String order and hidden topological symmetry in the SO(2n+1) symmetric matrix product states

We have introduced a class of exactly soluble Hamiltonian with either SO(2n+1) or SU(2) symmetry, whose ground states are the SO(2n+1) symmetric matrix product states. The hidden topological order in these states can be fully identified and characterized by a set of nonlocal string order parameters. The Hamiltonian possesses a hidden $(Z_{2}\times Z_{2})^{n}$ topological symmetry. The breaking of this hidden symmetry leads to $4^{n}$ degenerate ground states with disentangled edge states in an open chain system. Such matrix product states can be regarded as cluster states, applicable to measurement-based quantum computation.Comment: 5 pages, 1 figur

State-constraint static Hamilton-Jacobi equations in nested domains

We study state-constraint static Hamilton-Jacobi equations in a sequence of domains $\{\Omega_k\}_{k \in \mathbb{N}}$ in $\mathbb{R}^n$ such that $\Omega_k \subset \Omega_{k+1}$ for all $k\in \mathbb{N}$. We obtain rates of convergence of $u_k$, the solution to the state-constraint problem in $\Omega_k$, to $u$, the solution to the corresponding problem in $\Omega = \bigcup_{k \in \mathbb{N}} \Omega_k$. In many cases, the rates obtained are proven to be optimal. Various new examples and discussions are provided at the end of the paper.Comment: 23 pages, 1 figur

Frustration Effects in Antiferromagnetic FCC Heisenberg Films

We study the effects of frustration in an antiferromagnetic film of FCC lattice with Heisenberg spin model including an Ising-like anisotropy. Monte Carlo (MC) simulations have been used to study thermodynamic properties of the film. We show that the presence of the surface reduces the ground state (GS) degeneracy found in the bulk. The GS is shown to depend on the surface in-plane interaction $J_s$ with a critical value at which ordering of type I coexists with ordering of type II. Near this value a reentrant phase is found. Various physical quantities such as layer magnetizations and layer susceptibilities are shown and discussed. The nature of the phase transition is also studied by histogram technique. We have also used the Green's function (GF) method for the quantum counterpart model. The results at low-$T$ show interesting effects of quantum fluctuations. Results obtained by the GF method at high $T$ are compared to those of MC simulations. A good agreement is observed.Comment: 11 pages, 19 figures, submitted to J. Phys.: Condensed Matte

Multicarrier Approaches for High-Baudrate Optical-Fiber Transmission Systems with a Single Coherent Receiver

In this paper, we show the remarkable timing error (TE) and residual chromatic dispersion (CD) tolerance improvements of the filter bank multicarrier (FBMC) over orthogonal frequency division multiplexing (OFDM) for high-baudrate spectral slicing transmitter and single coherent receiver transmissions. For a 512 Gb/s 16 quadrature amplitude modulated (16QAM) spectrum slicing system at 1600 km of fiber transmission, the FBMC-based system reduces TE and residual CD penalties by more than 1.5 dB and 3 dB, in comparison to the OFDM-based system, respectively

A Note on the Gauge Equivalence between the Manin-Radul and Laberge-Mathieu Super KdV Hierarchies

The gauge equivalence between the Manin-Radul and Laberge-Mathieu super KdV hierarchies is revisited. Apart from the Inami-Kanno transformation, we show that there is another gauge transformation which also possess the canonical property. We explore the relationship of these two gauge transformations from the Kupershmidt-Wilson theorem viewpoint and, as a by-product, obtain the Darboux-Backlund transformation for the Manin-Radul super KdV hierarchy. The geometrical intepretation of these transformations is also briefly discussed.Comment: 8 pages, revtex, 1 figur

Conformal Covariantization of Moyal-Lax Operators

A covariant approach to the conformal property associated with Moyal-Lax operators is given. By identifying the conformal covariance with the second Gelfand-Dickey flow, we covariantize Moyal-Lax operators to construct the primary fields of one-parameter deformation of classical $W$-algebras.Comment: 13 pages, Revtex, no figures, v.2: typos corrected, references added and conclusion modifie

On the Toda Lattice Equation with Self-Consistent Sources

The Toda lattice hierarchy with self-consistent sources and their Lax representation are derived. We construct a forward Darboux transformation (FDT) with arbitrary functions of time and a generalized forward Darboux transformation (GFDT) for Toda lattice with self-consistent sources (TLSCS), which can serve as a non-auto-Backlund transformation between TLSCS with different degrees of sources. With the help of such DT, we can construct many type of solutions to TLSCS, such as rational solution, solitons, positons, negetons, and soliton-positons, soliton-negatons, positon-negatons etc., and study properties and interactions of these solutions.Comment: 20 page

Bounds on the cosmogenic neutrino flux

Under the assumption that some part of the observed highest energy cosmic rays consists of protons originating from cosmological distances, we derive bounds on the associated flux of neutrinos generated by inelastic processes with the cosmic microwave background photons. We exploit two methods. First, a power-like injection spectrum is assumed. Then, a model-independent technique, based on the inversion of the observed proton flux, is presented. The inferred lower bound is quite robust. As expected, the upper bound depends on the unknown composition of the highest energy cosmic rays. Our results represent benchmarks for all ultrahigh energy neutrino telescopes.Comment: 12 pages, 6 figure

Detection of Siderite (FeCO3) in Glen Torridon Samples by the Mars Science Laboratory Rover

Siderite (FeCO3) has been detected in Gale Crater for the first time by the Mars Science Laboratory (MSL) Curiosity and is seen in multiple samples in the Glen Torridon (GT) region. The identification of siderite is based on evolved gas analysis (EGA) data from the Sample Analysis at Mars (SAM) instrument and X-ray diffraction (XRD) data from the Chemistry and Mineralogy (CheMin) instrument. Curiosity descended off of the Vera Rubin ridge (VRR) into the Glen Torridon region on Sol 2300. Glen Torridon is of particular interest because a strong clay mineral signature had been detected by orbital instruments [1]. To date, four drilled samples have been collected at two different drill locations: Kilmarie and Aberlady from adjacent blocks at the base of the south side of VRR in the Jura member and Glen Etive 1 and 2 on the same block in the Knockfarril member