Weak and strong coupling limits of the two-dimensional Fr\"ohlich polaron with spin-orbit Rashba interaction

The continuous progress in fabricating low-dimensional systems with large spin-orbit couplings has reached a point in which nowadays materials may display spin-orbit splitting energies ranging from a few to hundreds of meV. This situation calls for a better understanding of the interplay between the spin-orbit coupling and other interactions ubiquitously present in solids, in particular when the spin-orbit splitting is comparable in magnitude with characteristic energy scales such as the Fermi energy and the phonon frequency. In this article, the two-dimensional Fr\"ohlich electron-phonon problem is reformulated by introducing the coupling to a spin-orbit Rashba potential, allowing for a description of the spin-orbit effects on the electron-phonon interaction. The ground state of the resulting Fr\"ohlich-Rashba polaron is studied in the weak and strong coupling limits of the electron-phonon interaction for arbitrary values of the spin-orbit splitting. The weak coupling case is studied within the Rayleigh-Schr\"odinger perturbation theory, while the strong-coupling electron-phonon regime is investigated by means of variational polaron wave functions in the adiabatic limit. It is found that, for both weak and strong coupling polarons, the ground state energy is systematically lowered by the spin-orbit interaction, indicating that the polaronic character is strengthened by the Rashba coupling. It is also shown that, consistently with the lowering of the ground state, the polaron effective mass is enhanced compared to the zero spin-orbit limit. Finally, it is argued that the crossover between weakly and strongly coupled polarons can be shifted by the spin-orbit interaction.Comment: 11 pages, 5 figure

Poynting's theorem and energy conservation in the propagation of light in bounded media

Starting from the Maxwell-Lorentz equations, Poynting's theorem is reconsidered. The energy flux vector is introduced as S_e=(E x B)/mu_0 instead of E x H, because only by this choice the energy dissipation can be related to the balance of the kinetic energy of the matter subsystem. Conservation of the total energy as the sum of kinetic and electromagnetic energy follows. In our discussion, media and their microscopic nature are represented exactly by their susceptibility functions, which do not necessarily have to be known. On this footing, it can be shown that energy conservation in the propagation of light through bounded media is ensured by Maxwell's boundary conditions alone, even for some frequently used approximations. This is demonstrated for approaches using additional boundary conditions and the dielectric approximation in detail, the latter of which suspected to violate energy conservation for decades.Comment: 5 pages, RevTeX4, changes: complete rewrit

Electromagnetic wave refraction at an interface of a double wire medium

Plane-wave reflection and refraction at an interface with a double wire medium is considered. The problem of additional boundary conditions (ABC) in application to wire media is discussed and an ABC-free approach, known in the solid state physics, is used. Expressions for the fields and Poynting vectors of the refracted waves are derived. Directions and values of the power density flow of the refracted waves are found and the conservation of the power flow through the interface is checked. The difference between the results, given by the conventional model of wire media and the model, properly taking into account spatial dispersion, is discussed.Comment: 17 pages, 11 figure

Quantum simulation of small-polaron formation with trapped ions

We propose a quantum simulation of small-polaron physics using a one-dimensional system of trapped ions acted upon by off-resonant standing waves. This system, envisioned as an array of microtraps, in the single-excitation case allows the realization of the anti-adiabatic regime of the Holstein model. We show that the strong excitation-phonon coupling regime, characterized by the formation of small polarons, can be reached using realistic values of the relevant system parameters. Finally, we propose measurements of the quasiparticle residue and the average number of phonons in the ground state, experimental probes validating the polaronic character of the phonon-dressed excitation.Comment: accepted for publication in Phys. Rev. Let

Improving Reliability of Subject-Level Resting-State fMRI Parcellation with Shrinkage Estimators

A recent interest in resting state functional magnetic resonance imaging (rsfMRI) lies in subdividing the human brain into anatomically and functionally distinct regions of interest. For example, brain parcellation is often used for defining the network nodes in connectivity studies. While inference has traditionally been performed on group-level data, there is a growing interest in parcellating single subject data. However, this is difficult due to the low signal-to-noise ratio of rsfMRI data, combined with typically short scan lengths. A large number of brain parcellation approaches employ clustering, which begins with a measure of similarity or distance between voxels. The goal of this work is to improve the reproducibility of single-subject parcellation using shrinkage estimators of such measures, allowing the noisy subject-specific estimator to "borrow strength" in a principled manner from a larger population of subjects. We present several empirical Bayes shrinkage estimators and outline methods for shrinkage when multiple scans are not available for each subject. We perform shrinkage on raw intervoxel correlation estimates and use both raw and shrinkage estimates to produce parcellations by performing clustering on the voxels. Our proposed method is agnostic to the choice of clustering method and can be used as a pre-processing step for any clustering algorithm. Using two datasets---a simulated dataset where the true parcellation is known and is subject-specific and a test-retest dataset consisting of two 7-minute rsfMRI scans from 20 subjects---we show that parcellations produced from shrinkage correlation estimates have higher reliability and validity than those produced from raw estimates. Application to test-retest data shows that using shrinkage estimators increases the reproducibility of subject-specific parcellations of the motor cortex by up to 30%.Comment: body 21 pages, 11 figure

Phonon Coherence and New Set of Sidebands in Phonon-Assisted Photoluminescence

We investigate excitonic polaron states comprising a local exciton and phonons in the longitudinal optical (LO) mode by solving the Schr\"{o}dinger equation. We derive an exact expression for the ground state (GS), which includes multi-phonon components with coefficients satisfying the Huang-Rhys factors. The recombination of GS and excited polaron states gives one set of sidebands in photoluminescence (PL): the multi-phonon components in the GS produce the Stokes lines and the zero-phonon components in the excited states produce the anti-Stokes lines. By introducing the mixing of the LO mode and environal phonon modes, the exciton will also couple with the latter, and the resultant polaron states result in another set of phonon sidebands. This set has a zero-phonon line higher and wider than that of the first set due to the tremendous number of the environal modes. The energy spacing between the zero-phonon lines of the first and second sets is proved to be the binding energy of the GS state. The common exciton origin of these two sets can be further verified by a characteristic Fano lineshape induced by the coherence in the mixing of the LO and the environal modes.Comment: 5 pages, 3 figures 1 figure (fig. 1) replaced 1 figure (fig. 2) remove

Research Note:<br>Use of a distributed erosion model (AGNPS) for planning small reservoirs in the Upper Torysa basin

International audienceThis paper assesses the vulnerability to erosion of the soils in the upper Torysa catchment down to the planned drinking water reservoir at Tichy Potok (Slovakia). Experimental observations in the Torysa catchment, together with the outputs of the AGricultural Non-Point Source pollution model (AGNPS), have been used to select optimal sites for small sediment-trapping dams on the Torysa tributaries. The rainfall scenario for the upper Torysa was determined from records at the Plavec climate station from 1980?1998. In addition, an extreme rainfall event scenario was envisaged (100 mm rainfall in three hours); AGNPS model simulations suggest that such an event might produce as much as half or even the total amount of sediment generated by all the rainfalls over the whole period of simulation, 1980?1998. Keywords: erosion, sediment transport, simulation, AGNPS model, Torysa basi