Discovery of the Acoustic Faraday Effect in Superfluid 3He-B

We report the discovery of the acoustic Faraday effect in superfluid 3He-B. The observation of this effect provides the first direct evidence for propagating transverse acoustic waves in liquid 3He, a mode first predicted by Landau in 1957. The Faraday rotation is large and observable because of spontaneously broken spin-orbit symmetry in 3He-B. We compare the experimental observations with a simulation of the transverse acoustic impedance that includes the field-induced circular birefringence of transverse waves.Comment: 4 pages in RevTex plus 3 postscript figures; new version includes: minor corrections to the text and an updated of list of reference

Slepian functions and their use in signal estimation and spectral analysis

It is a well-known fact that mathematical functions that are timelimited (or spacelimited) cannot be simultaneously bandlimited (in frequency). Yet the finite precision of measurement and computation unavoidably bandlimits our observation and modeling scientific data, and we often only have access to, or are only interested in, a study area that is temporally or spatially bounded. In the geosciences we may be interested in spectrally modeling a time series defined only on a certain interval, or we may want to characterize a specific geographical area observed using an effectively bandlimited measurement device. It is clear that analyzing and representing scientific data of this kind will be facilitated if a basis of functions can be found that are "spatiospectrally" concentrated, i.e. "localized" in both domains at the same time. Here, we give a theoretical overview of one particular approach to this "concentration" problem, as originally proposed for time series by Slepian and coworkers, in the 1960s. We show how this framework leads to practical algorithms and statistically performant methods for the analysis of signals and their power spectra in one and two dimensions, and on the surface of a sphere.Comment: Submitted to the Handbook of Geomathematics, edited by Willi Freeden, Zuhair M. Nashed and Thomas Sonar, and to be published by Springer Verla

Conformally rescaled spacetimes and Hawking radiation

We study various derivations of Hawking radiation in conformally rescaled metrics. We focus on two important properties, the location of the horizon under a conformal transformation and its associated temperature. We find that the production of Hawking radiation cannot be associated in all cases to the trapping horizon because its location is not invariant under a conformal transformation. We also find evidence that the temperature of the Hawking radiation should transform simply under a conformal transformation, being invariant for asymptotic observers in the limit that the conformal transformation factor is unity at their location.Comment: 22 pages, version submitted to journa

Scalar and vector Slepian functions, spherical signal estimation and spectral analysis

It is a well-known fact that mathematical functions that are timelimited (or spacelimited) cannot be simultaneously bandlimited (in frequency). Yet the finite precision of measurement and computation unavoidably bandlimits our observation and modeling scientific data, and we often only have access to, or are only interested in, a study area that is temporally or spatially bounded. In the geosciences we may be interested in spectrally modeling a time series defined only on a certain interval, or we may want to characterize a specific geographical area observed using an effectively bandlimited measurement device. It is clear that analyzing and representing scientific data of this kind will be facilitated if a basis of functions can be found that are "spatiospectrally" concentrated, i.e. "localized" in both domains at the same time. Here, we give a theoretical overview of one particular approach to this "concentration" problem, as originally proposed for time series by Slepian and coworkers, in the 1960s. We show how this framework leads to practical algorithms and statistically performant methods for the analysis of signals and their power spectra in one and two dimensions, and, particularly for applications in the geosciences, for scalar and vectorial signals defined on the surface of a unit sphere.Comment: Submitted to the 2nd Edition of the Handbook of Geomathematics, edited by Willi Freeden, Zuhair M. Nashed and Thomas Sonar, and to be published by Springer Verlag. This is a slightly modified but expanded version of the paper arxiv:0909.5368 that appeared in the 1st Edition of the Handbook, when it was called: Slepian functions and their use in signal estimation and spectral analysi

An efficient algorithm for numerical computations of continuous densities of states

In Wang-Landau type algorithms, Monte-Carlo updates are performed with respect to the density of states, which is iteratively refined during simulations. The partition function and thermodynamic observables are then obtained by standard integration. In this work, our recently introduced method in this class (the LLR approach) is analysed and further developed. Our approach is a histogram free method particularly suited for systems with continuous degrees of freedom giving rise to a continuum density of states, as it is commonly found in Lattice Gauge Theories and in some Statistical Mechanics systems. We show that the method possesses an exponential error suppression that allows us to estimate the density of states over several orders of magnitude with nearly-constant relative precision. We explain how ergodicity issues can be avoided and how expectation values of arbitrary observables can be obtained within this framework. We then demonstrate the method using Compact U(1) Lattice Gauge Theory as a show case. A thorough study of the algorithm parameter dependence of the results is performed and compared with the analytically expected behaviour. We obtain high precision values for the critical coupling for the phase transition and for the peak value of the specific heat for lattice sizes ranging from 84 to 204. Our results perfectly agree with the reference values reported in the literature, which covers lattice sizes up to 184. Robust results for the 204 volume are obtained for the first time. This latter investigation, which, due to strong metastabilities developed at the pseudo-critical coupling of the system, so far has been out of reach even on supercomputers with importance sampling approaches, has been performed to high accuracy with modest computational resources. This shows the potential of the method for studies of first order phase transitions. Other situations where the method is expected to be superior to importance sampling techniques are pointed out

