Inverse problems of identifying the time-dependent source coefficient for subelliptic heat equations

We discuss inverse problems of determining the time-dependent source coefficient for a general class of subelliptic heat equations. We show that a single data at an observation point guarantees the existence of a (smooth) solution pair for the inverse problem. Moreover, additional data at the observation point implies an explicit formula for the time-dependent source coefficient. We also explore an inverse problem with nonlocal additional data, which seems a new approach even in the Laplacian case

New Supporting Evidence for the Overdensity of Galaxies around the Radio-Loud Quasar SDSS J0836+0054 at z =5.8

Recently, Zheng et al. (2005) found evidence for an overdensity of galaxies around a radio-loud quasar, SDSS J0836+0054, at z=5.8 (a five arcmin$^2$ region). We have examined our deep optical imaging data (B, V, r', i', z', and NB816) taken with the Suprime-Cam on the Subaru Telescope. The NB816 narrow-band filter (lambda_c = 815 nm and $\Delta\lambda = 12$ nm) is suitable for searching for Ly$\alpha$ emitters at $z\approx 5.7$. We have found a new strong Ly$\alpha$ emitter at $z \approx 5.7$ close to object B identified by Zheng et al. Further, the non detection of the nine objects selected by Zheng et al. (2005) in our B, V, and r' images provides supporting evidence that they are high-z objects.Comment: 5 pages, 1 figure, accepted for PAS

Strong Emission-Line Galaxies at Low Redshift in the Field around the Quasar SDSSp J104433.04-012502.2

We discuss observational properties of strong emission-line galaxies at low redshift found by our deep imaging survey for high-redshift Ly alpha emitters. In our surveys, we used the narrowband filter, NB816 (lambda_center=8150A with FWHM = 120A), and the intermediate-band filter, IA827 (lambda_center = 8270A with FWHM = 340A). In this survey, 62 NB816-excess (> 0.9 mag) and 21 IA827-excess (> 0.8 mag) objects were found. Among them, we found 20 NB816-excess and 4 IA827-excess Ly alpha emitter candidates. Therefore, it turns out that 42 NB816-excess and 17 IA827-excess objects are strong emission-line objects at lower redshift. Since 4 objects in the two low-z samples are common, the total number of strong low-z emitters is 55. Applying our photometric redshift technique, we identify 7 H alpha emitters at z~0.24, 20 H beta-[OIII] ones at z~0.65, and 11 [OII] ones at z~1.19. However, we cannot determine reliable photometric redshifts of the remaining 17 emitters. The distributions of their rest frame equivalent widths are consistently understood with recent studies of galaxy evolution from z~1 to z~0.Comment: 28 pages, 8 figures, PASJ, Vol. 58, No. 1, in pres

Inverse problems of identifying the time-dependent source coefficient for subelliptic heat equations

We discuss inverse problems of determining the time-dependent source coefficient for a general class of subelliptic heat equations. We show that a single data at an observation point guarantees the existence of a (smooth) solution pair for the inverse problem. Moreover, additional data at the observation point implies an explicit formula for the time-dependent source coefficient. We also explore an inverse problem with nonlocal additional data, which seems a new approach even in the Laplacian case

Topology dependent quantities at the Anderson transition

The boundary condition dependence of the critical behavior for the three dimensional Anderson transition is investigated. A strong dependence of the scaling function and the critical conductance distribution on the boundary conditions is found, while the critical disorder and critical exponent are found to be independent of the boundary conditions

Anderson transitions in three-dimensional disordered systems with randomly varying magnetic flux

The Anderson transition in three dimensions in a randomly varying magnetic flux is investigated in detail by means of the transfer matrix method with high accuracy. Both, systems with and without an additional random scalar potential are considered. We find a critical exponent of $\nu=1.45\pm0.09$ with random scalar potential. Without it, $\nu$ is smaller but increases with the system size and extrapolates within the error bars to a value close to the above. The present results support the conventional classification of universality classes due to symmetry.Comment: 4 pages, 2 figures, to appear in Phys. Rev.

Anderson transition in three-dimensional disordered systems with symplectic symmetry

The Anderson transition in a 3D system with symplectic symmetry is investigated numerically. From a one-parameter scaling analysis the critical exponent $\nu$ of the localization length is extracted and estimated to be $\nu = 1.3 \pm 0.2$. The level statistics at the critical point are also analyzed and shown to be scale independent. The form of the energy level spacing distribution $P(s)$ at the critical point is found to be different from that for the orthogonal ensemble suggesting that the breaking of spin rotation symmetry is relevant at the critical point.Comment: 4 pages, revtex, to appear in Physical Review Letters. 3 figures available on request either by fax or normal mail from [email protected] or [email protected]

Symmetry Breaking and Finite Size Effects in Quantum Many-Body Systems

We consider a quantum many-body system on a lattice with a continuous symmetry which exhibits a spontaneous symmetry breaking in its infinite volume ground states, but in which the order operator does not commute with the Hamiltonian. A typical example is the Heisenberg antiferromagnet with a Neel order. In the corresponding finite system, the symmetry breaking is usually "obscured" by "quantum fluctuation" and one gets a symmetric ground state with a long range order. In such a situation, we prove that there exist ever increasing numbers of low-lying eigenstates whose excitation energies are bounded by a constant times 1/N, where N denotes the number of sites. By forming linear combinations of these low-lying states and the (finite-volume) ground state, and by taking infinite volume limits, we construct infinite volume ground states with explicit symmetry breaking. Our general theorems do not only shed light on the nature ofsymmetry breaking in quantum many-body systems, but provide indispensable information for numerical approaches to these systems. We also discuss applications of our general results to a variety of examples. The present paper is intended to be accessible to the readers without background in mathematical approaches to quantum many-body systems.Comment: LaTeX, 58 pages, no figures. Notes about Bose-Einstein condenstaion are added after the publicatio