Arago (1810): the first experimental result against the ether

95 years before Special Relativity was born, Arago attempted to detect the absolute motion of the Earth by measuring the deflection of starlight passing through a prism fixed to the Earth. The null result of this experiment gave rise to the Fresnel's hypothesis of an ether partly dragged by a moving substance. In the context of Einstein's Relativity, the sole frame which is privileged in Arago's experiment is the proper frame of the prism, and the null result only says that Snell's law is valid in that frame. We revisit the history of this premature first evidence against the ether theory and calculate the Fresnel's dragging coefficient by applying the Huygens' construction in the frame of the prism. We expose the dissimilar treatment received by the ray and the wave front as an unavoidable consequence of the classical notions of space and time.Comment: 16 pages. To appear in European Journal of Physic

Chiral molecules split light: Reflection and refraction in a chiral liquid

A light beam changes direction as it enters a liquid at an angle from another medium, such as air. Should the liquid contain molecules that lack mirror symmetry, then it has been predicted by Fresnel that the light beam will not only change direction, but will actually split into two separate beams with a small difference in the respective angles of refraction. Here we report the observation of this phenomenon. We also demonstrate that the angle of reflection does not equal the angle of incidence in a chiral medium. Unlike conventional optical rotation, which depends on the path-length through the sample, the reported reflection and refraction phenomena arise within a few wavelengths at the interface and thereby suggest a new approach to polarimetry that can be used in microfluidic volumes

A Technical Introduction to Transmission Electron Microscopy for Soft-Matter:Imaging, Possibilities, Choices, and Technical Developments

With a significant role in material sciences, physics, (soft matter) chemistry, and biology, the transmission electron microscope is one of the most widely applied structural analysis tool to date. It has the power to visualize almost everything from the micrometer to the angstrom scale. Technical developments keep opening doors to new fields of research by improving aspects such as sample preservation, detector performance, computational power, and workflow automation. For more than half a century, and continuing into the future, electron microscopy has been, and is, a cornerstone methodology in science. Herein, the technical considerations of imaging with electrons in terms of optics, technology, samples and processing, and targeted soft materials are summarized. Furthermore, recent advances and their potential for application to soft matter chemistry are highlighted

Observation of light dragging in rubidium vapor cell

We report on the experimental demonstration of light dragging effect due to atomic motion in a rubidium vapor cell. We found that the minimum group velocity is achieved for light red-shifted from the center of the atomic resonance, and that the value of this shift increases with decreasing group velocity, in agreement with the theoretical predictions by Kocharovskaya, Rostovtsev, and Scully [Phys. Rev. Lett. {\bf 86}, 628 (2001)].Comment: 4 pages 4 figures, submitted to PR

"Fresnel light drag in a coherently driven moving medium"

We theoretically study how the phase of a light plane wave propagating in a resonant medium under electromagnetically induced transparency (EIT) is affected by the uniform motion of the medium. For cuprous oxide (Cu2O), where EIT can be implemented through a typical pump-probe configuration, the resonant probe beam experiences a phase shift (Fresnel-Fizeau effect) that may vary over a wide range of values, positive or negative, and even vanishing, due to the combined effects of the strong frequency dispersion and anisotropy both induced by the pump. The use of such a coherently driven dragging medium may improve by at least 1 order of magnitude the sensitivity at low velocity in optical drag experiments

Tannakian duality for Anderson-Drinfeld motives and algebraic independence of Carlitz logarithms

We develop a theory of Tannakian Galois groups for t-motives and relate this to the theory of Frobenius semilinear difference equations. We show that the transcendence degree of the period matrix associated to a given t-motive is equal to the dimension of its Galois group. Using this result we prove that Carlitz logarithms of algebraic functions that are linearly independent over the rational function field are algebraically independent.Comment: 39 page

Relativistic Effects of Light in Moving Media with Extremely Low Group Velocity

A moving dielectric medium acts as an effective gravitational field on light. One can use media with extremely low group velocities [Lene Vestergaard Hau et al., Nature 397, 594 (1999)] to create dielectric analogs of astronomical effects on Earth. In particular, a vortex flow imprints a long-ranging topological effect on incident light and can behave like an optical black hole.Comment: Physical Review Letters (accepted

Analytic curves in algebraic varieties over number fields

We establish algebraicity criteria for formal germs of curves in algebraic varieties over number fields and apply them to derive a rationality criterion for formal germs of functions, which extends the classical rationality theorems of Borel-Dwork and P\'olya-Bertrandias valid over the projective line to arbitrary algebraic curves over a number field. The formulation and the proof of these criteria involve some basic notions in Arakelov geometry, combined with complex and rigid analytic geometry (notably, potential theory over complex and $p$-adic curves). We also discuss geometric analogues, pertaining to the algebraic geometry of projective surfaces, of these arithmetic criteria.Comment: 55 pages. To appear in "Algebra, Arithmetic, and Geometry: In Honor of Y.i. Manin", Y. Tschinkel & Yu. Manin editors, Birkh\"auser, 200

Optics of Nonuniformly Moving Media

A moving dielectric appears to light as an effective gravitational field. At low flow velocities the dielectric acts on light in the same way as a magnetic field acts on a charged matter wave. We develop in detail the geometrical optics of moving dispersionless media. We derive a Hamiltonian and a Lagrangian to describe ray propagation. We elucidate how the gravitational and the magnetic model of light propagation are related to each other. Finally, we study light propagation around a vortex flow. The vortex shows an optical Aharonov--Bohm effect at large distances from the core, and, at shorter ranges, the vortex may resemble an optical black hole.Comment: Physical Review A (submitted

Linearization in ultrametric dynamics in fields of characteristic zero - equal characteristic case

Let $K$ be a complete ultrametric field of charactersitic zero whose corresponding residue field $\Bbbk$ is also of charactersitic zero. We give lower and upper bounds for the size of linearization disks for power series over $K$ near an indifferent fixed point. These estimates are maximal in the sense that there exist exemples where these estimates give the exact size of the corresponding linearization disc. Similar estimates in the remaning cases, i.e. the cases in which $K$ is either a $p$-adic field or a field of prime characteristic, were obtained in various papers on the $p$-adic case (Ben-Menahem:1988,Thiran/EtAL:1989,Pettigrew/Roberts/Vivaldi:2001,Khrennikov:2001) later generalized in (Lindahl:2009 arXiv:0910.3312), and in (Lindahl:2004 http://iopscience.iop.org/0951-7715/17/3/001/,Lindahl:2010Contemp. Math) concerning the prime characteristic case