The Multicomponent KP Hierarchy: Differential Fay Identities and Lax Equations

In this article, we show that four sets of differential Fay identities of an $N$-component KP hierarchy derived from the bilinear relation satisfied by the tau function of the hierarchy are sufficient to derive the auxiliary linear equations for the wave functions. From this, we derive the Lax representation for the $N$-component KP hierarchy, which are equations satisfied by some pseudodifferential operators with matrix coefficients. Besides the Lax equations with respect to the time variables proposed in \cite{2}, we also obtain a set of equations relating different charge sectors, which can be considered as a generalization of the modified KP hierarchy proposed in \cite{3}.Comment: 19 page

Non-degenerate solutions of universal Whitham hierarchy

The notion of non-degenerate solutions for the dispersionless Toda hierarchy is generalized to the universal Whitham hierarchy of genus zero with $M+1$ marked points. These solutions are characterized by a Riemann-Hilbert problem (generalized string equations) with respect to two-dimensional canonical transformations, and may be thought of as a kind of general solutions of the hierarchy. The Riemann-Hilbert problem contains $M$ arbitrary functions $H_a(z_0,z_a)$, $a = 1,...,M$, which play the role of generating functions of two-dimensional canonical transformations. The solution of the Riemann-Hilbert problem is described by period maps on the space of $(M+1)$-tuples $(z_\alpha(p) : \alpha = 0,1,...,M)$ of conformal maps from $M$ disks of the Riemann sphere and their complements to the Riemann sphere. The period maps are defined by an infinite number of contour integrals that generalize the notion of harmonic moments. The $F$-function (free energy) of these solutions is also shown to have a contour integral representation.Comment: latex2e, using amsmath, amssym and amsthm packages, 32 pages, no figur

Fabrication and Characterization of Topological Insulator Bi2_2Se3_3 Nanocrystals

In the recently discovered class of materials known as topological insulators, the presence of strong spin-orbit coupling causes certain topological invariants in the bulk to differ from their values in vacuum. The sudden change of invariants at the interface results in metallic, time reversal invariant surface states whose properties are useful for applications in spintronics and quantum computation. However, a key challenge is to fabricate these materials on the nanoscale appropriate for devices and probing the surface. To this end we have produced 2 nm thick nanocrystals of the topological insulator Bi$_2$Se$_3$ via mechanical exfoliation. For crystals thinner than 10 nm we observe the emergence of an additional mode in the Raman spectrum. The emergent mode intensity together with the other results presented here provide a recipe for production and thickness characterization of Bi$_2$Se$_3$ nanocrystals.Comment: 4 pages, 3 figures (accepted for publication in Applied Physics Letters

Three dimensional collective charge excitations in electron-doped cuprate superconductors

High temperature cuprate superconductors consist of stacked CuO2 planes, with primarily two dimensional electronic band structures and magnetic excitations, while superconducting coherence is three dimensional. This dichotomy highlights the importance of out-of-plane charge dynamics, believed to be incoherent in the normal state, yet lacking a comprehensive characterization in energy-momentum space. Here, we use resonant inelastic x-ray scattering (RIXS) with polarization analysis to uncover the pure charge character of a recently discovered collective mode in electron-doped cuprates. This mode disperses along both the in- and, importantly, out-of-plane directions, revealing its three dimensional nature. The periodicity of the out-of-plane dispersion corresponds to the CuO2 plane distance rather than the crystallographic c-axis lattice constant, suggesting that the interplane Coulomb interaction drives the coherent out-of-plane charge dynamics. The observed properties are hallmarks of the long-sought acoustic plasmon, predicted for layered systems and argued to play a substantial role in mediating high temperature superconductivity.Comment: This is the version of first submission. The revised manuscript according to peer reviews is now accepted by Nature and will be published online on 31st Oct., 201

Probing the Intermediate-Age Globular Clusters in NGC 5128 from Ultraviolet Observations

We explore the age distribution of the globular cluster (GC) system of the nearby elliptical galaxy NGC 5128 using ultraviolet (UV) photometry from Galaxy Evolution Explorer (GALEX) observations, with UV - optical colors used as the age indicator. Most GCs in NGC 5128 follow the general trends of GCs in M31 and Milky Way in UV - optical color-color diagram, which indicates that the majority of GCs in NGC 5128 are old similar to the age range of old GCs in M31 and Milky Way. A large fraction of spectroscopically identified intermediate-age GC (IAGC) candidates with ~ 3-8 Gyr are not detected in the FUV passband. Considering the nature of intermediate-age populations being faint in the far-UV (FUV) passband, we suggest that many of the spectroscopically identified IAGCs may be truly intermediate in age. This is in contrast to the case of M31 where a large fraction of spectroscopically suggested IAGCs are detected in FUV and therefore may not be genuine IAGCs but rather older GCs with developed blue horizontal branch stars. Our UV photometry strengthens the results previously suggesting the presence of GC and stellar subpopulation with intermediate age in NGC 5128. The existence of IAGCs strongly indicates the occurrence of at least one more major star formation episode after a starburst at high redshift.Comment: 8 pages, 3 figures, accepted for ApJ Lette

Density waves and 1/f1/f density fluctuations in granular flow

We simulate the granular flow in a narrow pipe with a lattice-gas automaton model. We find that the density in the system is characterized by two features. One is that spontaneous density waves propagate through the system with well-defined shapes and velocities. The other is that density waves are so distributed to make the power spectra of density fluctuations as $1/f^{\alpha}$ noise. Three important parameters make these features observable and they are energy dissipation, average density and the rougness of the pipe walls.Comment: Latex (with ps files appended

