Thermal conductance of thin film YIG determined using Bayesian statistics

Thin film YIG (Y$_3$Fe$_5$O$_{12}$) is a prototypical material for experiments on thermally generated pure spin currents and the spin Seebeck effect. The 3-omega method is an established technique to measure the cross-plane thermal conductance of thin films, but can not be used in YIG/GGG (Ga$_3$Gd$_5$O$_{12}$) systems in its standard form. We use two-dimensional modeling of heat transport and introduce a technique based on Bayesian statistics to evaluate measurement data taken from the 3-omega method. Our analysis method allows us to study materials systems that have not been accessible with the conventionally used 3-omega analysis. Temperature dependent thermal conductance data of thin film YIG are of major importance for experiments in the field of spin-caloritronics. Here we show data between room temperature and 10 K for films covering a wide thickness range as well as the magnetic field effect on the thermal conductance between 10 K and 50 K

Construction of the Pauli-Villars-regulated Dirac vacuum in electromagnetic fields

Using the Pauli-Villars regularization and arguments from convex analysis, we construct solutions to the classical time-independent Maxwell equations in Dirac's vacuum, in the presence of small external electromagnetic sources. The vacuum is not an empty space, but rather a quantum fluctuating medium which behaves as a nonlinear polarizable material. Its behavior is described by a Dirac equation involving infinitely many particles. The quantum corrections to the usual Maxwell equations are nonlinear and nonlocal. Even if photons are described by a purely classical electromagnetic field, the resulting vacuum polarization coincides to first order with that of full Quantum Electrodynamics.Comment: Final version to appear in Arch. Rat. Mech. Analysi

From Lagrangian to Quantum Mechanics with Symmetries

We present an old and regretfully forgotten method by Jacobi which allows one to find many Lagrangians of simple classical models and also of nonconservative systems. We underline that the knowledge of Lie symmetries generates Jacobi last multipliers and each of the latter yields a Lagrangian. Then it is shown that Noether's theorem can identify among those Lagrangians the physical Lagrangian(s) that will successfully lead to quantization. The preservation of the Noether symmetries as Lie symmetries of the corresponding Schr\"odinger equation is the key that takes classical mechanics into quantum mechanics. Some examples are presented.Comment: To appear in: Proceedings of Symmetries in Science XV, Journal of Physics: Conference Series, (2012

Radiative Corrections to the Casimir Energy

The lowest radiative correction to the Casimir energy density between two parallel plates is calculated using effective field theory. Since the correlators of the electromagnetic field diverge near the plates, the regularized energy density is also divergent. However, the regularized integral of the energy density is finite and varies with the plate separation L as 1/L^7. This apparently paradoxical situation is analyzed in an equivalent, but more transparent theory of a massless scalar field in 1+1 dimensions confined to a line element of length L and satisfying Dirichlet boundary conditions.Comment: 7 pages, Late

Photon-Neutrino Interactions in Magnetic Field through Neutrino Magnetic Moment

We study the neutrino-photon processes like $\gamma\gamma\to\nu\bar{\nu}$ in the presence of uniform external magnetic field for the case when neutrinos can couple to the electromagnetic field directly through their dipole magnetic moment and obtain the stellar energy loss. The process would be of special relevance in astrophysical situations where standard left-handed neutrinos are trapped and the right handed neutrinos produced through the spin flip interaction induced by neutrino magnetic moment alone can freely stream out.Comment: LaTex2e file, 9 page

Thirty-two Goldbach Variations

We give thirty-two diverse proofs of a small mathematical gem--the fundamental Euler sum identity zeta(2,1)=zeta(3) =8zeta(\bar 2,1). We also discuss various generalizations for multiple harmonic (Euler) sums and some of their many connections, thereby illustrating both the wide variety of techniques fruitfully used to study such sums and the attraction of their study.Comment: v1: 34 pages AMSLaTeX. v2: 41 pages AMSLaTeX. New introductory material added and material on inequalities, Hilbert matrix and Witten zeta functions. Errors in the second section on Complex Line Integrals are corrected. To appear in International Journal of Number Theory. Title change

gamma nu -> gamma gamma nu and crossed processes at energies below m_W

The cross sections for the processes $\gamma \nu\to \gamma \gamma \nu$, $\gamma\gamma\to\gamma\nu\bar{\nu}$ and $\nu\bar{\nu}\to\gamma\gamma\gamma$ are calculated for a range of center of mass energies from below $m_e$ to considerably above $m_e$, but much less than $m_W$. This enables us to treat the neutrino--electron coupling as a four--Fermi interaction and results in amplitudes which are electron box diagrams with three real photons and one virtual photon at their vertices. These calculations extend our previous low--energy effective interaction results to higher energies and enable us to determine where the effective theory is reliable.Comment: 12 pages, RevTex, 10 postscript figures include

