Spectral properties of locally correlated electrons in a BCS superconductor

We present a detailed study of the spectral properties of a locally correlated site embedded in a BCS superconducting medium. To this end the Anderson impurity model with superconducting bath is analysed by numerical renormalisation group (NRG) calculations. We calculate one and two-particle dynamic response function to elucidate the spectral excitation and the nature of the ground state for different parameter regimes with and without particle-hole symmetry. The position and weight of the Andreev bound states is given for all relevant parameters. We also present phase diagrams for the different ground state parameter regimes. This work is also relevant for dynamical mean field theory extensions with superconducting symmetry breaking.Comment: 22 pages, 12 figure

A spin-dependent local moment approach to the Anderson impurity model

We present an extension of the local moment approach to the Anderson impurity model with spin-dependent hybridization. By employing the two-self-energy description, as originally proposed by Logan and co-workers, we applied the symmetry restoration condition for the case with spin-dependent hybridization. Self-consistent ground states were determined through variational minimization of the ground state energy. The results obtained with our spin-dependent local moment approach applied to a quantum dot system coupled to ferromagnetic leads are in good agreement with those obtained from previous work using numerical renormalization group calculations

Antiferromagnetic Order of Strongly Interacting Fermions in a Trap: Real-Space Dynamical Mean-Field Analysis

We apply Dynamical Mean-Field Theory to strongly interacting fermions in an inhomogeneous environment. With the help of this Real-Space Dynamical Mean-Field Theory (R-DMFT) we investigate antiferromagnetic states of repulsively interacting fermions with spin 1/2 in a harmonic potential. Within R-DMFT, antiferromagnetic order is found to be stable in spatial regions with total particle density close to one, but persists also in parts of the system where the local density significantly deviates from half filling. In systems with spin imbalance, we find that antiferromagnetism is gradually suppressed and phase separation emerges beyond a critical value of the spin imbalance.Comment: 4 pages 5 figures, published versio

Numerical renormalization group calculation of near-gap peaks in spectral functions of the Anderson model with superconducting leads

We use the numerical renormalization group method (NRG) to investigate a single-impurity Anderson model with a coupling of the impurity to a superconducting host. Analysis of the energy flow shows, in contrast to previous belief, that NRG iterations can be performed up to a large number of sites, corresponding to energy differences far below the superconducting gap. This allows us to calculate the impurity spectral function very accurately for frequencies near the gap edge, and to resolve, in a certain parameter regime, sharp peaks in the spectral function close to the gap edge.Comment: 18 pages, 7 figures, accepted for publication in Journal of Physics: Condensed Matte

Bound states in straight quantum waveguides with combined boundary conditions

We investigate the discrete spectrum of the Hamiltonian describing a quantum particle living in the two-dimensional straight strip. We impose the combined Dirichlet and Neumann boundary conditions on different parts of the boundary. Several statements on the existence or the absence of the discrete spectrum are proven for two models with combined boundary conditions. Examples of eigenfunctions and eigenvalues are computed numerically.Comment: 24 pages, LaTeX 2e with 4 eps figure

Andreev Bound States in the Kondo Quantum Dots Coupled to Superconducting Leads

We have studied the Kondo quantum dot coupled to two superconducting leads and investigated the subgap Andreev states using the NRG method. Contrary to the recent NCA results [Clerk and Ambegaokar, Phys. Rev. B 61, 9109 (2000); Sellier et al., Phys. Rev. B 72, 174502 (2005)], we observe Andreev states both below and above the Fermi level.Comment: 5 pages, 5 figure

Optimising the observation of optical kilonovae with medium size telescopes

We consider the optimisation of the observing strategy (cadence, exposure time and filter choice) using medium size (2-m class) optical telescopes in the follow-up of kilonovae localised with arcminute accuracy to be able to distinguish among various kilonova models and viewing angles. To develop an efficient observation plan, we made use of the synthetic light curves obtained with the Monte Carlo radiative transfer code POSSIS for different kilonova models and as a function of different viewing angles and distances. By adding the appropriate photon counting noise to the synthetic light curves, we analysed four alternative sequences having the same total time exposure of 8 hours, with different time windows (0.5, 1, 2, 4 h), each with $i$, $r$, and $u$ filters, to determine the observing sequence that maximises the chance of a correct identification of the model parameters. We suggest to avoid $u$ filter and to avoid the use of colour curves. We also found that, if the error on distance is $\le$ 2%, 0.5, 1, 2-hour time window sequences are equivalent, so we suggest to use 2-hour one, because it has 1 day cadence, so it can be easily realised. When the distance of the source is unknown, 0.5 h time window sequence is preferable.Comment: 9 pages, 8 figures, published in MNRA

Geometric coupling thresholds in a two-dimensional strip

We consider the Laplacian in a strip $\mathbb{R}\times (0,d)$ with the boundary condition which is Dirichlet except at the segment of a length $2a$ of one of the boundaries where it is switched to Neumann. This operator is known to have a non-empty and simple discrete spectrum for any $a>0$. There is a sequence $0<a_1<a_2<...$ of critical values at which new eigenvalues emerge from the continuum when the Neumann window expands. We find the asymptotic behavior of these eigenvalues around the thresholds showing that the gap is in the leading order proportional to $(a-a_n)^2$ with an explicit coefficient expressed in terms of the corresponding threshold-energy resonance eigenfunction

Low energy fixed points of the sigma-tau and the O(3) symmetric Anderson models

We study the single channel (compactified) models, the sigma-tau model and the O(3) symmetric Anderson model, which were introduced by Coleman et al., and Coleman and Schofield, as a simplified way to understand the low energy behaviour of the isotropic and anisotropic two channel Kondo systems. These models display both Fermi liquid and marginal Fermi liquid behaviour and an understanding of the nature of their low energy fixed points may give some general insights into the low energy behaviour of other strongly correlated systems. We calculate the excitation spectrum at the non-Fermi liquid fixed point of the sigma-tau model using conformal field theory, and show that the results are in agreement with those obtained in recent numerical renormalization group (NRG) calculations. For the O(3) Anderson model we find further logarithmic corrections in the weak coupling perturbation expansion to those obtained in earlier calculations, such that the renormalized interaction term now becomes marginally stable rather than marginally unstable. We derive a Ward identity and a renormalized form of the perturbation theory that encompasses both the weak and strong coupling regimes and show that the chi/gamma ratio is 8/3 (chi is the total susceptibility, spin plus isospin), independent of the interaction U and in agreement with the NRG calculations.Comment: 23 pages, LaTeX, 11 figures includes as eps-files, submitted to Phys. Rev.