The S-Matrix in Twistor Space

The simplicity and hidden symmetries of (Super) Yang-Mills and (Super)Gravity scattering amplitudes suggest the existence of a "weak-weak" dual formulation in which these structures are made manifest at the expense of manifest locality. We suggest that this dual description lives in (2,2) signature and is naturally formulated in twistor space. We recast the BCFW recursion relations in an on-shell form that begs to be transformed into twistor space. Our twistor transformation is inspired by Witten's, but differs in treating twistor and dual twistor variables more equally. In these variables the three and four-point amplitudes are amazingly simple; the BCFW relations are represented by diagrammatic rules that precisely define the "twistor diagrams" of Andrew Hodges. The "Hodges diagrams" for Yang-Mills theory are disks and not trees; they reveal striking connections between amplitudes and suggest a new form for them in momentum space. We also obtain a twistorial formulation of gravity. All tree amplitudes can be combined into an "S-Matrix" functional which is the natural holographic observable in asymptotically flat space; the BCFW formula turns into a quadratic equation for this "S-Matrix", providing a holographic description of N=4 SYM and N=8 Supergravity at tree level. We explore loop amplitudes in (2,2) signature and twistor space, beginning with a discussion of IR behavior. We find that the natural pole prescription renders the amplitudes well-defined and free of IR divergences. Loop amplitudes vanish for generic momenta, and in twistor space are even simpler than their tree-level counterparts! This further supports the idea that there exists a sharply defined object corresponding to the S-Matrix in (2,2) signature, computed by a dual theory naturally living in twistor space.Comment: V1: 46 pages + 23 figures. Less telegraphic abstract in the body of the paper. V2: 49 pages + 24 figures. Largely expanded set of references included. Some diagrammatic clarifications added, minor typo fixe

Mirror Dark Matter

There appear to be three challenges that any theory of dark matter must face: (i) why is $\Omega_{DM}$ of the same order as $\Omega_{Baryons}$ ? (ii) what are the near solar mass objects ($\sim 0.5 M_{\odot}$) observed by the MACHO microlensing project ? and (iii) understanding the shallow core density profile of the halos of dwarf as well as low surface brightness galaxies. The popular cold dark matter candidates, the SUSY LSP and the axion fail to meet these challenges. We argue that in the mirror model suggested recently to explain the neutrino anomalies, the mirror baryons being 15-20 times heavier than familiar baryons, can play the role of the cold dark matter and provide reasonable explanation of all three above properties without extra assumptions.Comment: Latex, 10 pages; Invited talk presented in PASCOS99 workshop, held in Lake Tahoe, Dec. 1999 and DM2000 workshop held in Los Angeles, February, 200

Normal Fermi Liquid Behavior of Quasiholes in the Spin-Polaron Model for Copper Oxides

Based on the t-J model and the self-consistent Born approximation, the damping of quasiparticle hole states near the Fermi surface is calculated in a low doping regime. Renormalization of spin-wave excitations due to hole doping is taken into account. The damping is shown to be described by a familiar form $\text{Im}\Sigma({\bf k}^{\prime},\epsilon)\propto (\epsilon^{2}/ \epsilon_{F})\ln(\epsilon/ \epsilon_{F})$ characteristic of the 2-dimensional Fermi liquid, in contrast with the earlier statement reported by Li and Gong [Phys. Rev. B {\bf 51}, 6343 (1995)] on the marginal Fermi liquid behavior of quasiholes

Thermal and Electrical Properties of gamma-NaxCoO2 (0.70 < x < 0.78)

We have performed specific heat and electric resistivity measurements of Na$_{x}$CoO$_{2}$ ($x=0.70$-0.78). Two anomalies have been observed in the specific heat data for $x=0.78$, corresponding to magnetic transitions at $T_{c}=22$ K and $T_{k}\simeq 9$ K reported previously. In the electrical resistivity, a steep decrease at $T_{c}$ and a bending-like variation at $T_{b}$(=120K for $x=0.78$) have been observed. Moreover, we have investigated the $x$-dependence of these parameters in detail. The physical properties of this system are very sensitive to $x$, and the inconsistent results of previous reports can be explained by a small difference in $x$. Furthermore, for a higher $x$ value, a phase separation into Na-rich and Na-poor domains occurs as we previously proposed, while for a lower $x$ value, from characteristic behaviors of the specific heat and the electrical resistivity at the low-temperature region, the system is expected to be in the vicinity of the magnetic instability which virtually exists below $x=0.70$.Comment: 4 pages (3 figures included) and an extra figure (gif), to be published in J. Phys. Soc. Jpn. 73 (9) with possible minor revision

A Phase transition in acoustic propagation in 2D random liquid media

Acoustic wave propagation in liquid media containing many parallel air-filled cylinders is considered. A self-consistent method is used to compute rigorously the propagation, incorporating all orders of multiple scattering. It is shown that under proper conditions, multiple scattering leads to a peculiar phase transition in acoustic propagation. When the phase transition occurs, a collective behavior of the cylinders appears and the acoustic waves are confined in a region of space in the neighborhood of the transmission source. A novel phase diagram is used to describe such phase transition. Originally submitted on April 6, 99.Comment: 5 pages, 5 color figure

