Noncommutative Quantum Mechanics Viewed from Feynman Formalism

Dyson published in 1990 a proof due to Feynman of the Maxwell equations. This proof is based on the assumption of simple commutation relations between position and velocity. We first study a nonrelativistic particle using Feynman formalism. We show that Poincar\'{e}'s magnetic angular momentum and Dirac magnetic monopole are the direct consequences of the structure of the sO(3) Lie algebra in Feynman formalism. Then we show how to extend this formalism to the dual momentum space with the aim of introducing Noncommutative Quantum Mechanics which was recently the subject of a wide range of works from particle physics to condensed matter physics.Comment: 11 pages, To appear in the Proceedings of the Lorentz Workshop "Beyond the Quantum", eds. Th.M. Nieuwenhuizen et al., World Scientific, Singapore, 2007. Added reference

From Feynman Proof of Maxwell Equations to Noncommutative Quantum Mechanics

In 1990, Dyson published a proof due to Feynman of the Maxwell equations assuming only the commutation relations between position and velocity. With this minimal assumption, Feynman never supposed the existence of Hamiltonian or Lagrangian formalism. In the present communication, we review the study of a relativistic particle using ``Feynman brackets.'' We show that Poincar\'e's magnetic angular momentum and Dirac magnetic monopole are the consequences of the structure of the Lorentz Lie algebra defined by the Feynman's brackets. Then, we extend these ideas to the dual momentum space by considering noncommutative quantum mechanics. In this context, we show that the noncommutativity of the coordinates is responsible for a new effect called the spin Hall effect. We also show its relation with the Berry phase notion. As a practical application, we found an unusual spin-orbit contribution of a nonrelativistic particle that could be experimentally tested. Another practical application is the Berry phase effect on the propagation of light in inhomogeneous media.Comment: Presented at the 3rd Feynman Festival (Collage Park, Maryland, U.S.A., August 2006

Spin Hall effect of Photons in a Static Gravitational Field

Starting from a Hamiltonian description of the photon within the set of Bargmann-Wigner equations we derive new semiclassical equations of motion for the photon propagating in static gravitational field. These equations which are obtained in the representation diagonalizing the Hamiltonian at the order $\hbar$, present the first order corrections to the geometrical optics. The photon Hamiltonian shows a new kind of helicity-magnetotorsion coupling. However, even for a torsionless space-time, photons do not follow the usual null geodesic as a consequence of an anomalous velocity term. This term is responsible for the gravitational birefringence phenomenon: photons with distinct helicity follow different geodesics in a static gravitational field.Comment: 6 page

Cross-dimensional Weighting for Aggregated Deep Convolutional Features

We propose a simple and straightforward way of creating powerful image representations via cross-dimensional weighting and aggregation of deep convolutional neural network layer outputs. We first present a generalized framework that encompasses a broad family of approaches and includes cross-dimensional pooling and weighting steps. We then propose specific non-parametric schemes for both spatial- and channel-wise weighting that boost the effect of highly active spatial responses and at the same time regulate burstiness effects. We experiment on different public datasets for image search and show that our approach outperforms the current state-of-the-art for approaches based on pre-trained networks. We also provide an easy-to-use, open source implementation that reproduces our results.Comment: Accepted for publications at the 4th Workshop on Web-scale Vision and Social Media (VSM), ECCV 201

Appearance of Gauge Fields and Forces beyond the adiabatic approximation

We investigate the origin of quantum geometric phases, gauge fields and forces beyond the adiabatic regime. In particular, we extend the notions of geometric magnetic and electric forces discovered in studies of the Born-Oppenheimer approximation to arbitrary quantum systems described by matrix valued quantum Hamiltonians. The results are illustrated by several physical relevant examples

Semiclassical quantization of electrons in magnetic fields: the generalized Peierls substitution

A generalized Peierls substitution which takes into account a Berry phase term must be considered for the semiclassical treatment of electrons in a magnetic field. This substitution turns out to be an essential element for the correct determination of the semiclassical equations of motion as well as for the semiclassical Bohr-Sommerfeld quantization condition for energy levels. A general expression for the cross-sectional area is derived and used as an illustration for the calculation of the energy levels of Bloch and Dirac electrons

Fourfold oscillations and anomalous magnetic irreversibility of magnetoresistance in the non-metallic regime of Pr1.85Ce0.15CuO4