Vortices in (2+1)d Conformal Fluids

We study isolated, stationary, axially symmetric vortex solutions in (2+1)-dimensional viscous conformal fluids. The equations describing them can be brought to the form of three coupled first order ODEs for the radial and rotational velocities and the temperature. They have a rich space of solutions characterized by the radial energy and angular momentum fluxes. We do a detailed study of the phases in the one-parameter family of solutions with no energy flux. This parameter is the product of the asymptotic vorticity and temperature. When it is large, the radial fluid velocity reaches the speed of light at a finite inner radius. When it is below a critical value, the velocity is everywhere bounded, but at the origin there is a discontinuity. We comment on turbulence, potential gravity duals, non-viscous limits and non-relativistic limits.Comment: 39 pages, 10 eps figures, v2: Minor changes, refs, preprint numbe

ARPES: A probe of electronic correlations

Angle-resolved photoemission spectroscopy (ARPES) is one of the most direct methods of studying the electronic structure of solids. By measuring the kinetic energy and angular distribution of the electrons photoemitted from a sample illuminated with sufficiently high-energy radiation, one can gain information on both the energy and momentum of the electrons propagating inside a material. This is of vital importance in elucidating the connection between electronic, magnetic, and chemical structure of solids, in particular for those complex systems which cannot be appropriately described within the independent-particle picture. Among the various classes of complex systems, of great interest are the transition metal oxides, which have been at the center stage in condensed matter physics for the last four decades. Following a general introduction to the topic, we will lay the theoretical basis needed to understand the pivotal role of ARPES in the study of such systems. After a brief overview on the state-of-the-art capabilities of the technique, we will review some of the most interesting and relevant case studies of the novel physics revealed by ARPES in 3d-, 4d- and 5d-based oxides.Comment: Chapter to appear in "Strongly Correlated Systems: Experimental Techniques", edited by A. Avella and F. Mancini, Springer Series in Solid-State Sciences (2013). A high-resolution version can be found at: http://www.phas.ubc.ca/~quantmat/ARPES/PUBLICATIONS/Reviews/ARPES_Springer.pdf. arXiv admin note: text overlap with arXiv:cond-mat/0307085, arXiv:cond-mat/020850

On General BCJ Relation at One-loop Level in Yang-Mills Theory

BCJ relation reveals a dual between color structures and kinematic structure and can be used to reduce the number of independent color-ordered amplitudes at tree level. Refer to the loop-level in Yang-Mills theory, we investigate the similar BCJ relation in this paper. Four-point 1-loop example in N = 4 SYM can hint about the relation of integrands. Five-point example implies that the general formula can be proven by unitary- cut method. We will then prove a 'general' BCJ relation for 1-loop integrands by D-dimension unitary cut, which can be regarded as a non-trivial generalization of the (fundamental)BCJ relation given by Boels and Isermann in [arXiv:1109.5888 [hep-th]] and [arXiv:1110.4462 [hep-th]].Comment: 18 pages, 6 figure

Wall roughness induces asymptotic ultimate turbulence

Turbulence is omnipresent in Nature and technology, governing the transport of heat, mass, and momentum on multiple scales. For real-world applications of wall-bounded turbulence, the underlying surfaces are virtually always rough; yet characterizing and understanding the effects of wall roughness for turbulence remains a challenge, especially for rotating and thermally driven turbulence. By combining extensive experiments and numerical simulations, here, taking as example the paradigmatic Taylor-Couette system (the closed flow between two independently rotating coaxial cylinders), we show how wall roughness greatly enhances the overall transport properties and the corresponding scaling exponents. If only one of the walls is rough, we reveal that the bulk velocity is slaved to the rough side, due to the much stronger coupling to that wall by the detaching flow structures. If both walls are rough, the viscosity dependence is thoroughly eliminated in the boundary layers and we thus achieve asymptotic ultimate turbulence, i.e. the upper limit of transport, whose existence had been predicted by Robert Kraichnan in 1962 (Phys. Fluids {\bf 5}, 1374 (1962)) and in which the scalings laws can be extrapolated to arbitrarily large Reynolds numbers

Towards DNS of the Ultimate Regime of Rayleigh--B\'enard Convection

In this contribution we have briefly introduced the problem of turbulent thermal convection with a particular look at its transition to the ultimate regime and the resolution requirements needed for the direct numerical simulation of this flow.Comment: 10 pages, 6 figure