Shape Space Methods for Quantum Cosmological Triangleland

With toy modelling of conceptual aspects of quantum cosmology and the problem of time in quantum gravity in mind, I study the classical and quantum dynamics of the pure-shape (i.e. scale-free) triangle formed by 3 particles in 2-d. I do so by importing techniques to the triangle model from the corresponding 4 particles in 1-d model, using the fact that both have 2-spheres for shape spaces, though the latter has a trivial realization whilst the former has a more involved Hopf (or Dragt) type realization. I furthermore interpret the ensuing Dragt-type coordinates as shape quantities: a measure of anisoscelesness, the ellipticity of the base and apex's moments of inertia, and a quantity proportional to the area of the triangle. I promote these quantities at the quantum level to operators whose expectation and spread are then useful in understanding the quantum states of the system. Additionally, I tessellate the 2-sphere by its physical interpretation as the shape space of triangles, and then use this as a back-cloth from which to read off the interpretation of dynamical trajectories, potentials and wavefunctions. I include applications to timeless approaches to the problem of time and to the role of uniform states in quantum cosmological modelling.Comment: A shorter version, as per the first stage in the refereeing process, and containing some new reference

Magnetic Properties of a Superconductor with no Inversion Symmetry

We study the magnetic properties of a superconductor in a crystal without $z \to -z$ symmetry, in particular how the lack of this symmetry exhibits itself. We show that, though the penetration depth itself shows no such effect, for suitable orientation of magnetic field, there is a magnetic field discontinuity at the interface which shows this absence of symmetry. The magnetic field profile of a vortex in the $x-y$ plane is shown to be identical to that of an ordinary anisotropic superconductor except for a shift in the $-z$ direction by ${\tilde \kappa} \lambda_x$ (see errata). For a vortex along $z$, there is an induced magnetization along the radial direction.Comment: J. Low Temp. Physics, 140, 67 (2005); with Errat

Microwave properties of Nd_0.5Sr_0.5MnO_3: a key role of the (x^2-y^2)-orbital effects

Transmittance of the colossal magnetoresistive compound Nd_0.5Sr_0.5MnO_3 showing metal-insulator phase transition has been studied by means of the submm- and mm-wavelength band spectroscopy. An unusually high transparency of the material provided direct evidence for the significant suppression of the coherent Drude weight in the ferromagnetic metallic state. Melting of the A-type antiferromagnetic states has been found to be responsible for a considerable increase in the microwave transmission, which was observed at the transition from the insulating to the metallic phase induced by magnetic field or temperature. This investigation confirmed a dominant role of the (x^2-y^2)-orbital degree of freedom in the low-energy optical properties of Nd_0.5Sr_0.5MnO_3 and other doped manganites with planar (x^2-y^2)-orbital order, as predicted theoretically. The results are discussed in terms of the orbital-liquid concept.Comment: 8 pages, 3 figure

Charge occupancy of two interacting electrons on artificial molecules - exact results

We present exact solutions for two interacting electrons on an artificial atom and on an artificial molecule made by one and two (single level) quantum dots connected by ideal leads. Specifically, we calculate the accumulated charge on the dots as function of the gate voltage, for various strengths of the electron-electron interaction and of the hybridization between the dots and the (one-dimensional) leads. With increasing of the (negative) gate voltage, the accumulated charge in the two-electron ground state increases in gradual steps from 0 to 1 and then to 2. The value 0 represents an "insulating" state, where both electrons are bound to shallow states on the impurities. The value of 1 corresponds to a "metal", with one electron localized on the dots and the other extended on the leads. The value of 2 corresponds to another "insulator", with both electrons strongly localized. The width of the "metallic" regime diverges with strength of the electron-electron interaction for the single dot, but remains very narrow for the double dot. These results are contrasted with the simple Coulomb blockade picture.Comment: 12 pages, 7 figure

Weakly-Interacting Bosons in a Trap within Approximate Second Quantization Approach

The theory of Bogoliubov is generalized for the case of a weakly-interacting Bose-gas in harmonic trap. A set of nonlinear matrix equations is obtained to make the diagonalization of Hamiltonian possible. Its perturbative solution is used for the calculation of the energy and the condensate fraction of the model system to show the applicability of the method.Comment: 6 pages, two figures .Presented at the International Symposium on Quantum Fluids and Solids QFS2006 (Kyoto, Japan

COVID-19 one year into the pandemic: from genetics and genomics to therapy, vaccination, and policy

COVID-19 has engulfed the world and it will accompany us all for some time to come. Here, we review the current state at the milestone of 1 year into the pandemic, as declared by the WHO (World Health Organization). We review several aspects of the on-going pandemic, focusing first on two major topics: viral variants and the human genetic susceptibility to disease severity. We then consider recent and exciting new developments in therapeutics, such as monoclonal antibodies, and in prevention strategies, such as vaccines. We also briefly discuss how advances in basic science and in biotechnology, under the threat of a worldwide emergency, have accelerated to an unprecedented degree of the transition from the laboratory to clinical applications. While every day we acquire more and more tools to deal with the on-going pandemic, we are aware that the path will be arduous and it will require all of us being community-minded. In this respect, we lament past delays in timely full investigations, and we call for bypassing local politics in the interest of humankind on all continents

