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Mesoscopic superconductivity in ultrasmall metallic grains
A nano-scale metallic grain (nanoparticle) with irregular boundaries in which
the single-particle dynamics are chaotic is a zero-dimensional system described
by the so-called universal Hamiltonian in the limit of a large number of
electrons. The interaction part of this Hamiltonian includes a superconducting
pairing term and a ferromagnetic exchange term. Spin-orbit scattering breaks
spin symmetry and suppresses the exchange interaction term. Of particular
interest is the fluctuation-dominated regime, typical of the smallest grains in
the experiments, in which the bulk pairing gap is comparable to or smaller than
the single-particle mean-level spacing, and the Bardeen-Cooper-Schrieffer (BCS)
mean-field theory of superconductivity is no longer valid. Here we study the
crossover between the BCS and fluctuation-dominated regimes in two limits. In
the absence of spin-orbit scattering, the pairing and exchange interaction
terms compete with each other. We describe the signatures of this competition
in thermodynamic observables, the heat capacity and spin susceptibility. In the
presence of strong spin-orbit scattering, the exchange interaction term can be
ignored. We discuss how the magnetic-field response of discrete energy levels
in such a nanoparticle is affected by pairing correlations. We identify
signatures of pairing correlations in this response, which are detectable even
in the fluctuation-dominated regime.Comment: 9 pages, 5 figures, Proceedings of the Fourth Conference on Nuclei
and Mesoscopic Physics (NMP14
Magnetic Properties of a Pressure-induced Superconductor UGe
We performed the DC-magnetization and neutron scattering experiments under
pressure {\it P} for a pressure-induced superconductor UGe. We found that
the magnetic moment is enhanced at a characteristic temperature {\it T}
in the ferromagnetic state, where {\it T} is smaller than a Curie
temperature {\it T}. This enhancement becomes remarkable in the
vicinity of {\it P} = 1.20 GPa, where {\it T} becomes 0 K
and the superconducting transition temperature {\it T} shows a
maximum. The characteristic temperature {\it T}, which decreases with
increasing pressure, also depends on the magnetic field.Comment: To be published in J.Phys.Soc.Jp
Stability and bifurcations in an epidemic model with varying immunity period
An epidemic model with distributed time delay is derived to describe the
dynamics of infectious diseases with varying immunity. It is shown that
solutions are always positive, and the model has at most two steady states:
disease-free and endemic. It is proved that the disease-free equilibrium is
locally and globally asymptotically stable. When an endemic equilibrium exists,
it is possible to analytically prove its local and global stability using
Lyapunov functionals. Bifurcation analysis is performed using DDE-BIFTOOL and
traceDDE to investigate different dynamical regimes in the model using
numerical continuation for different values of system parameters and different
integral kernels.Comment: 16 pages, 5 figure
Superconductivity induced by longitudinal ferromagnetic fluctuations in UCoGe
From detailed angle-resolved NMR and Meissner measurements on a ferromagnetic
(FM) superconductor UCoGe (T_Curie ~ 2.5 K and T_SC ~ 0.6 K), we show that
superconductivity in UCoGe is tightly coupled with longitudinal FM spin
fluctuations along the c axis. We found that magnetic fields along the c axis
(H || c) strongly suppress the FM fluctuations and that the superconductivity
is observed in the limited magnetic field region where the longitudinal FM spin
fluctuations are active. These results combined with model calculations
strongly suggest that the longitudinal FM spin fluctuations tuned by H || c
induce the unique spin-triplet superconductivity in UCoGe. This is the first
clear example that FM fluctuations are intimately related with
superconductivity.Comment: 4 pages, 5 figures, to appear in PR
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