Renormalization-group investigation of a superconducting U(r)U(r)-phase transition using five loops calculations

We have studied a Fermi system with attractive $U(r)$-symmetric interaction at the finite temperatures by the quantum field renormalization group (RG) method. The RG functions have been calculated in the framework of dimensional regularization and minimal subtraction scheme up to five loops. It has been found that for $r\geq 4$ the RG flux leaves the system's stability region -- the system undergoes a first order phase transition. To estimate the temperature of the transition to superconducting or superfluid phase the RG analysis for composite operators has been performed using three-loops approximation. As the result this analysis shows that for $3D$ systems estimated phase transition temperature is higher then well known theoretical estimations based on continuous phase transition formalism

Renormalization Group in Non-Relativistic Quantum Statistics

Dynamic behaviour of a boson gas near the condensation transition in the symmetric phase is analyzed with the use of an effective large-scale model derived from time-dependent Green functions at finite temperature. A renormalization-group analysis shows that the scaling exponents of critical dynamics of the effective multi-charge model coincide with those of the standard model A. The departure of this result from the descrip tion of the superfluid transition by either model E or F of the standard phenomenological stochastic models is corroborated by the analysis of a generalization of model F, which takes into account the effect of compressible fluid velocity. It is also shown that, con trary to the single-charge model A, there are several correction exponents in the effective model, which are calculated at the leading order of the = 4 − d expansion

Effects of fabrication errors on the focusing performance of a sector metalens

Using e-beam lithography, a 16-sector spiral metalens was fabricated in an amorphous silicon, capable of converting linearly polarized incident light into an azimuthally polarized optical vortex. When illuminated by a 633-nm linearly polarized laser beam, the metalens generated a near-surface subwavelength focal spot equal to 0.75 of the incident wavelength at full-width of half-maximum intensity. The focusing performance of the spiral metalens was numerically shown to be sensitive to the deviation of the factual microrelief from the calculated height. For the designed microrelief height, a circularly polarized incident beam was focused into a bright ring with a reverse energy flow occurring at its center. For the microrelief height other than the designed one, the energy backflow effect did not occur

Microlens-aided focusing of linearly and azimuthally polarized laser light

Funding: Russian Foundation for Basic Research (RFBR) (14-29-07133, 14-07-97039, 15-07-01174, 15-47-02492, 15-37-20723, 16-07-00990, 16-47-630483); Ministry of Education and Science of the Russian Federation (NSh-4128.2016.9, MK-9019.2016.2); European Research Council (337508).We have investigated a four-Sector transmission Polarization Converter (4-SPC) for a wavelength of 633 nm, that enables the conversion of a linearly polarized incident beam into a mixture of linearly and azimuthally polarized beams. It was numerically shown that by placing a Fresnel zone plate of focal length 532 nm immediately after the 4-SPC, the incident light can be focused into an oblong subwavelength focal spot whose size is smaller than the diffraction limit (with width and breadth, respectively, measuring FWHM = 0.28λ and FWHM = 0.45λ, where λ is the incident wavelength and FWHM stands for full-width at half maximum of the intensity). After passing through the 4-SPC, light propagates in free space over a distance of 300 μm before being focused by a Fresnel zone plate (ZP), resulting in focal spot measuring 0.42λ and 0.81λ. The focal spot was measured by a near-field microscope SNOM, and the transverse E-field component of the focal spot was calculated to be 0.42λ and 0.59λ. This numerical result was verified experimentally, giving a focal spot of smaller and larger size, respectively, measuring 0.46λ and 0.57λ. To our knowledge, this is the first implementation of polarization conversion and subwavelength focusing of light using a pair of transmission micro-optic elements.PostprintPeer reviewe

Tight focusing of laser light using a chromium Fresnel zone plate

Funding: Russian Scientific Foundation (17-19-01186).Using near-field scanning microscopy, we demonstrate that a 15-µm zone plate fabricated in a 70-nm chromium film sputtered on a glass substrate and having a focal length and outermost zone's width equal to the incident wavelength λ = 532 nm, focuses a circularly polarized Gaussian beam into a circular subwavelength focal spot whose diameter at the full-width of half-maximum intensity is FWHM = 0.47λ. This value is in near-accurate agreement with the FDTD-aided numerical estimate of FWHM = 0.46λ. When focusing a Gaussian beam linearly polarized along the y-axis, an elliptic subwavelength focal spot is experimentally found to measure FWHMx = 0.42λ (estimated value FWHMx = 0.40λ) and FWHMy = 0.64λ. The subwavelength focal spots presented here are the tightest among all attained so far for homogeneously polarized beams by use of non-immersion amplitude zone plates.PostprintPeer reviewe

On the finite-time splash and splat singularities for the 3-D free-surface Euler equations

We prove that the 3-D free-surface incompressible Euler equations with regular initial geometries and velocity fields have solutions which can form a finite-time "splash" (or "splat") singularity first introduced in [9], wherein the evolving 2-D hypersurface, the moving boundary of the fluid domain, self-intersects at a point (or on surface). Such singularities can occur when the crest of a breaking wave falls unto its trough, or in the study of drop impact upon liquid surfaces. Our approach is founded upon the Lagrangian description of the free-boundary problem, combined with a novel approximation scheme of a finite collection of local coordinate charts; as such we are able to analyze a rather general set of geometries for the evolving 2-D free-surface of the fluid. We do not assume the fluid is irrotational, and as such, our method can be used for a number of other fluid interface problems, including compressible flows, plasmas, as well as the inclusion of surface tension effects.Comment: 40 pages, 5 figures, to appear in Comm. Math. Phys, abstract added for UK RE

