Cryogenic masers

Various factors affecting the frequency stability of hydrogen masers are described and related to maser design parameters. The long-term frequency stability of a hydrogen maser is limited by the mechanical stability of the cavity, and the magnitudes of the wall relaxation, spin exchange, and recombination rates which affect the Q of the line. Magnetic resonance studies of hydrogen atoms at temperatures below 1 K and in containers coated with liquid helium films demonstrated that cryogenic masers may allow substantial improvements in all of these parameters. In particular the thermal expansion coefficients of most materials are negligible at 1 K. Spin exchange broadening is three orders of magnitude smaller at 1 K than at room temperature, and the recombination and wall relaxation rates are negligible at 0.52 K where the frequency shift due to the 4 He-coated walls of the container has a broad minimum as a function of temperature. Other advantages of the helium-cooled maser result from the high purity, homogeneity, and resilence of helium-film-coated walls and the natural compatibility of the apparatus with helium-cooled amplifiers

Impurity scattering and localization in dd-wave superconductors

Strong evidence is presented for the localization of low energy quasiparticle states in disordered $d$-wave superconductors. Within the framework of the Bogoliubov-de Gennes (BdG) theory applied to the extended Hubbard model with a finite concentration of non-magnetic impurities, we carry out a fully self-consistent numerical diagonalization of the BdG equations on finite clusters containing up to $50\times 50$ sites. Localized states are identified by probing their sensitivity to the boundary conditions and by analyzing the finite size dependence of inverse participation ratios.Comment: 4 pages REVTeX with 2 embedded .ps figures; submitted to PRB as Rapid Communicatio