N-fold Supersymmetry in Quantum Mechanics - Analyses of Particular Models -

We investigate particular models which can be N-fold supersymmetric at specific values of a parameter in the Hamiltonians. The models to be investigated are a periodic potential and a parity-symmetric sextic triple-well potential. Through the quantitative analyses on the non-perturbative contributions to the spectra by the use of the valley method, we show how the characteristic features of N-fold supersymmetry which have been previously reported by the authors can be observed. We also clarify the difference between quasi-exactly solvable and quasi-perturbatively solvable case in view of the dynamical property, that is, dynamical N-fold supersymmetry breaking.Comment: 32 pages, 10 figures, REVTeX

Dynamical Generation of Non-Abelian Gauge Group via the Improved Perturbation Theory

It was suggested that the massive Yang-Mills-Chern-Simons matrix model has three phases and that in one of them a non-Abelian gauge symmetry is dynamically generated. The analysis was at the one-loop level around a classical solution of fuzzy sphere type. We obtain evidences that three phases are indeed realized as nonperturbative vacua by using the improved perturbation theory. It also gives a good example that even if we start from a trivial vacuum, the improved perturbation theory around it enables us to observe nontrivial vacua.Comment: 31 pages, published versio

Equal-Spin Pairing State of Superfluid 3^3He in Aerogel

The equal-spin pairing (ESP) state, the so-called A-like phase, of superfluid $^3$He in aerogels is studied theoretically in the Ginzburg-Landau (GL) region by examining thermodynamics, and the resulting equilibrium phase diagram is mapped out. We find that, among the ABM, planar, and robust pairing states, the ABM state with presumably quasi long-ranged superfluid order is the best candidate of the A-like phase with a strange lowering of the polycritical point (PCP) observed experimentally.Comment: 4 pages, 1 figure, one reference added, accepted for publication in Phys. Rev.

Orbital order and Hund\u27s rule frustration in Kondo lattices

We analyze a microscopic origin of the Kondo effect-assisted orbital order in heavy-fermion materials. By studying the periodic two-orbital Anderson model with two local electrons, we show that frustration of Hund\u27s rule coupling due to the Kondo effect leads to an incommensurate spiral orbital and magnetic order, which exists only inside the Kondo screened (heavy-electron) phase. This spiral state can be observed in neutron and resonant x-ray scattering measurements in U- and Pr-based heavy-fermion compounds, and realized in cold atomic gases, e.g., fermionic Yb173. © 2013 American Physical Society

Testing new physics with the electron g-2

We argue that the anomalous magnetic moment of the electron (a_e) can be used to probe new physics. We show that the present bound on new-physics contributions to a_e is 8*10^-13, but the sensitivity can be improved by about an order of magnitude with new measurements of a_e and more refined determinations of alpha in atomic-physics experiments. Tests on new-physics effects in a_e can play a crucial role in the interpretation of the observed discrepancy in the anomalous magnetic moment of the muon (a_mu). In a large class of models, new contributions to magnetic moments scale with the square of lepton masses and thus the anomaly in a_mu suggests a new-physics effect in a_e of (0.7 +- 0.2)*10^-13. We also present examples of new-physics theories in which this scaling is violated and larger effects in a_e are expected. In such models the value of a_e is correlated with specific predictions for processes with violation of lepton number or lepton universality, and with the electric dipole moment of the electron.Comment: 34 pages, 7 figures. Minor changes and references adde

Inhomogeneous superconducting states of mesoscopic thin-walled cylinders in external magnetic fields

We theoretically investigate the appearance of spatially modulated superconducting states in mesoscopic superconducting thin-wall cylinders in a magnetic field at low temperatures. Quantization of the electron motion around the circumference of the cylinder leads to a discontinuous evolution of the spatial modulation of the superconducting order parameter along the transition line Tc(H). We show that this discontinuity leads to the nonmonotonic behavior of the specific heat jump at the onset of superconductivity as a function of temperature and field. We argue that this geometry provides an excellent opportunity to directly and unambiguously detect distinctive signatures of the Fulde-Ferrell-Larkin-Ovchinnikov modulation of the superconducting order. © 2013 American Physical Society

Intra-Landau level polarization effect for a striped Hall gas

We calculate the polarization function including only intra-Landau level correlation effects of striped Hall gas. Using the polarization function, the dielectric function, the dispersion of the plasmon and the correlation energy are computed in a random phase approximation (RPA) and generalized random phase approximation (GRPA). The plasmon becomes anisotropic and gapless owing to the anisotropy of the striped Hall gas and two dimensionality of the quantum Hall system. The plasmon approximately agrees with the phonon derived before by the single mode approximation. The (G)RPA correlation energy is compared with other numerical calculations.Comment: 15 pages,15 figures, revtex4, published versio

Fluctuation and Order of Antiferromagnetism induced by Paramagnetic Pair-Breaking in Superconducting Vortex Lattice

Effects of the strong Pauli-paramagnetic pair-breaking (PPB) on the vortex lattice in d-wave superconductors are theoretically studied by putting emphasis on consequences of the PPB-induced antiferromagnetic (AFM) ordering in the spatial modulation in the vortex lattice. It is shown that the PPB-induced AFM fluctuation in the superconducting state leads to an enhancement of the vortex lattice form factor which is a measure of spatial variations of the internal magnetic field and that the enhancement becomes more remarkable as an AFM instability is approached. It is also demonstrated that the PPB-induced AFM ordering is assisted by the vortex-lattice modulation, and thus, that the resulting AFM order is spatially modulated, while it is not localized in the vortex cores but coexistent with the nonvanishing superconducting order parameter. These results are discussed in connection with two phenomena observed in CeCoIn5, the anomalous field dependence of the vortex lattice form factor and the AFM order appearing inside the high-field and low-temperature superconducting phase.Comment: 26 pages, 13 figure

Superfluid 3^3He in globally isotropic random media

Recent theoretical and experimental studies of superfluid $^3$He in aerogels with a global anisotropy, e.g., due to an external stress, have definitely shown that the A-like phase with an equal spin pairing (ESP) in such aerogel samples is in the ABM (or, axial) pairing state. In this paper, the A-like phase of superfluid $^3$He in globally {\it isotropic} aerogel is studied in details by assuming a weakly disordered system in which singular topological defects are absent. Through calculation of the free energy, a disordered ABM state is found to be the best candidate of the pairing state of the globally isotropic A-like phase. Further, it is found through a one-loop renormalization group calculation that the coreless continuous vortices (or, vortex-skyrmions) are irrelevant to the long-distance behavior of the disorder-induced textures, and that the superfluidity is maintained in spite of lack of the conventional off-diagonal long range order. Therefore, the globally isotropic A-like phase at weak disorder is, like in the case with a global stretched anisotropy, a superfluid glass with the ABM pairing.Comment: Revised version accepted for publication in Phys.Rev.