Fermi-liquid effects in the Fulde-Ferrell-Larkin-Ovchinnikov state of two-dimensional d-wave superconductors

We study the effects of Fermi-liquid interactions on quasi-two-dimensional d-wave superconductors in a magnetic field. The phase diagram of the superconducting state, including the periodic Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state in high magnetic fields, is discussed for different strengths of quasiparticle many-body interactions within Landau's theory of Fermi liquids. Decreasing the Fermi-liquid parameter $F_0^a$ causes the magnetic spin susceptibility to increase, which in turn leads to a reduction of the FFLO phase. It is shown that a negative $F_0^a$ results in a first-order phase transition from the normal to the uniform superconducting state in a finite temperature interval. Finally, we discuss the thermodynamic implications of a first-order phase transition for CeCoIn$_5$.Comment: published version; removed direct comparison with experiment for the upper critical field, as required by the referee

The colour of the narrow line Sy1-blazar 0324+3410

Aims. We investigate the properties of the host galaxy of the blazar J0324+3410 (B2 0321+33) by the analysis of B and R images obtained with the NOT under good photometric conditions. Methods: The galaxy was studied using different methods: Sersic model fitting, unsharp-masked images, B-R image and B-R profile analysis. Results: The images show that the host galaxy has a ring-like morphology. The B-R colour image reveals two bluish zones: one that coincides with the nuclear region, interpreted as the signature of emission related to the active nucleus, the other zone is extended and is located in the host ring-structure. We discuss the hypothesis that the later is thermal emission from a burst of star formation triggered by an interacting/merging process

Factorizations of Rational Matrix Functions with Application to Discrete Isomonodromic Transformations and Difference Painlev\'e Equations

We study factorizations of rational matrix functions with simple poles on the Riemann sphere. For the quadratic case (two poles) we show, using multiplicative representations of such matrix functions, that a good coordinate system on this space is given by a mix of residue eigenvectors of the matrix and its inverse. Our approach is motivated by the theory of discrete isomonodromic transformations and their relationship with difference Painlev\'e equations. In particular, in these coordinates, basic isomonodromic transformations take the form of the discrete Euler-Lagrange equations. Secondly we show that dPV equations, previously obtained in this context by D. Arinkin and A. Borodin, can be understood as simple relationships between the residues of such matrices and their inverses.Comment: 9 pages; minor typos fixed, journal reference adde

Trident pair production in strong laser pulses

We calculate the trident pair production amplitude in a strong laser background. We allow for finite pulse duration, while still treating the laser fields nonperturbatively in strong-field QED. Our approach reveals explicitly the individual contributions of the one-step and two-step processes. We also expose the role gauge invariance plays in the amplitudes and discuss the relation between our results and the optical theorem.Comment: 4 pages, 1 .eps figure. Version 2: reference added, published versio

Pauli-Limited Superconductivity with Classical Magnetic Fluctuations

We examine the effect of classical magnetic fluctuations on the phase diagram of paramagneticallylimited two-dimensional superconductors under a Zeeman magnetic field. We derive the free energy expansion in powers of the superconducting order parameter and analyze the character of the normalsuperconducting transition. While the transition is of the second order for all temperatures in the absence of magnetic fluctuations, we find that proximity to magnetism drives both the transition into the uniform state and that into the modulated (Fulde-Ferrell-Larkin-Ovchinnikov, FFLO) state to first order at intermediate temperatures. We compute the thermodynamic signatures of the normal-superconducting transition along the upper critical field.Comment: 16 pages, 9 figure

Електрофільні реакції 7-(трифлуорометил)-2,3-дигідро-1H-піролізину – шлях до нових будівельних блоків

Aim. To synthesize new fluoro-containing building blocks for medicinal chemistry purposes using electrophilic reactions of 7-(trifluoromethyl)-2,3-dihydro-1H-pyrrolizine.Results and discussion. Synthetic approaches to 5-halogeno- and 5-acyl-7-(trifluoromethyl)-2,3-dihydro-1H-pyrrolizines have been developed. The obtained new trifluoromethyl-containing pyrrolyzines are promising building blocks for medicinal chemistry.Experimental part. The synthesis of the target compounds began with known 7-(trifluoromethyl)-2,3-dihydro-1H-pyrrolizine and included halogenation and acylation reactions using N-halogen succinimides and acylating reagents.Conclusions. New synthetic approaches to a number of 7-(trifluoromethyl)-2,3-dihydro-1H-pyrrolizines with various substituents, such as halogen atoms or acyl groups, at the position 5 of the pyrrole ring have been developed. This opens the door to the use of such promising trifluoromethyl-containing building blocks for medicinal chemistry needs.Мета. Синтезувати нові флуоровмісні будівельні блоки для потреб медичної хімії за допомогою електрофільних реакцій 7-(трифлуорометил)-2,3-дигідро-1H-піролізину.Результати та їх обговорення. Було розроблено синтетичні підходи до 5-галогено- та 5-ацил-7-(трифлуорометил)-2,3-дигідро-1H-піролізинів. Отримані нові трифлуорометил-вмісні піролізини є перспективними будівельними блокамидля медичної хімії.Експериментальна частина. Синтез цільових сполук було здійснено на основі відомого 7-(трифлуорометил)-2,3-дигідро-1H-піролізину з використанням реакцій галогенування та ацилювання дією N-галогеносукцинімідів і ацилювальних реагентів.Висновки. Розроблено нові синтетичні підходи до одержання ряду 7-(трифлуорометил)-2,3-дигідро-1H-піролізинів з різноманітними замісниками: атомами галогенів або ацильними групами в положенні 5 пірольного циклу. Це дозволяє використовувати синтезовані речовини як перспективні трифлуорометилвмісні будівельні блоки в дослідженнях у царині медичної хімії

Accurate measurement of a 96% input coupling into a cavity using polarization tomography

Pillar microcavities are excellent light-matter interfaces providing an electromagnetic confinement in small mode volumes with high quality factors. They also allow the efficient injection and extraction of photons, into and from the cavity, with potentially near-unity input and output-coupling efficiencies. Optimizing the input and output coupling is essential, in particular, in the development of solid-state quantum networks where artificial atoms are manipulated with single incoming photons. Here we propose a technique to accurately measure input and output coupling efficiencies using polarization tomography of the light reflected by the cavity. We use the residual birefringence of pillar microcavities to distinguish the light coupled to the cavity from the uncoupled light: the former participates to rotating the polarization of the reflected beam, while the latter decreases the polarization purity. Applying this technique to a micropillar cavity, we measure a $53 \pm2 \%$ output coupling and a $96 \pm 1\%$ input coupling with unprecedented precision.Comment: 6 pages, 3 figure

Infra-red divergences in plane wave backgrounds

We show that the emission of soft photons via nonlinear Compton scattering in a pulsed plane wave (laser field) is in general infra-red divergent. We give examples of both soft and soft-collinear divergences, and we pay particular attention to the case of crossed fields in both classical and quantum theories.Comment: 15 pages, 7 figure