Implementation of the Backlund transformations for the Ablowitz-Ladik hierarchy

The derivation of the Backlund transformations (BTs) is a standard problem of the theory of the integrable systems. Here, I discuss the equations describing the BTs for the Ablowitz-Ladik hierarchy (ALH), which have been already obtained by several authors. The main aim of this work is to solve these equations. This can be done in the framework of the so-called functional representation of the ALH, when an infinite number of the evolutionary equations are replaced, using the Miwa's shifts, with a few equations linking tau-functions with different arguments. It is shown that starting from these equations it is possible to obtain explicit solutions of the BT equations. In other words, the main result of this work is a presentation of the discrete BTs as a superposition of an infinite number of evolutionary flows of the hierarchy. These results are used to derive the superposition formulae for the BTs as well as pure soliton solutions.Comment: 20 page

Viking navigation

A comprehensive description of the navigation of the Viking spacecraft throughout their flight from Earth launch to Mars landing is given. The flight path design, actual inflight control, and postflight reconstruction are discussed in detail. The preflight analyses upon which the operational strategies and performance predictions were based are discussed. The inflight results are then discussed and compared with the preflight predictions and, finally, the results of any postflight analyses are presented

First Observation of Quantum Oscillations in the Ferromagnetic Superconductor UCoGe

We succeeded in growing high quality single crystals of the ferromagnetic superconductor UCoGe and measured the magnetoresistance at fields up to 34T. The Shubnikov-de Haas signal was observed for the first time in a U-111 system (UTGe, UTSi, T: transition metal). A small pocket Fermi surface (F~1kT) with large cyclotron effective mass 25m0 was detected at high fields above 22T, implying that UCoGe is a low carrier system accompanyed with heavy quasi-particles. The observed frequency decreases with increasing fields, indicating that the volume of detected Fermi surface changes nonlinearly with field. The cyclotron mass also decreases, which is consistent with the decrease of the A coefficient of resistivity.Comment: 5 pages, 5 figures, accepted for publication in J. Phys. Soc. Jp

Fermiology and electronic homogeneity of the superconducting overdoped cuprate Tl-2201 revealed by quantum oscillations

We report an angular quantum oscillation study of Tl_2Ba_2CuO_{6+delta} for two different doping levels (Tc = 10K and 26 K) and determine the Fermi surface size and topology in considerable detail. Our results show that Fermi liquid behavior is not confined to the edge of the superconducting dome and is robust up to at least T_c^{max}/3.5. Superconductivity is found to survive up to a larger doping p_c = 0.31 than in La_{2-x}Sr_xCuO_4. Our data imply that electronic inhomogeneity does not play a significant role in the loss of superconductivity and superfluid density in overdoped cuprates, and point towards a purely magnetic or electronic pairing mechanismComment: 4 page

Fermi-surface reconstruction and two-carrier model for the Hall effect in YBa2Cu4O8

Pulsed field measurements of the Hall resistivity and magnetoresistance of underdoped YBa2Cu4O8 are analyzed self-consistently using a simple model based on coexisting electron and hole carriers. The resultant mobilities and Hall numbers are found to vary markedly with temperature. The conductivity of the hole carriers drops by one order of magnitude below 30 K, explaining the absence of quantum oscillations from these particular pockets. Meanwhile the Hall coefficient of the electron carriers becomes strongly negative below 50 K. The overall quality of the fits not only provides strong evidence for Fermi-surface reconstruction in Y-based cuprates, it also strongly constrains the type of reconstruction that might be occurring.Comment: 5 pages, 4 figures, updated after publication in Physical Review B (Rapid Communication

High-Field Superconductivity at an Electronic Topological Transition in URhGe

The emergence of superconductivity at high magnetic fields in URhGe is regarded as a paradigm for new state formation approaching a quantum critical point. Until now, a divergence of the quasiparticle mass at the metamagnetic transition was considered essential for superconductivity to survive at magnetic fields above 30 tesla. Here we report the observation of quantum oscillations in URhGe revealing a tiny pocket of heavy quasiparticles that shrinks continuously with increasing magnetic field, and finally disappears at a topological Fermi surface transition close to or at the metamagnetic field. The quasiparticle mass decreases and remains finite, implying that the Fermi velocity vanishes due to the collapse of the Fermi wavevector. This offers a novel explanation for the re-emergence of superconductivity at extreme magnetic fields and makes URhGe the first proven example of a material where magnetic field-tuning of the Fermi surface, rather than quantum criticality alone, governs quantum phase formation.Comment: A revised version has been accepted for publication in Nature Physic

Multi-Band Exotic Superconductivity in the New Superconductor Bi4O4S3

Resistivity, Hall effect and magnetization have been investigated on the new superconductor Bi4O4S3. A weak insulating behavior has been induced in the normal state when the superconductivity is suppressed. Hall effect measurements illustrate clearly a multiband feature dominated by electron charge carriers, which is further supported by the magnetoresistance data. Interestingly, a kink appears on the temperature dependence of resistivity at about 4 K at all high magnetic fields when the bulk superconductivity is completely suppressed. This kink can be well traced back to the upper critical field Hc2(T) in the low field region, and is explained as the possible evidence of residual Cooper pairs on the one dimensional chains.Comment: 5 pages, 5 figure

Topological gravity on plumbed V-cobordisms

An ensemble of cosmological models based on generalized BF-theory is constructed where the role of vacuum (zero-level) coupling constants is played by topologically invariant rational intersection forms (cosmological-constant matrices) of 4-dimensional plumbed V-cobordisms which are interpreted as Euclidean spacetime regions. For these regions describing topology changes, the rational and integer intersection matrices are calculated. A relation is found between the hierarchy of certain elements of these matrices and the hierarchy of coupling constants of the universal (low-energy) interactions. PACS numbers: 0420G, 0240, 0460Comment: 29 page