Coherent neutrino radiation in supernovae at two loops

We develop a neutrino transport theory, in terms of the real-time non-equilibrium Green's functions, which is applicable to physical conditions arbitrary far from thermal equilibrium. We compute the coherent neutrino radiation in cores of supernovae by evaluating the two-particle-two-hole (2p-2h) polarization function with dressed propagators. The propagator dressing is carried out in the particle-particle channel to all orders in the interaction. We show that at two loops there are two distinct sources of coherence effects in the bremsstrahlung. One is the generically off-shell intermediate state propagation, which leads to the Landau-Pomeranchuk-Migdal type suppression of radiation. We extend previous perturbative results, obtained in the leading order in quasiparticle width, by deriving the exact non-perturbative expression. A new contribution due to off-shell finial/initial baryon states is treated in the leading order in the quasiparticle width. The latter contribution corresponds to processes of higher order than second order in the virial expansion in the number of quasiparticles. At 2p-2h level, the time component of the polarization tensor for the vector transitions vanishes identically in the soft neutrino limit. Vector current thereby is conserved. The contraction of the neutral axial vector current with tensor interaction among the baryons leads to a non-vanishing contribution to the bremsstrahlung rate. These rates are evaluated numerically for finite temperature pure neutron matter at and above the nuclear saturation density.Comment: 26 pages, 5 figures, uses Revte

Spontaneous breaking of rotational symmetry in superconductors

We show that homogeneous superconductors with broken spin/isospin symmetry lower their energy via a transition to a novel superconducting state where the Fermi-surfaces are deformed to a quasi-ellipsoidal form at zero total momentum of Cooper pairs. In this state, the gain in the condensation energy of the pairs dominates over the loss in the kinetic energy caused by the lowest order (quadrupole) deformation of Fermi-surfaces from the spherically symmetric form. There are two energy minima in general, corresponding to the deformations of the Fermi-spheres into either prolate or oblate forms. The phase transition from spherically symmetric state to the superconducting state with broken rotational symmetry is of the first order.Comment: 5 pages, including 3 figures, published versio

Response functions of cold neutron matter: density fluctuations

We compute the finite temperature density response function of nonrelativistic cold fermions with an isotropic condensate. The pair-breaking contribution to the response function is evaluated in the limit of small three-momentum transfers q within an effective theory which exploits series expansion in powers of small q/p_F, where p_F is the Fermi momentum. The leading order O(q^2) contribution is universal and depends only on two fundamental scales, the Fermi energy and the pairing gap. The particle-hole Landau Fermi-liquid interaction contributes first at the next-to-leading-order O(q^4). The scattering contribution to the polarization tensor is nonperturbative (in the above sense) and is evaluated numerically. The spectral functions of density fluctuations are constructed and the relevance of the q^2 scaling for the pair-breaking neutrino emission from neutron stars is discussed.Comment: v2: 11 pages, 4 figures, matches published version

Color-magnetic flux tubes in quark matter cores of neutron stars

We argue that if color-superconducting quark matter exists in the core of a neutron star, it may contain a high density of flux tubes, carrying flux that is mostly color-magnetic, with a small admixture of ordinary magnetic flux. We focus on the two-flavor color-superconducting ("2SC") phase, and assume that the flux tubes are energetically stable, although this has not yet been demonstrated. The density of flux tubes depends on the nature of the transition to the color-superconducting phase, and could be within an order of magnitude of the density of magnetic flux tubes that would be found if the core were superconducting nuclear matter. We calculate the cross-section for Aharonov-Bohm scattering of gapless fermions off the flux tubes, and the associated collision time and frictional force on a moving flux tube. We discuss the other forces on the flux tube, and find that if we take in to account only the forces that arise within the 2SC core region then the timescale for expulsion of the color flux tubes from the 2SC core is of order 10^10 years.Comment: 28 pages, LaTeX, 1 figure, 2 appendices; added discussion of energetic stability of flux tube

Damping of differential rotation in neutron stars

We derive the transport relaxation times for quasiparticle-vortex scattering processes via nuclear force, relevant for the damping of differential rotation of superfluids in the quantum liquid core of a neutron star. The proton scattering off the neutron vortices provides the dominant resistive force on the vortex lattice at all relevant temperatures in the phase where neutrons only are in the paired state. If protons are superconducting, a small fraction of hyperons and resonances in the normal state would be the dominant source of friction on neutron and proton vortex lattices at the core temperatures $T\ge 10^{7}$ K.Comment: 5 pages, Revtex, Phys. Rev. D 58, Rapid Communication, in pres