| Research Abstract |
1 Heavy Fermion Superconductors
Temperature dependencies of specific heat,sound attenuation constant,spin-lattice relaxation time, critical magnetic field, magnetic penetration depth etc., of heavy fermion superconductors(HFS) are non-BCS and all power-law like, suggesting anisotropic energy gap having points or lines of nodes. The anisotropy,found also in other physical quantities like critical field,sound attenuation,etc., implies an additional participation of orbital and/or spin degrees of freedom. Associated with the new degrees of freedom we may expect collective modes in HFS. Taking some p-and d-wave phases as representative pairing-states we have found collective excitations characteristic to the phases concerned. We have developed theory of response of these phases to applied fields, taking the Coulomb interaction and the gauge invariance properly into account and located appearance of these modes in various quantities like sound attenuation constant,magnetic penetration depth,
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etc. The observation of these collective modes in the corresponding experiments and comparison with our results will help us identifying ground-state,thus, the superconducting mechanisms in actual HFS.
2 Nonlinear sound propagation in Superfluid ^3He-B
Soliton-like sound propagation in superfluid ^3He-B suggests that a similar mechanism found in optical two-level systems(OTLS) works in ^3He also. To derive the corresponding nonlinear equation for sound propagation we first solve equation of motion for order-parameters and find the eigenfunctions for collective modes. By projecting out the degree of freedom ofthe real squashing mode from the order-parameters we introduce the quasi-spin. Then we find out the interaction of it with zero-sounds to obtain the coupled nonlinear equations corresponding to those employed in OTLS,thereby proviede a microscopic foundation to the phenomenological analysis based on OTLS.
3 Two-Dimensional Electron System on Liquid He
To understand 2D electronic system bound on liquid He surface we have to take into account the electron-electron and electron-He surface interactions on equal footing. To do this we have developed a unified theory giving free energy based on path integral formalism. We have applied the theory to transport and melting properties of 2D electron system, especially under magnetic field, and compared our results with experiments. Less
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