Yang-Lee Theory for a Nonequilibrium Phase Transition

To analyze phase transitions in a nonequilibrium system we study its grand canonical partition function as a function of complex fugacity. Real and positive roots of the partition function mark phase transitions. This behavior, first found by Yang and Lee under general conditions for equilibrium systems, can also be applied to nonequilibrium phase transitions. We consider a one-dimensional diffusion model with periodic boundary conditions. Depending on the diffusion rates, we find real and positive roots and can distinguish two regions of analyticity, which can identified with two different phases. In a region of the parameter space both of these phases coexist. The condensation point can be computed with high accuracy.Comment: 4 pages, accepted for publication in Phys.Rev.Let

Exact Solution for the Time Evolution of Network Rewiring Models

We consider the rewiring of a bipartite graph using a mixture of random and preferential attachment. The full mean field equations for the degree distribution and its generating function are given. The exact solution of these equations for all finite parameter values at any time is found in terms of standard functions. It is demonstrated that these solutions are an excellent fit to numerical simulations of the model. We discuss the relationship between our model and several others in the literature including examples of Urn, Backgammon, and Balls-in-Boxes models, the Watts and Strogatz rewiring problem and some models of zero range processes. Our model is also equivalent to those used in various applications including cultural transmission, family name and gene frequencies, glasses, and wealth distributions. Finally some Voter models and an example of a Minority game also show features described by our model.Comment: This version contains a few footnotes not in published Phys.Rev.E versio

Criterion for phase separation in one-dimensional driven systems

A general criterion for the existence of phase separation in driven one-dimensional systems is proposed. It is suggested that phase separation is related to the size dependence of the steady-state currents of domains in the system. A quantitative criterion for the existence of phase separation is conjectured using a correspondence made between driven diffusive models and zero-range processes. Several driven diffusive models are discussed in light of the conjecture

The Effect of Weak Interactions on the Ultra-Relativistic Bose-Einstein Condensation Temperature

We calculate the ultra-relativistic Bose-Einstein condensation temperature of a complex scalar field with weak lambda Phi^4 interaction. We show that at high temperature and finite density we can use dimensional reduction to produce an effective three-dimensional theory which then requires non-perturbative analysis. For simplicity and ease of implementation we illustrate this process with the linear delta expansion.Comment: Latex2e, 12 pages, three eps figures, replacement with additional discussion and extra figur

Phase Transition in Two Species Zero-Range Process

We study a zero-range process with two species of interacting particles. We show that the steady state assumes a simple factorised form, provided the dynamics satisfy certain conditions, which we derive. The steady state exhibits a new mechanism of condensation transition wherein one species induces the condensation of the other. We study this mechanism for a specific choice of dynamics.Comment: 8 pages, 3 figure

A Gaussian process framework for modelling instrumental systematics: application to transmission spectroscopy

Transmission spectroscopy, which consists of measuring the wavelength-dependent absorption of starlight by a planet's atmosphere during a transit, is a powerful probe of atmospheric composition. However, the expected signal is typically orders of magnitude smaller than instrumental systematics, and the results are crucially dependent on the treatment of the latter. In this paper, we propose a new method to infer transit parameters in the presence of systematic noise using Gaussian processes, a technique widely used in the machine learning community for Bayesian regression and classification problems. Our method makes use of auxiliary information about the state of the instrument, but does so in a non-parametric manner, without imposing a specific dependence of the systematics on the instrumental parameters, and naturally allows for the correlated nature of the noise. We give an example application of the method to archival NICMOS transmission spectroscopy of the hot Jupiter HD 189733, which goes some way towards reconciling the controversy surrounding this dataset in the literature. Finally, we provide an appendix giving a general introduction to Gaussian processes for regression, in order to encourage their application to a wider range of problems.Comment: 6 figures, 1 table, accepted for publication in MNRA

A 125GeV Higgs Boson and Muon g-2 in More Generic Gauge Mediation

Recently, the ATLAS and CMS collaborations reported exciting hints of a Standard Model-like Higgs boson with a mass around 125GeV. A Higgs boson this heavy is difficult to realize in conventional models of gauge mediation. Here we revisit the lightest Higgs boson mass in "more generic gauge mediation," where the Higgs doublets mix with the messenger doublets. We show that a Higgs boson mass around 125GeV can be realized in more generic gauge mediation models, even for a relatively light gluino mass ~1TeV. We also show that the muon anomalous magnetic moment can be within 1sigma of the experimental value for these models, even when the Higgs boson is relatively heavy. We also discuss the LHC constraints and the prospects of discovery.Comment: 28 pages, 7 figures. Corrections and references are adde