3P2^3P_2-3F2^3F_2 Pairing in Dense Neutron Matter: The Spectrum of Solutions

The $^3P_2$-$^3F_2$ pairing model is generally considered to provide an adequate description of the superfluid states of neutron matter at densities some 2-3 times that of saturated symmetrical nuclear matter. The problem of solving the system of BCS gap equations expressing the $^3P_2$-$^3F_2$ model is attacked with the aid of the separation approach. This method, developed originally for quantitative study of S-wave pairing in the presence of strong short-range repulsions, serves effectively to reduce the coupled, singular, nonlinear BCS integral equations to a set of coupled algebraic equations. For the first time, sufficient precision becomes accessible to resolve small energy splittings between the different pairing states. Adopting a perturbative strategy, we are able to identify and characterize the full repertoire of real solutions of the $^3P_2$-$^3F_2$ pairing model, in the limiting regime of small tensor-coupling strength. The P-F channel coupling is seen to lift the striking parametric degeneracies revealed by a earlier separation treatment of the pure, uncoupled $^3P_2$ pairing problem. Remarkably, incisive and robust results are obtained solely on the basis of analytic arguments. Unlike the traditional Ginzburg-Landau approach, the analysis is not restricted to the immediate vicinity of the critical temperature, but is equally reliable at zero temperature. Interesting connections and contrasts are drawn between triplet pairing in dense neutron matter and triplet pairing in liquid $^3$He.Comment: 23 pages, 1 figur

The Effective Action For Brane Localized Gauge Fields

The low energy effective action including gauge field degrees of freedom on a non-BPS p=2 brane embedded in a N=1, D=4 target superspace is obtained through the method of nonlinear realizations of the associated super-Poincare symmetries. The invariant interactions of the gauge fields and the brane excitation modes corresponding to the Nambu-Goldstone degrees of freedom resulting from the broken space translational symmetry and the target space supersymmetries are determined. Brane localized matter field interactions with the gauge fields are obtained through the construction of the combined gauge and super-Poincare covariant derivatives for the matter fields.Comment: 12 pages, no figure

Entropy paradox in strongly correlated Fermi systems

A system of interacting, identical fermions described by standard Landau Fermi-liquid (FL) theory can experience a rearrangement of its Fermi surface if the correlations grow sufficiently strong, as occurs at a quantum critical point where the effective mass diverges. As yet, this phenomenon defies full understanding, but salient aspects of the non-Fermi-liquid (NFL) behavior observed beyond the quantum critical point are still accessible within the general framework of the Landau quasiparticle picture. Self-consistent solutions of the coupled Landau equations for the quasiparticle momentum distribution $n(p)$ and quasiparticle energy spectrum $\epsilon(p)$ are shown to exist in two distinct classes, depending on coupling strength and on whether the quasiparticle interaction is regular or singular at zero momentum transfer. One class of solutions maintains the idempotency condition $n^2(p)=n(p)$ of standard FL theory at zero temperature $T$ while adding pockets to the Fermi surface. The other solutions are characterized by a swelling of the Fermi surface and a flattening of the spectrum $\epsilon(p)$ over a range of momenta in which the quasiparticle occupancies lie between 0 and 1 even at T=0. The latter, non-idempotent solution is revealed by analysis of a Poincar\'e mapping associated with the fundamental Landau equation connecting $n(p)$ and $\epsilon(p)$ and validated by solution of a variational condition that yields the symmetry-preserving ground state. Paradoxically, this extraordinary solution carries the burden of a large temperature-dependent excess entropy down to very low temperatures, threatening violation of the Nernst Theorem. It is argued that certain low-temperature phase transitions offer effective mechanisms for shedding the entropy excess. Available measurements in heavy-fermion compounds provide concrete support for such a scenario.Comment: 34 pages, 6 figure

Inverse spectral problems for Dirac operators with summable matrix-valued potentials

We consider the direct and inverse spectral problems for Dirac operators on $(0,1)$ with matrix-valued potentials whose entries belong to $L_p(0,1)$, $p\in[1,\infty)$. We give a complete description of the spectral data (eigenvalues and suitably introduced norming matrices) for the operators under consideration and suggest a method for reconstructing the potential from the corresponding spectral data.Comment: 32 page

Insights from the shell proteome : Biomineralization to adaptation

Acknowledgments This work was supported by funding from the CACHE (Calcium in a Changing Environment) initial training network (ITN) under the European Union Seventh Framework Programme, reference grant agreement number 605051. We acknowledge E. Dufour (UMR 7209, MNHN) for shell sample preparation. We thank G. Bolbach and L. Matheron (IBPS-FR3631, Paris) for proteomic analysis and discussionsPeer reviewedPublisher PD