Clinical history , interictal EEG and home-made video diagnostic accuracy: comparison with the VEPSG

Poiché la diagnosi differenziale degli episodi parossistici notturni è affidata alla VEPSG, tenendo conto dei limiti di tale metodica, il progetto attuale ha lo scopo di definire la resa diagnostica di strumenti alternativi alla VEPSG: anamnesi, home-made video ed EEG intercritico. Sono stati reclutati consecutivamente 13 pazienti, afferiti al nostro Dipartimento per episodi parossistici notturni. Ciascun paziente è stato sottoposto ad un protocollo diagnostico standardizzato. A 5 Medici Esperti in Epilessia e Medicina del Sonno è stato chiesto di formulare un orientamento diagnostico sulla base di anamnesi, EEG intercritico, home-made video e VEPSG. Attraverso l’elaborazione degli orientamenti diagnostici è stata calcolata la resa diagnostica delle procedure esaminate, a confronto con la VEPSG, attraverso il concetto di “accuratezza diagnostica”. Per 6 pazienti è stato possibile porre una diagnosi di Epilessia Frontale Notturna, per 2 di parasonnia, in 5 la diagnosi è rimasta dubbia. L’accuratezza diagnostica di ciascuna procedura è risultata moderata, con lievi differenze tra le diverse procedure (61.5% anamnesi; 66% home-made video; 69,2 % EEG intercritico). E’ essenziale migliorare ulteriormente l’accuratezza diagnostica di anamnesi, EEG intercritico ed home-made video, che possono risultare cruciali nei casi in cui la diagnosi non è certa o quando la VEPSG non è disponibile.Nocturnal frontal lobe epilepsy (NFLE) seizures appear almost exclusively during sleep. The differential diagnosis between this condition and sleep-related non-epileptic paroxysmal motor phenomena, in particular parasomnias, is arduous. Moreover, accepted criteria for the diagnosis of NFLE are lacking. At present video-polysomnographic recording of the seizures during sleep is the gold standard for the diagnosis but this technique is expensive and not available everywhere. The aim of this study is to measure the diagnostic accuracy of clinical history, interictal EEG and home-made video in distinguishing NFLE from non-epileptic paroxysmal sleep disorders. 13 patients who presented paroxysmal motor phenomena during sleep were consecutively enrolled in our Department and a specific diagnostic examination battery was performed. After the completion of the examinations the results were analyzed by five experts in clinical sleep medicine and epilepsy and a diagnostic decision was made: 6 subjects were classified as NFLE, 2 as parasomnias and 5 as “uncertain” diagnosis. From experts diagnostic decision, the clinical history, interictal EEG and home-made video diagnostic accuracy were calculated. The diagnostic accuracy was overall moderate and showed only slight differences between the procedures. However, it is essential to improve the diagnostic accuracy of clinical history, interictal EEG and home-made video recording that could be helpful in cases difficult to diagnose or when VEPSG monitoring is not available. In addition, future research should define reliable clinical and VEPSG criteria for the diagnosis of nocturnal frontal lobe seizures

Optical Vortex Beams with a Symmetric OAM Spectrum beyond a Sector Aperture

In this work, we theoretically and numerically show that in the superposition of optical Gaussian vortices with a symmetric OAM spectrum, the normalized orbital angular momentum (OAM) carried by the beam and the topological charge (TC) equal TC of the middle constituent vortex. We also show that after passing a sector-shaped aperture, the symmetric superposition preserves the OAM carried, with the TC becoming fractional and proportional to the angle of the sector aperture. As it further propagates in free space after the sector aperture, the TC of the superposition becomes an integer, albeit indefinite, thanks to the aperture edges generating a multitude of extra optical vortices with positive and negative unit TC, irregularly arranged across the beam

Topological Charge and Asymptotic Phase Invariants of Vortex Laser Beams

It is well known that the orbital angular momentum (OAM) of a light field is conserved on propagation. In this work, in contrast to the OAM, we analytically study conservation of the topological charge (TC), which is often confused with OAM, but has quite different physical meaning. To this end, we propose a huge-ring approximation of the Huygens–Fresnel principle, when the observation point is located on an infinite-radius ring. Based on this approximation, our proof of TC conservation reveals that there exist other quantities that are also propagation-invariant, and the number of these invariants is theoretically infinite. Numerical simulation confirms the conservation of two such invariants for two light fields. The results of this work can find applications in optical data transmission to identify optical signals

Optical Vortex Beams with a Symmetric OAM Spectrum beyond a Sector Aperture

In this work, we theoretically and numerically show that in the superposition of optical Gaussian vortices with a symmetric OAM spectrum, the normalized orbital angular momentum (OAM) carried by the beam and the topological charge (TC) equal TC of the middle constituent vortex. We also show that after passing a sector-shaped aperture, the symmetric superposition preserves the OAM carried, with the TC becoming fractional and proportional to the angle of the sector aperture. As it further propagates in free space after the sector aperture, the TC of the superposition becomes an integer, albeit indefinite, thanks to the aperture edges generating a multitude of extra optical vortices with positive and negative unit TC, irregularly arranged across the beam