Fixed Number and Quantum Size Effects in Nanoscale Superconductors

In recent experiments on nanoscale Al particles, whose electron number was fixed by charging effects, a ``negative gap'' was observed in particles with an odd number of electrons. This observation has called into question the use of a grand canonical ensemble in describing superconductivity in such ultrasmall particles. We have studied the effects of fixed electron number and finite size in nanoscale superconductors, by applying the canonical BCS theory for the attractive Hubbard model. The ground state energy and the energy gap are compared with the conventional and parity-projected grand canonical BCS results, and in one dimension also with the exact solutions by the Bethe ansatz. The crossover from the bulk to quantum limit is studied for various regimes of electron density and coupling strength. The effects of boundary conditions and different lattice structures are also examined. A ``negative gap'' for odd electron number emerges most naturally in the canonical scheme. For even electron number, the gap is particularly large for ``magic numbers'' of electrons for a given system size or of atoms for a fixed electron density. These features are in accordance with the exact solutions, but are essentially missed in the grand canonical results.Comment: 2 pages, 4 figures, submitted to Physica C for M2S-HTSC-VI Proceeding

The Way of the Gift

(Excerpt) In his classic work on stewardship Helge Brattgard said that it is only as the Spirit of God, working through Word and Sacrament, leads [people] to be grateful for spiritual and material gifts received, and to see their responsibility for the administration of these gifts, that congregational life can result. 1 Unfortunately, after making this wonderful assertion, he like most other writers on stewardship remained surprisingly silent about how liturgical action a~d the broader life of the Christian shape one another

Electronic Shell Structure of Nanoscale Superconductors

Motivated by recent experiments on Al nanoparticles, we have studied the effects of fixed electron number and small size in nanoscale superconductors, by applying the canonical BCS theory for the attractive Hubbard model in two and three dimensions. A negative ``gap'' in particles with an odd number of electrons as observed in the experiments is obtained in our canonical scheme. For particles with an even number of electrons, the energy gap exhibits shell structure as a function of electron density or system size in the weak-coupling regime: the gap is particularly large for ``magic numbers'' of electrons for a given system size or of atoms for a fixed electron density. The grand canonical BCS method essentially misses this feature. Possible experimental methods for observing such shell effects are discussed.Comment: 5 pages, 5 figure

Gaussian Post-selection for Continuous Variable Quantum Cryptography

We extend the security proof for continuous variable quantum key distribution protocols using post selection to account for arbitrary eavesdropping attacks by employing the concept of an equivalent protocol where the post-selection is implemented as a series of quantum operations including a virtual distillation. We introduce a particular `Gaussian' post selection and demonstrate that the security can be calculated using only experimentally accessible quantities. Finally we explicitly evaluate the performance for the case of a noisy Gaussian channel in the limit of unbounded key length and find improvements over all pre-existing continuous variable protocols in realistic regimes.Comment: 4+4 pages. arXiv admin note: substantial text overlap with arXiv:1106.082

Generation of highly non-classical n-photon polarization states by super-bunching at a photon bottleneck

It is shown that coherent superpositions of two oppositely polarized n-photon states can be created by post-selecting the transmission of n independently generated photons into a single mode transmission line. It is thus possible to generate highly non-classical n-photon polarization states using only the bunching effects associated with the bosonic nature of photons. The effects of mode-matching errors are discussed and the possibility of creating n-photon entanglement by redistributing the photons into n separate modes is considered.Comment: 8 pages, including 4 figures, extended version of the original letter paper, includes discussion of linear polarization statistic

The Treasury-Fed Accord : a new narrative account

Treasury-Federal Reserve Accord

After the accord : reminiscences on the birth of the modern Fed

Treasury-Federal Reserve Accord