Performance of the ARIANNA Hexagonal Radio Array

Installation of the ARIANNA Hexagonal Radio Array (HRA) on the Ross Ice Shelf of Antarctica has been completed. This detector serves as a pilot program to the ARIANNA neutrino telescope, which aims to measure the diffuse flux of very high energy neutrinos by observing the radio pulse generated by neutrino-induced charged particle showers in the ice. All HRA stations ran reliably and took data during the entire 2014-2015 austral summer season. A new radio signal direction reconstruction procedure is described, and is observed to have a resolution better than a degree. The reconstruction is used in a preliminary search for potential neutrino candidate events in the data from one of the newly installed detector stations. Three cuts are used to separate radio backgrounds from neutrino signals. The cuts are found to filter out all data recorded by the station during the season while preserving 85.4% of simulated neutrino events that trigger the station. This efficiency is similar to that found in analyses of previous HRA data taking seasons.Comment: Proceedings from the 34th ICRC2015, http://icrc2015.nl/ . 8 pages, 6 figure

Physics of the Riemann Hypothesis

Physicists become acquainted with special functions early in their studies. Consider our perennial model, the harmonic oscillator, for which we need Hermite functions, or the Laguerre functions in quantum mechanics. Here we choose a particular number theoretical function, the Riemann zeta function and examine its influence in the realm of physics and also how physics may be suggestive for the resolution of one of mathematics' most famous unconfirmed conjectures, the Riemann Hypothesis. Does physics hold an essential key to the solution for this more than hundred-year-old problem? In this work we examine numerous models from different branches of physics, from classical mechanics to statistical physics, where this function plays an integral role. We also see how this function is related to quantum chaos and how its pole-structure encodes when particles can undergo Bose-Einstein condensation at low temperature. Throughout these examinations we highlight how physics can perhaps shed light on the Riemann Hypothesis. Naturally, our aim could not be to be comprehensive, rather we focus on the major models and aim to give an informed starting point for the interested Reader.Comment: 27 pages, 9 figure

Single-valued harmonic polylogarithms and the multi-Regge limit

We argue that the natural functions for describing the multi-Regge limit of six-gluon scattering in planar N=4 super Yang-Mills theory are the single-valued harmonic polylogarithmic functions introduced by Brown. These functions depend on a single complex variable and its conjugate, (w,w*). Using these functions, and formulas due to Fadin, Lipatov and Prygarin, we determine the six-gluon MHV remainder function in the leading-logarithmic approximation (LLA) in this limit through ten loops, and the next-to-LLA (NLLA) terms through nine loops. In separate work, we have determined the symbol of the four-loop remainder function for general kinematics, up to 113 constants. Taking its multi-Regge limit and matching to our four-loop LLA and NLLA results, we fix all but one of the constants that survive in this limit. The multi-Regge limit factorizes in the variables (\nu,n) which are related to (w,w*) by a Fourier-Mellin transform. We can transform the single-valued harmonic polylogarithms to functions of (\nu,n) that incorporate harmonic sums, systematically through transcendental weight six. Combining this information with the four-loop results, we determine the eigenvalues of the BFKL kernel in the adjoint representation to NNLLA accuracy, and the MHV product of impact factors to NNNLLA accuracy, up to constants representing beyond-the-symbol terms and the one symbol-level constant. Remarkably, only derivatives of the polygamma function enter these results. Finally, the LLA approximation to the six-gluon NMHV amplitude is evaluated through ten loops.Comment: 71 pages, 2 figures, plus 10 ancillary files containing analytic expressions in Mathematica format. V2: Typos corrected and references added. V3: Typos corrected; assumption about single-Reggeon exchange made explici