Conformal Mappings and Dispersionless Toda hierarchy

Let $\mathfrak{D}$ be the space consists of pairs $(f,g)$, where $f$ is a univalent function on the unit disc with $f(0)=0$, $g$ is a univalent function on the exterior of the unit disc with $g(\infty)=\infty$ and $f'(0)g'(\infty)=1$. In this article, we define the time variables $t_n, n\in \Z$, on $\mathfrak{D}$ which are holomorphic with respect to the natural complex structure on $\mathfrak{D}$ and can serve as local complex coordinates for $\mathfrak{D}$. We show that the evolutions of the pair $(f,g)$ with respect to these time coordinates are governed by the dispersionless Toda hierarchy flows. An explicit tau function is constructed for the dispersionless Toda hierarchy. By restricting $\mathfrak{D}$ to the subspace $\Sigma$ consists of pairs where $f(w)=1/\bar{g(1/\bar{w})}$, we obtain the integrable hierarchy of conformal mappings considered by Wiegmann and Zabrodin \cite{WZ}. Since every $C^1$ homeomorphism $\gamma$ of the unit circle corresponds uniquely to an element $(f,g)$ of $\mathfrak{D}$ under the conformal welding $\gamma=g^{-1}\circ f$, the space $\text{Homeo}_{C}(S^1)$ can be naturally identified as a subspace of $\mathfrak{D}$ characterized by $f(S^1)=g(S^1)$. We show that we can naturally define complexified vector fields \pa_n, n\in \Z on $\text{Homeo}_{C}(S^1)$ so that the evolutions of $(f,g)$ on $\text{Homeo}_{C}(S^1)$ with respect to \pa_n satisfy the dispersionless Toda hierarchy. Finally, we show that there is a similar integrable structure for the Riemann mappings $(f^{-1}, g^{-1})$. Moreover, in the latter case, the time variables are Fourier coefficients of $\gamma$ and $1/\gamma^{-1}$.Comment: 23 pages. This is to replace the previous preprint arXiv:0808.072

Magnetic excitations and phonons simultaneously studied by resonant inelastic x-ray scattering in optimally doped Bi1.5_{1.5}Pb0.55_{0.55}Sr1.6_{1.6}La0.4_{0.4}CuO6+δ_{6+\delta}

Magnetic excitations in the optimally doped high-$T_\mathrm{c}$ superconductor Bi$_{1.5}$Pb$_{0.55}$Sr$_{1.6}$La$_{0.4}$CuO$_{6+\delta}$ (OP-Bi2201, $T_\mathrm{c}\simeq 34$ K) are investigated by Cu $L_3$ edge resonant inelastic x-ray scattering (RIXS), below and above the pseudogap opening temperature. At both temperatures the broad spectral distribution disperses along the (1,0) direction up to $\sim$350~meV at zone boundary, similarly to other hole-doped cuprates. However, above $\sim$0.22 reciprocal lattice units, we observe a concurrent intensity decrease for magnetic excitations and quasi-elastic signals with weak temperature dependence. This anomaly seems to indicate a coupling between magnetic, lattice and charge modes in this compound. We also compare the magnetic excitation spectra near the anti-nodal zone boundary in the single layer OP-Bi2201 and in the bi-layer optimally doped Bi$_{1.5}$Pb$_{0.6}$Sr$_{1.54}$CaCu$_2$O$_{8+\delta}$ (OP-Bi2212, $T_\mathrm{c}\simeq96$ K). The strong similarities in the paramagnon dispersion and in their energy at zone boundary indicate that the strength of the super-exchange interaction and the short-range magnetic correlation cannot be directly related to $T_\mathrm{c}$, not even within the same family of cuprates

Morphologies of High Redshift, Dust Obscured Galaxies from Keck Laser Guide Star Adaptive Optics

Spitzer MIPS images in the Bootes field of the NOAO Deep Wide-Field Survey have revealed a class of extremely dust obscured galaxy (DOG) at z~2. The DOGs are defined by very red optical to mid-IR (observed-frame) colors, R - [24 um] > 14 mag, i.e. f_v (24 um) / f_v (R) > 1000. They are Ultra-Luminous Infrared Galaxies with L_8-1000 um > 10^12 -10^14 L_sun, but typically have very faint optical (rest-frame UV) fluxes. We imaged three DOGs with the Keck Laser Guide Star Adaptive Optics (LGSAO) system, obtaining ~0.06'' resolution in the K'-band. One system was dominated by a point source, while the other two were clearly resolved. Of the resolved sources, one can be modeled as a exponential disk system. The other is consistent with a de Vaucouleurs profile typical of elliptical galaxies. The non-parametric measures of their concentration and asymmetry, show the DOGs to be both compact and smooth. The AO images rule out double nuclei with separations of greater than 0.1'' (< 1 kpc at z=2), making it unlikely that ongoing major mergers (mass ratios of 1/3 and greater) are triggering the high IR luminosities. By contrast, high resolution images of z~2 SCUBA sources tend to show multiple components and a higher degree of asymmetry. We compare near-IR morphologies of the DOGs with a set of z=1 luminous infrared galaxies (LIRGs; L_IR ~ 10^11 L_sun) imaged with Keck LGSAO by the Center for Adaptive Optics Treasury Survey. The DOGs in our sample have significantly smaller effective radii, ~1/4 the size of the z=1 LIRGs, and tend towards higher concentrations. The small sizes and high concentrations may help explain the globally obscured rest-frame blue-to-UV emission of the DOGs.Comment: 9 pages, 7 figures, 2 tables, accepted for publication in the Astronomical Journa