Keeping a Single Qubit Alive by Experimental Dynamic Decoupling

We demonstrate the use of dynamic decoupling techniques to extend the coherence time of a single memory qubit by nearly two orders of magnitude. By extending the Hahn spin-echo technique to correct for unknown, arbitrary polynomial variations in the qubit precession frequency, we show analytically that the required sequence of pi-pulses is identical to the Uhrig dynamic decoupling (UDD) sequence. We compare UDD and CPMG sequences applied to a single Ca-43 trapped-ion qubit and find that they afford comparable protection in our ambient noise environment.Comment: 5 pages, 5 figure

Tree-Level Formalism

We review two novel techniques used to calculate tree-level scattering amplitudes efficiently: MHV diagrams, and on-shell recursion relations. For the MHV diagrams, we consider applications to tree-level amplitudes and focus in particular on the N=4 supersymmetric formulation. We also briefly describe the derivation of loop amplitudes using MHV diagrams. For the recursion relations, after presenting their general proof, we discuss several applications to massless theories with and without supersymmetry, to theories with massive particles, and to graviton amplitudes in General Relativity. This article is an invited review for a special issue of Journal of Physics A devoted to "Scattering Amplitudes in Gauge Theories".Comment: 40 pages, 8 figures, invited review for a special issue of Journal of Physics A devoted to "Scattering Amplitudes in Gauge Theories", R. Roiban(ed), M. Spradlin(ed), A. Volovich(ed); v2: minor corrections, references adde

Diffusive and localization behavior of electromagnetic waves in a two-dimensional random medium

In this paper, we discuss the transport phenomena of electromagnetic waves in a two-dimensional random system which is composed of arrays of electrical dipoles, following the model presented earlier by Erdogan, et al. (J. Opt. Soc. Am. B {\bf 10}, 391 (1993)). A set of self-consistent equations is presented, accounting for the multiple scattering in the system, and is then solved numerically. A strong localization regime is discovered in the frequency domain. The transport properties within, near the edge of and nearly outside the localization regime are investigated for different parameters such as filling factor and system size. The results show that within the localization regime, waves are trapped near the transmitting source. Meanwhile, the diffusive waves follow an intuitive but expected picture. That is, they increase with travelling path as more and more random scattering incurs, followed by a saturation, then start to decay exponentially when the travelling path is large enough, signifying the localization effect. For the cases that the frequencies are near the boundary of or outside the localization regime, the results of diffusive waves are compared with the diffusion approximation, showing less encouraging agreement as in other systems (Asatryan, et al., Phys. Rev. E {\bf 67}, 036605 (2003).)Comment: 8 pages 9 figure

Foaming Behavior of Polymer-Coated Colloids: The Need for Thick Liquid Films

The current study examined the foaming behavior of poly(vinylpyrrolidone) (PVP)–silica composite nanoparticles. Individually, the two components, PVP and silica nanoparticles, exhibited very little potential to partition at the air–water interface, and as such, stable foams could not be generated. In contrast, combining the two components to form silica–PVP core–shell nanocomposites led to good “foamability” and long-term foam stability. Addition of an electrolyte (Na2SO4) was shown to have a marked effect on the foam stability. By varying the concentration of electrolyte between 0 and 0.55 M, three regions of foam stability were observed: rapid foam collapse at low electrolyte concentrations, delayed foam collapse at intermediate concentrations, and long-term stability (∼10 days) at the highest electrolyte concentration. The observed transitions in foam stability were better understood by studying the microstructure and physical and mechanical properties of the particle-laden interface. For rapidly collapsing foams the nanocomposite particles were weakly retained at the air–water interface. The interfaces in this case were characterized as being “liquid-like” and the foams collapsed within 100 min. At an intermediate electrolyte concentration (0.1 M), delayed foam collapse over ∼16 h was observed. The particle-laden interface was shown to be pseudo-solid-like as measured under shear and compression. The increased interfacial rigidity was attributed to adhesion between interpenetrating polymer layers. For the most stable foam (prepared in 0.55 M Na2SO4), the ratio of the viscoelastic moduli, G′/G″, was found to be equal to ∼3, confirming a strongly elastic interfacial layer. Using optical microscopy, enhanced foam stability was assessed and attributed to a change in the mechanism of foam collapse. Bubble–bubble coalescence was found to be significantly retarded by the aggregation of nanocomposite particles, with the long-term destabilization being recognized to result from bubble coarsening. For rapidly destabilizing foams, the contribution from bubble–bubble coalescence was shown to be more significant

Correlations in intermediate-energy two-proton removal reactions

We report final-state-exclusive measurements of the light charged fragments in coincidence with 26Ne residual nuclei following the direct two-proton removal from a neutron-rich 28Mg secondary beam. A Dalitz-plot analysis and comparisons with simulations show that a majority of the triple- coincidence events with two protons display phase-space correlations consistent with the (two-body) kinematics of a spatially-correlated pair-removal mechanism. The fraction of such correlated events, 56(12) %, is consistent with the fraction of the calculated cross section, 64 %, arising from spin S = 0 two-proton configurations in the entrance-channel (shell-model) 28Mg ground state wave function. This result promises access to an additional and more specific probe of the spin and spatial correlations of valence nucleon pairs in exotic nuclei produced as fast secondary beams.Comment: accepted for publication in Physical Review Letter