Using magnetoresistance measurements as a function of applied magnetic field and its direction of application, we present sharp angular-dependent magnetoresistance oscillations for the electron-doped cuprates in their low-temperature non-metallic regime. The presence of irreversibility in the magnetoresistance measurements and the related strong anisotropy of the field dependence for different in-plane magnetic field orientations indicate that magnetic domains play an important role for the determination of electronic properties. These domains are likely related to the stripe phase reported previously in hole-doped cuprates.Comment: 11 pages, 5 figure

Diagonal Representation for a Generic Matrix Valued Quantum Hamiltonian

A general method to derive the diagonal representation for a generic matrix valued quantum Hamiltonian is proposed. In this approach new mathematical objects like non-commuting operators evolving with the Planck constant promoted as a running variable are introduced. This method leads to a formal compact expression for the diagonal Hamiltonian which can be expanded in a power series of the Planck constant. In particular, we provide an explicit expression for the diagonal representation of a generic Hamiltonian to the second order in the Planck constant. This last result is applied, as a physical illustration, to Dirac electrons and neutrinos in external fields.Comment: Significant revision, typos corrected and references adde

Modelling waving crops using large-eddy simulation: Comparison with experiments and a linear stability analysis

International audienceIn order to investigate the possibility of modelling plant motion at the landscape scale, an equation for crop plant motion, forced by an instantaneous velocity field, is introduced in a large-eddy simulation (LES) airflow model, previously validated over homogeneous and heterogeneous canopies. The canopy is simply represented as a poroelastic continuous medium, which is similar in its discrete form to an infinite row of identical oscillating stems. Only one linear mode of plant vibration is considered. Two-way coupling between plant motion and the wind flow is insured through the drag force term. The coupled model is validated on the basis of a comparison with measured movements of an alfalfa crop canopy. It is also compared with the outputs of a linear stability analysis. The model is shown to reproduce the well-known phenomenon of honami which is typical of wave-like crop motions on windy days. The wavelength of the main coherent waving patches, extracted using a bi-orthogonal decomposition (BOD) of the crop velocity fields, is in agreement with that deduced from video recordings. The main spatial and temporal characteristics of these waving patches exhibit the same variation with mean wind velocity as that observed with the measurements. However they differ from the coherent eddy structures of the wind flow at canopy top, so that coherent waving patches cannot be seen as direct signatures of coherent eddy structures. Finally, it is shown that the impact of crop motion on the wind dynamics is negligible for current wind speed values. No lock-in mechanism of coherent eddy structures on plant motion is observed, in contradiction with the linear stability analysis. This discrepancy may be attributed to the presence of a nonlinear saturation mechanism in LES. © 2010 Cambridge University Press

Soil organic carbon development and turnover in natural and disturbed salt marsh environments

Author Posting. © American Geophysical Union, 2021. This article is posted here by permission of American Geophysical Union for personal use, not for redistribution. The definitive version was published in Geophysical Research Letters 48(2), (2021): e2020GL090287, https://doi.org/10.1029/2020GL090287.Salt marsh survival with sea‐level rise (SLR) increasingly relies on soil organic carbon (SOC) accumulation and preservation. Using a novel combination of geochemical approaches, we characterized fine SOC (≤1 mm) supporting marsh elevation maintenance. Overlaying thermal reactivity, source (δ13C), and age (F14C) information demonstrates several processes contributing to soil development: marsh grass production, redeposition of eroded material, and microbial reworking. Redeposition of old carbon, likely from creekbanks, represented ∼9%–17% of shallow SOC (≤26 cm). Soils stored marsh grass‐derived compounds with a range of reactivities that were reworked over centuries‐to‐millennia. Decomposition decreases SOC thermal reactivity throughout the soil column while the decades‐long disturbance of ponding accelerated this shift in surface horizons. Empirically derived estimates of SOC turnover based on geochemical composition spanned a wide range (640–9,951 years) and have the potential to inform predictions of marsh ecosystem evolution.This work was supported by NSF (OCE1233678) and NOAA (NA14OAR4170104 and NA14NOS4190145) grants to ACS, USGS Coastal & Marine Geology Program, and PIE‐LTER (NSF OCE1238212 and OCE1637630).2021-06-1