The plasmonic eigenvalue problem

A plasmon of a bounded domain $\Omega\subset\mathbb{R}^n$ is a non-trivial bounded harmonic function on $\mathbb{R}^n\setminus\partial\Omega$ which is continuous at $\partial\Omega$ and whose exterior and interior normal derivatives at $\partial\Omega$ have a constant ratio. We call this ratio a plasmonic eigenvalue of $\Omega$. Plasmons arise in the description of electromagnetic waves hitting a metallic particle $\Omega$. We investigate these eigenvalues and prove that they form a sequence of numbers converging to one. Also, we prove regularity of plasmons, derive a variational characterization, and prove a second order perturbation formula. The problem can be reformulated in terms of Dirichlet-Neumann operators, and as a side result we derive a formula for the shape derivative of these operators.Comment: 22 pages; replacement 8-March-14: minor corrections; to appear in Review in Mathematical Physic

A Quantum-Classical Brackets from p-Mechanics

We provide an answer to the long standing problem of mixing quantum and classical dynamics within a single formalism. The construction is based on p-mechanical derivation (quant-ph/0212101, quant-ph/0304023) of quantum and classical dynamics from the representation theory of the Heisenberg group. To achieve a quantum-classical mixing we take the product of two copies of the Heisenberg group which represent two different Planck's constants. In comparison with earlier guesses our answer contains an extra term of analytical nature, which was not obtained before in purely algebraic setup. Keywords: Moyal brackets, Poisson brackets, commutator, Heisenberg group, orbit method, representation theory, Planck's constant, quantum-classical mixingComment: LaTeX, 7 pages (EPL style), no figures; v2: example of dynamics with two different Planck's constants is added, minor corrections; v3: major revion, a complete example of quantum-classic dynamics is given; v4: few grammatic correction

Spatial and temporal agreement in climate model simulations of the Interdecadal Pacific Oscillation

Accelerated warming and hiatus periods in the long-term rise of Global Mean Surface Temperature (GMST) have, in recent decades, been associated with the Interdecadal Pacific Oscillation (IPO). Critically, decadal climate prediction relies on the skill of state-of-the-art climate models to reliably represent these low-frequency climate variations. We undertake a systematic evaluation of the simulation of the IPO in the suite of Coupled Model Intercomparison Project 5 (CMIP5) models. We track the IPO in pre-industrial (control) and all-forcings (historical) experiments using the IPO tripole index (TPI). The TPI is explicitly aligned with the observed spatial pattern of the IPO, and circumvents assumptions about the nature of global warming. We find that many models underestimate the ratio of decadal-to-total variance in sea surface temperatures (SSTs). However, the basin-wide spatial pattern of positive and negative phases of the IPO are simulated reasonably well, with spatial pattern correlation coefficients between observations and models spanning the range 0.4–0.8. Deficiencies are mainly in the extratropical Pacific. Models that better capture the spatial pattern of the IPO also tend to more realistically simulate the ratio of decadal to total variance. Of the 13% of model centuries that have a fractional bias in the decadal-to-total TPI variance of 0.2 or less, 84% also have a spatial pattern correlation coefficient with the observed pattern exceeding 0.5. This result is highly consistent across both IPO positive and negative phases. This is evidence that the IPO is related to one or more inherent dynamical mechanisms of the climate system

The unexpected resurgence of Weyl geometry in late 20-th century physics

Weyl's original scale geometry of 1918 ("purely infinitesimal geometry") was withdrawn by its author from physical theorizing in the early 1920s. It had a comeback in the last third of the 20th century in different contexts: scalar tensor theories of gravity, foundations of gravity, foundations of quantum mechanics, elementary particle physics, and cosmology. It seems that Weyl geometry continues to offer an open research potential for the foundations of physics even after the turn to the new millennium.Comment: Completely rewritten conference paper 'Beyond Einstein', Mainz Sep 2008. Preprint ELHC (Epistemology of the LHC) 2017-02, 92 pages, 1 figur

The state of the Martian climate

60°N was +2.0°C, relative to the 1981–2010 average value (Fig. 5.1). This marks a new high for the record. The average annual surface air temperature (SAT) anomaly for 2016 for land stations north of starting in 1900, and is a significant increase over the previous highest value of +1.2°C, which was observed in 2007, 2011, and 2015. Average global annual temperatures also showed record values in 2015 and 2016. Currently, the Arctic is warming at more than twice the rate of lower latitudes

Quantum field theory: a tourist guide for mathematicians

Quantum field theory has been a great success for physics, but it is difficult for mathematicians to learn because it is mathematically incomplete. Folland, who is a mathematician, has spent considerable time digesting the physical theory and sorting out the mathematical issues in it. Fortunately for mathematicians, Folland is a gifted expositor. The purpose of this book is to present the elements of quantum field theory, with the goal of understanding the behavior of elementary particles rather than building formal mathematical structures, in a form that will be comprehensible to mathematicians. Rigorous definitions and arguments are presented as far as they are available, but the text proceeds on a more informal level when necessary, with due care in identifying the difficulties. The book begins with a review of classical physics and quantum mechanics, then proceeds through the construction of free quantum fields to the perturbation-theoretic development of interacting field theory and renormalization theory, with emphasis on quantum electrodynamics.The final two chapters present the functional integral approach and the elements of gauge field theory, including the Salam-Weinberg model of electromagnetic and weak interactions

Introduction to partial differential equations

Bibliography: p. 346-349.Vanderbauwhede, André L