scri.fsu.edu:hep-lat/papers/9210/9210032.ps.

Search for doubly charged Higgs bosons in like-sign dilepton final states at root s=7 TeV with the ATLAS detector

A search for doubly charged Higgs bosons decaying to pairs of electrons and/or muons is presented. The search is performed using a data sample corresponding to an integrated luminosity of 4.7 fb(-1) of pp collisions at root s = 7 TeV collected by the ATLAS detector at the LHC. Pairs of prompt, isolated, high-p(T) leptons with the same electric charge (e(+/-)e(+/-), e(+/-)mu, mu(+/-)mu(+/-)) are selected, and their invariant mass distribution is searched for a narrow resonance. No significant excess over Standard Model background expectations is observed, and limits are placed on the cross section times branching ratio for pair production of doubly charged Higgs bosons. The masses of doubly charged Higgs bosons are constrained depending on the branching ratio into these leptonic final states. Assuming pair production, coupling to left-handed fermions, and a branching ratio of 100% for each final state, masses below 409 GeV, 375 GeV, and 398 GeV are excluded for e(+/-)e(+/-), e(+/-)mu(+/-),and mu(+/-)mu(+/-), respectively