Energy scales and magnetoresistance at a quantum critical point

The magnetoresistance (MR) of CeCoIn_5 is notably different from that in many conventional metals. We show that a pronounced crossover from negative to positive MR at elevated temperatures and fixed magnetic fields is determined by the scaling behavior of quasiparticle effective mass. At a quantum critical point (QCP) this dependence generates kinks (crossover points from fast to slow growth) in thermodynamic characteristics (like specific heat, magnetization etc) at some temperatures when a strongly correlated electron system transits from the magnetic field induced Landau Fermi liquid (LFL) regime to the non-Fermi liquid (NFL) one taking place at rising temperatures. We show that the above kink-like peculiarity separates two distinct energy scales in QCP vicinity - low temperature LFL scale and high temperature one related to NFL regime. Our comprehensive theoretical analysis of experimental data permits to reveal for the first time new MR and kinks scaling behavior as well as to identify the physical reasons for above energy scales.Comment: 7 pages, 6 figure

Nodes of the Gap Function and Anomalies in Thermodynamic Properties of Superfluid 3^3He

Departures of thermodynamic properties of three-dimensional superfluid $^3$He from the predictions of BCS theory are analyzed. Attention is focused on deviations of the ratios $\Delta(T=0)/T_c$ and $[C_s(T_c)-C_n(T_c)]/C_n(T_c)$ from their BCS values, where $\Delta(T=0)$ is the pairing gap at zero temperature, $T_c$ is the critical temperature, and $C_s$ and $C_n$ are the superfluid and normal specific heats. We attribute these deviations to the momentum dependence of the gap function $\Delta(p)$, which becomes well pronounced when this function has a pair of nodes lying on either side of the Fermi surface. We demonstrate that such a situation arises if the P-wave pairing interaction $V(p_1,p_2)$, evaluated at the Fermi surface, has a sign opposite to that anticipated in BCS theory. Taking account of the momentum structure of the gap function, we derive a closed relation between the two ratios that contains no adjustable parameters and agrees with the experimental data. Some important features of the effective pairing interaction are inferred from the analysis.Comment: 17 pages, 4 figure

Triplet Pairing in Neutron Matter

The separation method developed earlier by us [Nucl. Phys. {\bf A598} 390 (1996)] to calculate and analyze solutions of the BCS gap equation for $^1$S$_0$ pairing is extended and applied to $^3$P$_2$--$^3$F$_2$ pairing in pure neutron matter. The pairing matrix elements are written as a separable part plus a remainder that vanishes when either momentum variable is on the Fermi surface. This decomposition effects a separation of the problem of determining the dependence of the gap components in a spin-angle representation on the magnitude of the momentum (described by a set of functions independent of magnetic quantum number) from the problem of determining the dependence of the gap on angle or magnetic projection. The former problem is solved through a set of nonsingular, quasilinear integral equations, providing inputs for solution of the latter problem through a coupled system of algebraic equations for a set of numerical coefficients. An incisive criterion is given for finding the upper critical density for closure of the triplet gap. The separation method and its development for triplet pairing exploit the existence of a small parameter, given by a gap-amplitude measure divided by the Fermi energy. The revised BCS equations admit analysis revealing universal properties of the full set of solutions for $^3$P$_2$ pairing in the absence of tensor coupling, referring especially to the energy degeneracy and energetic order of these solutions. The angle-average approximation introduced by Baldo et al. is illuminated in terms of the separation-transformed BCS problem and the small parameter expansion..

In medium T matrix for neutron matter

We calculate the equation of state of pure neutron matter, comparing the G-matrix calculation with the in-medium T-matrix result. At low densities, we obtain similar energies per nucleon, however some differences appear at higher densities. We use the self-consistent spectral functions from the T-matrix approach to calculate the 1S0 superfluid gap including self-energy effects. We find a reduction of the superfluid gap by 30%

Diffusive limit for a quantum linear Boltzmann dynamics

In this article, I study the diffusive behavior for a quantum test particle interacting with a dilute background gas. The model I begin with is a reduced picture for the test particle dynamics given by a quantum linear Boltzmann equation in which the gas particle scattering is assumed to occur through a hard-sphere interaction. The state of the particle is represented by a density matrix that evolves according to a translation-covariant Lindblad equation. The main result is a proof that the particle's position distribution converges to a Gaussian under diffusive rescaling.Comment: 51 pages. I have restructured Sections 2-4 from the previous version and corrected an error in the proof of Proposition 7.