Conformal Field Theory and the Exact Solution of the BCS Hamiltonian

We propose a connection between conformal field theory (CFT) and the exact solution and integrability of the reduced BCS model of superconductivity. The relevant CFT is given by the $SU(2)_k$-WZW model in the singular limit when the level k goes to -2. This theory has to be perturbed by an operator proportional to the inverse of the BCS coupling constant. Using the free field realization of this perturbed Wess-Zumino-Witten model, we derive the exact Richardson's wave function and the integrals of motion of the reduced BCS model in the saddle point approximation. The construction is reminiscent of the CFT approach to the Fractional Quantum Hall effect.Comment: 10 pages, RevTe

Perceptions of Cheating and Doping in E-Cycling

E-cycling is a growing area of cycling appealing to competitive cyclists and fitness enthusiasts. Zwift is the most popular e-cycling platform, with approx. 1 million subscribers and is a virtual environment that hosts regular races, including the UCI e-cycling world championships. Thepopularity of Zwift has given rise to cases of cheating and hacking the system to gain an advantagein e-racing. As a result, some high-profile professional riders have faced bans. We set out to understand the thoughts and concerns e-cyclists have about cheating, hacking, and doping in e-cycling.A total of 337 females and 1130 males were recruited over a 7-week period via social networkingsites to complete an online survey. Forty-four per cent had experienced cheating during e-racing,which made them feel angry, annoyed, disappointed, and cheated. However, 15% of those whoexperienced cheating said they did not care, possibly because many see e-racing as a game or training tool rather than a competitive event. Eighty-seven per cent of participants were in favour ofenforcing a ban on cheaters in e-cycling, while 34% wanted cheaters to be banned during in-personcycling events too. Results indicate that many e-cyclists have experienced cheating and would likeclearer rules and bans for cheaters during e-races

Neonatal 5,7-DHT Lesions Cause Sex-Specific Changes in Mouse Cortical Morphogenesis

Both monoaminergic and cholinergic afferent projections to the neocortex putatively modulate cortical morphogenesis and plasticity. Previously we showed that neonatal,electrolytic lesions: the cholinergic nucleus basalis magnocel!ularis (nBM) projections to the neocortex result in significant decreases-of cortical layer width that correlate with cognitive alterations. Such electrolytic lesions, performed for lack of a selective neurotoxin in mice, may affect mono- aminergic fibers of passage. Here, we investigate the effects of neonatal 5,7 dihydroxytryptamine (5,7-DHT) focal injections into the nBM region on cortical laminar morphology in adult male and female mice. 5,7-DHT lesions on the first postnatal day resulted in significant cortical depletion of both serotonin and norepinephrine that attenuated with age. Generally, cortical layer widths increased in response to the lesion; the effects were layer, region, and sex specific. Previous reports from our laboratories described longterm behavioral alterations after comparable focal, neonatal 5,7-DHT lesions. The studies described here provide an anatomical basis for such behavioral alterations. Our data suggest that monoaminergic and cholinergic projections to the cortex may have opposite effects on the developing cortical neuropil. Jointly, our morphological and behavioral findings may have important implications for a variety of developmental disorders in humans and provide some insights into sex differences in the penetrance of these disorders

Exact Study of the Effect of Level Statistics in Ultrasmall Superconducting Grains

The reduced BCS model that is commonly used for ultrasmall superconducting grains has an exact solution worked out long ago by Richardson in the context of nuclear physics. We use it to check the quality of previous treatments of this model, and to investigate the effect of level statistics on pairing correlations. We find that the ground state energies are on average somewhat lower for systems with non-uniform than uniform level spacings, but both have an equally smooth crossover from the bulk to the few-electron regime. In the latter, statistical fluctuations in ground state energies strongly depend on the grain's electron number parity.Comment: 4 pages, 3 eps figs, RevTe

Extracting non-linear integrate-and-fire models from experimental data using dynamic I - V curves

The dynamic I-V curve method was recently introduced for the efficient experimental generation of reduced neuron models. The method extracts the response properties of a neuron while it is subject to a naturalistic stimulus that mimics in vivo-like fluctuating synaptic drive. The resulting history-dependent, transmembrane current is then projected onto a one-dimensional current-voltage relation that provides the basis for a tractable non-linear integrate-and-fire model. An attractive feature of the method is that it can be used in spike-triggered mode to quantify the distinct patterns of post-spike refractoriness seen in different classes of cortical neuron. The method is first illustrated using a conductance-based model and is then applied experimentally to generate reduced models of cortical layer-5 pyramidal cells and interneurons, in injected-current and injected- conductance protocols. The resulting low-dimensional neuron models—of the refractory exponential integrate-and-fire type—provide highly accurate predictions for spike-times. The method therefore provides a useful tool for the construction of tractable models and rapid experimental classification of cortical neuron

Superconducting correlations in metallic nanoparticles: exact solution of the BCS model by the algebraic Bethe ansatz

Superconducting pairing of electrons in nanoscale metallic particles with discrete energy levels and a fixed number of electrons is described by the reduced BCS model Hamiltonian. We show that this model is integrable by the algebraic Bethe ansatz. The eigenstates, spectrum, conserved operators, integrals of motion, and norms of wave functions are obtained. Furthermore, the quantum inverse problem is solved, meaning that form factors and correlation functions can be explicitly evaluated. Closed form expressions are given for the form factors that describe superconducting pairing.Comment: revised version, 5 pages, revtex, no figure

Quantum Entanglement and Order Parameter in a Paired Finite Fermi System

We study the pairing correlations in a finite Fermi system from quantum entanglement point of view. We investigate the relation between the order parameter, which has been introduced recently to describe both finite and infinite superconductors, and the concurrence. For a proper definition of the concurrence, we argue that a possible generalization of spin flip transformation is time reversal operation. While for a system with indefinite number of particles concurrence is a good measure of entanglement, for a finite system it does not distinguish between normal and superconducting states. We propose that the expectation value of the radial operator for the total pseudospin can be used to identify entanglement of pairing.Comment: submitted to Solid State Communications (the Festschrift in the honor of Prof. Salim Ciraci's 60th birthday

Evolution of helicity in NOAA 10923 over three consecutive solar rotations

We have studied the evolution of magnetic helicity and chirality in an active region over three consecutive solar rotations. The region when it first appeared was named NOAA10923 and in subsequent rotations it was numbered NOAA 10930, 10935 and 10941. We compare the chirality of these regions at photospheric, chromospheric and coronal heights. The observations used for photospheric and chromospheric heights are taken from Solar Vector Magnetograph (SVM) and H_alpha imaging telescope of Udaipur Solar Observatory (USO), respectively. We discuss the chirality of the sunspots and associated H_alpha filaments in these regions. We find that the twistedness of superpenumbral filaments is maintained in the photospheric transverse field vectors also. We also compare the chirality at photospheric and chromospheric heights with the chirality of the associated coronal loops, as observed from the HINODE X-Ray Telescope.Comment: 8 pages, 4 figure