Integrals of motion in the Many-Body localized phase

We construct a complete set of quasi-local integrals of motion for the many-body localized phase of interacting fermions in a disordered potential. The integrals of motion can be chosen to have binary spectrum $\{0,1\}$, thus constituting exact quasiparticle occupation number operators for the Fermi insulator. We map the problem onto a non-Hermitian hopping problem on a lattice in operator space. We show how the integrals of motion can be built, under certain approximations, as a convergent series in the interaction strength. An estimate of its radius of convergence is given, which also provides an estimate for the many-body localization-delocalization transition. Finally, we discuss how the properties of the operator expansion for the integrals of motion imply the presence or absence of a finite temperature transition.Comment: 65 pages, 12 figures. Corrected typos, added reference

Differential Astrometry over 15 degrees

We observed the pair of radio sources 1150+812 and 1803+784 in November 1993 with a VLBI array, simultaneously recording at 8.4 and 2.3 GHz. We determined the angular separation between the two sources with submilliarcsecond accuracy by using differential techniques. This result demonstrates the feasibility of high precision differential astrometry for radio sources separated in the sky by almost 15 degrees, and opens the avenue to its application to larger samples of radio sources.Comment: 6 pages, latex2e, 2 figures, To appear in the proceedings of the EVN/JIVE Symposium No. 4, New Astronomy Reviews (eds. Garret, M. Campbell, R., and Gurvits, L.

Absolute kinematics of radio source components in the complete S5 polar cap sample. III. First wide-field high-precision astrometry at 15.4 GHz

We report on the first wide-field, high-precision astrometric analysis of the 13 extragalactic radio sources of the complete S5 polar cap sample at 15.4 GHz. We describe new algorithms developed to enable the use of differenced phase delays in wide-field astrometric observations and discuss the impact of using differenced phase delays on the precision of the wide-field astrometric analysis. From this global fit, we obtained estimates of the relative source positions with precisions ranging from 14 to 200 $\mu$as at 15.4 GHz, depending on the angular separation of the sources (from $\sim$1.6 to $\sim$20.8 degrees). These precisions are $\sim$10 times higher than the achievable precisions using the phase-reference mapping technique.Comment: 9 pages, 7 figure

NGC1052 - A study of the pc-scale twin jet

We present results of a VLBA multi-frequency study of the pc-scale twin jet in NGC1052. We observed this object at epoch 1998.99 with the VLBA at 5, 8.4, 22 and 43 GHz both in total and linearly polarized intensity. The spectral analysis confirms the necessity of a free-free absorbing medium, obscuring the innermost part of both jets. At 5 GHz we found a compact linearly polarized emission region at the base of the eastern jet with a degree of polarization of 1.5%. At higher frequencies there is no evidence for polarization in our data. A core shift analysis constrains the position of the central engine to ~0.03 pc. The shift rates of the apparent core position with frequency confirm the strong influence of free-free absorption in conjunction with steep pressure gradients at the bases of both jets.Comment: Proceedings of the conference "SRT: the impact of large antennas on Radio Astronomy and Space Science", Cagliari, Italy, 7-10 November 2001, in press; 6 pages, 5 figures, needs srt_style.st

Spectral geometry of submanifolds

These notes reflect the lectures given by the first author at the University of Lecce in June-July 1984.The work deals with geometry of Laplacian’s spectrum of submainfolds in the complex projective space.The second part contains a new way to study this subject given by the second author in his Ph. Dr.(Granada 1984).This idea can be exetended to other symmetric spaces