The low-energy phase-only action in a superconductor: a comparison with the XY model

The derivation of the effective theory for the phase degrees of freedom in a superconductor is still, to some extent, an open issue. It is commonly assumed that the classical XY model and its quantum generalizations can be exploited as effective phase-only models. In the quantum regime, however, this assumption leads to spurious results, such as the violation of the Galilean invariance in the continuum model. Starting from a general microscopic model, in this paper we explicitly derive the effective low-energy theory for the phase, up to fourth-order terms. This expansion allows us to properly take into account dynamic effects beyond the Gaussian level, both in the continuum and in the lattice model. After evaluating the one-loop correction to the superfluid density we critically discuss the qualitative and quantitative differences between the results obtained within the quantum XY model and within the correct low-energy theory, both in the case of s-wave and d-wave symmetry of the superconducting order parameter. Specifically, we find dynamic anharmonic vertices, which are absent in the quantum XY model, and are crucial to restore Galilean invariance in the continuum model. As far as the more realistic lattice model is concerned, in the weak-to-intermediate-coupling regime we find that the phase-fluctuation effects are quantitatively reduced with respect to the XY model. On the other hand, in the strong-coupling regime we show that the correspondence between the microscopically derived action and the quantum XY model is recovered, except for the low-density regime.Comment: 29 pages, 11 figures. Slightly revised presentation, accepted for publication in Phys. Rev.

Non-Centrosymmetric Heavy-Fermion Superconductors

In this chapter we discuss the physical properties of a particular family of non-centrosymmetric superconductors belonging to the class heavy-fermion compounds. This group includes the ferromagnet UIr and the antiferromagnets CeRhSi3, CeIrSi3, CeCoGe3, CeIrGe3 and CePt3Si, of which all but CePt3Si become superconducting only under pressure. Each of these superconductors has intriguing and interesting properties. We first analyze CePt3Si, then review CeRhSi3, CeIrSi3, CeCoGe3 and CeIrGe3, which are very similar to each other in their magnetic and electrical properties, and finally discuss UIr. For each material we discuss the crystal structure, magnetic order, occurrence of superconductivity, phase diagram, characteristic parameters, superconducting properties and pairing states. We present an overview of the similarities and differences between all these six compounds at the end.Comment: To appear in "Non-Centrosymmetric Superconductors: Introduction and Overview", Lecture Notes in Physics 847, edited by E. Bauer and M. Sigrist (Springer-Verlag, Berlin Heidelberg, 2012) Chap. 2, pp. 35-7

Probing the innermost regions of AGN jets and their magnetic fields with radioastron. I. Imaging BL LACERTAE at 21 μm as resolution

We present the first polarimetric space very long baseline interferometry (VLBI) imaging observations at 22 GHz. BL Lacertae was observed in 2013 November 10 with the RadioAstron space VLBI mission, including a ground array of 15 radio telescopes. The instrumental polarization of the space radio telescope is found to be less than 9%, demonstrating the polarimetric imaging capabilities of RadioAstron at 22 GHz. Ground-space fringes were obtained up to a projected baseline distance of 7.9 Earth diameters in length, allowing us to image the jet in BL Lacertae with a maximum angular resolution of 21 μas, the highest achieved to date. We find evidence for emission upstream of the radio core, which may correspond to a recollimation shock at about 40 μas from the jet apex, in a pattern that includes other recollimation shocks at approximately 100 and 250 μas from the jet apex. Polarized emission is detected in two components within the innermost 0.5 mas from the core, as well as in some knots 3 mas downstream. Faraday rotation analysis, obtained from combining RadioAstron 22 GHz and ground-based 15 and 43 GHz images, shows a gradient in rotation measure and Faraday-corrected polarization vector as a function of position angle with respect to the core, suggesting that the jet in BL Lacertae is threaded by a helical magnetic field. The intrinsic de-boosted brightness temperature in the unresolved core exceeds K, suggesting, at the very least, departure from equipartition of energy between the magnetic field and radiating particles.This research has been supported by the Spanish Ministry of Economy and Competitiveness grant AYA2013-40825-P, by the Russian Foundation for Basic Research (projects 13-02-12103, 14-02-31789, and 15-02-00949), and St. Petersburg University research grant 6.38.335.2015. The research at Boston University (BU) was funded in part by NASA Fermi Guest Investigator grant NNX14AQ58G. Y.M. acknowledges support from the ERC Synergy Grant >BlackHoleCam-Imaging the Event Horizon of Black Holes> (Grant 610058). Part of this work was supported by the COST Action MP1104 >Polarization as a tool to study the Solar System and beyond.> The RadioAstron project is led by the Astro Space Center of the Lebedev Physical Institute of the Russian Academy of Sciences and the Lavochkin Scientific and Production Association under a contract with the Russian Federal Space Agency, in collaboration with partner organizations in Russia and other countries.Peer Reviewe