Mesoscopic competition of superconductivity and ferromagnetism: conductance peak statistics in metallic grains

We investigate the competition between superconductivity and ferromagnetism in chaotic ultra-small metallic grains in a regime where both phases can coexist. We use an effective Hamiltonian that combines a BCS-like pairing term and a ferromagnetic Stoner-like spin exchange term. We study the transport properties of the grain in the Coulomb blockade regime and identify signatures of the coexistence between pairing and exchange correlations in the mesoscopic fluctuations of the conductance peak spacings and peak heights.Comment: 4 pages, 3 figure

The coexistence of superconductivity and ferromagnetism in nano-scale metallic grains

A nano-scale metallic grain in which the single-particle dynamics are chaotic is described by the so-called universal Hamiltonian. This Hamiltonian includes a superconducting pairing term and a ferromagnetic exchange term that compete with each other: pairing correlations favor minimal ground-state spin, while the exchange interaction favors maximal spin polarization. Of particular interest is the fluctuation-dominated regime where the bulk pairing gap is comparable to or smaller than the single-particle mean level spacing and the Bardeen-Cooper-Schrieffer theory of superconductivity breaks down. Superconductivity and ferromagnetism can coexist in this regime. We identify signatures of the competition between superconductivity and ferromagnetism in a number of quantities: ground-state spin, conductance fluctuations when the grain is weakly coupled to external leads and the thermodynamic properties of the grain, such as heat capacity and spin susceptibility.Comment: 13 pages, 13 figures, Proceedings of the Conference on the Frontiers of Quantum and Mesoscopic Thermodynamics (FQMT11

Effective models for gapped phases of strongly correlated quantum lattice models

We present a robust scheme to derive effective models non-perturbatively for quantum lattice models when at least one degree of freedom is gapped. A combination of graph theory and the method of continuous unitary transformations (gCUTs) is shown to efficiently capture all zero-temperature fluctuations in a controlled spatial range. The gCUT can be used either for effective quasi-particle descriptions or for effective low-energy descriptions in case of infinitely degenerate subspaces. We illustrate the method for 1d and 2d lattice models yielding convincing results in the thermodynamic limit. We find that the recently discovered spin liquid in the Hubbard model on the honeycomb lattice lies outside the perturbative strong-coupling regime. Various extensions and perspectives of the gCUT are discussed.Comment: 6 pages, 5 figures, extended discussion on J2/J1 for the honeycomb Hubbard model and on the properties of different generators for the continuous unitary transformatio

Coherent center domains from local Polyakov loops

We analyze properties of local Polyakov loops using quenched as well as dynamical SU(3) gauge configurations for a wide range of temperatures. It is demonstrated that for both, the confined and the deconfined regime, the local Polyakov loop prefers phase values near the center elements 1, exp(i 2 pi/3), exp(-i 2 pi/3). We divide the lattice sites into three sectors according to these phases and show that the sectors give rise to the formation of clusters. For a suitable definition of these clusters we find that in the quenched case deconfinement manifests itself as the onset of percolation of the clusters. A possible continuum limit of the center clusters is discussed

Quantum Condensates in Nuclear Matter: Problems

In connection with the contribution "Quantum Condensates in Nuclear Matter" some problems are given to become more familiar with the techniques of many-particle physics.Comment: 8 pages, 1 figur

A Compressed Sensing Algorithm for Sparse-View Pinhole Single Photon Emission Computed Tomography

Single Photon Emission Computed Tomography (SPECT) systems are being developed with multiple cameras and without gantry rotation to provide rapid dynamic acquisitions. However, the resulting data is angularly undersampled, due to the limited number of views. We propose a novel reconstruction algorithm for sparse-view SPECT based on Compressed Sensing (CS) theory. The algorithm models Poisson noise by modifying the Iterative Hard Thresholding algorithm to minimize the Kullback-Leibler (KL) distance by gradient descent. Because the underlying objects of SPECT images are expected to be smooth, a discrete wavelet transform (DWT) using an orthogonal spline wavelet kernel is used as the sparsifying transform. Preliminary feasibility of the algorithm was tested on simulated data of a phantom consisting of two Gaussian distributions. Single-pinhole projection data with Poisson noise were simulated at 128, 60, 15, 10, and 5 views over 360 degrees. Image quality was assessed using the coefficient of variation and the relative contrast between the two objects in the phantom. Overall, the results demonstrate preliminary feasibility of the proposed CS algorithm for sparse-view SPECT imaging

A Spectral CT Method to Directly Estimate Basis Material Maps From Experimental Photon-Counting Data

The proposed spectral CT method solves the constrained one-step spectral CT reconstruction (cOSSCIR) optimization problem to estimate basis material maps while modeling the nonlinear X-ray detection process and enforcing convex constraints on the basis map images. In order to apply the optimization-based reconstruction approach to experimental data, the presented method empirically estimates the effective energy-window spectra using a calibration procedure. The amplitudes of the estimated spectra were further optimized as part of the reconstruction process to reduce ring artifacts. A validation approach was developed to select constraint parameters. The proposed spectral CT method was evaluated through simulations and experiments with a photon-counting detector. Basis material map images were successfully reconstructed using the presented empirical spectral modeling and cOSSCIR optimization approach. In simulations, the cOSSCIR approach accurately reconstructed the basis map images

The Effects of Extending the Spectral Information Acquired by a Photon-counting Detector for Spectral CT

Photon-counting x-ray detectors with pulse-height analysis provide spectral information that may improve material decomposition and contrast-to-noise ratio (CNR) in CT images. The number of energy measurements that can be acquired simultaneously on a detector pixel is equal to the number of comparator channels. Some spectral CT designs have a limited number of comparator channels, due to the complexity of readout electronics. The spectral information could be extended by changing the comparator threshold levels over time, sub pixels, or view angle. However, acquiring more energy measurements than comparator channels increases the noise and/or dose, due to differences in noise correlations across energy measurements and decreased dose utilisation. This study experimentally quantified the effects of acquiring more energy measurements than comparator channels using a bench-top spectral CT system. An analytical and simulation study modeling an ideal detector investigated whether there was a net benefit for material decomposition or optimal energy weighting when acquiring more energy measurements than comparator channels. Experimental results demonstrated that in a two-threshold acquisition, acquiring the high-energy measurement independently from the low-energy measurement increased noise standard deviation in material-decomposition basis images by factors of 1.5–1.7 due to changes in covariance between energy measurements. CNR in energy-weighted images decreased by factors of 0.92–0.71. Noise standard deviation increased by an additional factor of due to reduced dose utilisation. The results demonstrated no benefit for two-material decomposition noise or energy-weighted CNR when acquiring more energy measurements than comparator channels. Understanding the noise penalty of acquiring more energy measurements than comparator channels is important for designing spectral detectors and for designing experiments and interpreting data from prototype systems with a limited number of comparator channels