An extension of Fourier analysis for the n-torus in the magnetic field and its application to spectral analysis of the magnetic Laplacian

We solved the Schr{\"o}dinger equation for a particle in a uniform magnetic field in the n-dimensional torus. We obtained a complete set of solutions for a broad class of problems; the torus T^n = R^n / {\Lambda} is defined as a quotient of the Euclidean space R^n by an arbitrary n-dimensional lattice {\Lambda}. The lattice is not necessary either cubic or rectangular. The magnetic field is also arbitrary. However, we restrict ourselves within potential-free problems; the Schr{\"o}dinger operator is assumed to be the Laplace operator defined with the covariant derivative. We defined an algebra that characterizes the symmetry of the Laplacian and named it the magnetic algebra. We proved that the space of functions on which the Laplacian acts is an irreducible representation space of the magnetic algebra. In this sense the magnetic algebra completely characterizes the quantum mechanics in the magnetic torus. We developed a new method for Fourier analysis for the magnetic torus and used it to solve the eigenvalue problem of the Laplacian. All the eigenfunctions are given in explicit forms.Comment: 32 pages, LaTeX, minor corrections are mad

Pressure-induced phase transitions of halogen-bridged binuclear metal complexes R_4[Pt_2(P_2O_5H_2)_4X]nH_2O

Recent contrasting observations for halogen (X)-bridged binuclear platinum complexes R_4[Pt_2(P_2O_5H_2)_4X]nH_2O, that is, pressure-induced Peierls and reverse Peierls instabilities, are explained by finite-temperature Hartree-Fock calculations. It is demonstrated that increasing pressure transforms the initial charge-polarization state into a charge-density-wave state at high temperatures, whereas the charge-density-wave state oppositely declines with increasing pressure at low temperatures. We further predict that higher-pressure experiments should reveal successive phase transitions around room temperature.Comment: 5 pages, 4 figures embedded, to be published in Phys. Rev. B 64, September 1 (2001) Rapid Commu

Magnetic translation groups in an n-dimensional torus

A charged particle in a uniform magnetic field in a two-dimensional torus has a discrete noncommutative translation symmetry instead of a continuous commutative translation symmetry. We study topology and symmetry of a particle in a magnetic field in a torus of arbitrary dimensions. The magnetic translation group (MTG) is defined as a group of translations that leave the gauge field invariant. We show that the MTG on an n-dimensional torus is isomorphic to a central extension of a cyclic group Z_{nu_1} x ... x Z_{nu_{2l}} x T^m by U(1) with 2l+m=n. We construct and classify irreducible unitary representations of the MTG on a three-torus and apply the representation theory to three examples. We shortly describe a representation theory for a general n-torus. The MTG on an n-torus can be regarded as a generalization of the so-called noncommutative torus.Comment: 29 pages, LaTeX2e, title changed, re-organized, to be published in Journal of Mathematical Physic

Parker-Jeans Instability of Gaseous Disks Including the Effect of Cosmic Rays

We use linear analysis to examine the effect of cosmic rays (CRs) on the Parker-Jeans instability of magnetized self-gravitating gaseous disks. We adopt a slab equilibrium model in which the gravity (including self-gravity) is perpendicular to the mid-plane, the magnetic field lies along the slab. CR is described as a fluid and only along magnetic field lines diffusion is considered. The linearised equations are solved numerically. The system is susceptible to Parker-Jeans instability. In general the system is less unstable when the CR diffusion coefficient is smaller (i.e., the coupling between the CRs and plasma is stronger). The system is also less unstable if CR pressure is larger. This is a reminiscence of the fact that Jeans instability and Parker instability are less unstable when the gas pressure is larger (or temperature is higher). Moreover, for large CR diffusion coefficient (or small CR pressure), perturbations parallel to the magnetic field are more unstable than those perpendicular to it. The other governing factor on the growth rate of the perturbations in different directions is the thickness of the disk or the strength of the external pressure on the disk. In fact, this is the determining factor in some parameter regimes.Comment: 19pages, 14figures submitted to Ap

Paramagnetic GaN:Fe and ferromagnetic (Ga,Fe)N - relation between structural, electronic, and magnetic properties

We report on the metalorganic chemical vapor deposition (MOCVD) of GaN:Fe and (Ga,Fe)N layers on c-sapphire substrates and their thorough characterization via high-resolution x-ray diffraction (HRXRD), transmission electron microscopy (TEM), spatially-resolved energy dispersive X-ray spectroscopy (EDS), secondary-ion mass spectroscopy (SIMS), photoluminescence (PL), Hall-effect, electron-paramagnetic resonance (EPR), and magnetometry employing a superconducting quantum interference device (SQUID). A combination of TEM and EDS reveals the presence of coherent nanocrystals presumably FexN with the composition and lattice parameter imposed by the host. From both TEM and SIMS studies, it is stated that the density of nanocrystals and, thus the Fe concentration increases towards the surface. In layers with iron content x<0.4% the presence of ferromagnetic signatures, such as magnetization hysteresis and spontaneous magnetization, have been detected. We link the presence of ferromagnetic signatures to the formation of Fe-rich nanocrystals, as evidenced by TEM and EDS studies. This interpretation is supported by magnetization measurements after cooling in- and without an external magnetic field, pointing to superparamagnetic properties of the system. It is argued that the high temperature ferromagnetic response due to spinodal decomposition into regions with small and large concentration of the magnetic component is a generic property of diluted magnetic semiconductors and diluted magnetic oxides showing high apparent Curie temperature.Comment: 21 pages, 30 figures, submitted to Phys. Rev.

Local atomic structure and discommensurations in the charge density wave of CeTe3

The local structure of CeTe3 in the incommensurate charge density wave (IC-CDW) state has been obtained using atomic pair distribution function (PDF) analysis of x-ray diffraction data. Local atomic distortions in the Te-nets due to the CDW are larger than observed crystallographically, resulting in distinct short and long Te-Te bonds. Observation of different distortion amplitudes in the local and average structures are explained by the discommensurated nature of the CDW since the PDF is sensitive to the local displacements within the commensurate regions whereas the crystallographic result averages over many discommensurated domains. The result is supported by STM data. This is the first quantitative local structural study within the commensurate domains in an IC-CDW system.Comment: 4 pages, 4 figure

Spectral isolation of naturally reductive metrics on simple Lie groups

We show that within the class of left-invariant naturally reductive metrics $\mathcal{M}_{\operatorname{Nat}}(G)$ on a compact simple Lie group $G$, every metric is spectrally isolated. We also observe that any collection of isospectral compact symmetric spaces is finite; this follows from a somewhat stronger statement involving only a finite part of the spectrum.Comment: 19 pages, new title and abstract, revised introduction, new result demonstrating that any collection of isospectral compact symmetric spaces must be finite, to appear Math Z. (published online Dec. 2009

A crib-shaped triplet pairing gap function for an orthogonal pair of quasi-one dimensional Fermi surfaces in Sr2_2RuO4_4

The competition between spin-triplet and singlet pairings is studied theoretically for the tight-binding $\alpha$-$\beta$ bands in Sr$_2$RuO$_4$, which arise from two sets of quasi-one dimensional Fermi surfaces. Using multiband FLEX approximation, where we incorporate an anisotropy in the spin fluctuations as suggested from experiments, we show that (i) the triplet can dominate over the singlet (which turns out to be extended s), and (ii) the triplet gap function optimized in the Eliashberg equation has an unusual, very non-sinusoidal form, whose time-reversal-broken combination exhibits a crib-shaped amplitude with dips.Comment: 5 pages, RevTeX, to appear in Phys.Rev.B (Rapid Communications