Mersenne Primes, Polygonal Anomalies and String Theory Classification

It is pointed out that the Mersenne primes $M_p=(2^p-1)$ and associated perfect numbers ${\cal M}_p=2^{p-1}M_p$ play a significant role in string theory; this observation may suggest a classification of consistent string theories.Comment: 10 pages LaTe

Accretion signatures in the X-shooter spectrum of the substellar companion to SR12

About a dozen substellar companions orbiting young stellar objects or pre-main sequence stars at several hundred au have been identified in the last decade. These objects are interesting both due to the uncertainties surrounding their formation, and because their large separation from the host star offers the potential to study the atmospheres of young giant planets and brown dwarfs. Here, we present X-shooter spectroscopy of SR 12 C, a ∼2 Myr young brown dwarf orbiting SR 12 at an orbital separation of 1083 au. We determine the spectral type, gravity, and effective temperature via comparison with models and observational templates of young brown dwarfs. In addition, we detect and characterize accretion using several accretion tracers. We find SR 12 C to be a brown dwarf of spectral type L0 ± 1, log g = 4 ± 0.5, an effective temperature of 2600 ± 100 K. Our spectra provide clear evidence for accretion at a rate of ∼10−10 M⊙ yr−1. This makes SR 12 one of the few sub-stellar companions with a reliable estimate for its accretion rate. A comparison of the ages and accretion rates of sub-stellar companions with young isolated brown dwarfs does not reveal any significant differences. If further accretion rate measurements of a large number of substellar companions can confirm this trend, this would hint towards a similar formation mechanism for substellar companions at large separations and isolated brown dwarfs

Strong Phase Separation in a Model of Sedimenting Lattices

We study the steady state resulting from instabilities in crystals driven through a dissipative medium, for instance, a colloidal crystal which is steadily sedimenting through a viscous fluid. The problem involves two coupled fields, the density and the tilt; the latter describes the orientation of the mass tensor with respect to the driving field. We map the problem to a 1-d lattice model with two coupled species of spins evolving through conserved dynamics. In the steady state of this model each of the two species shows macroscopic phase separation. This phase separation is robust and survives at all temperatures or noise levels--- hence the term Strong Phase Separation. This sort of phase separation can be understood in terms of barriers to remixing which grow with system size and result in a logarithmically slow approach to the steady state. In a particular symmetric limit, it is shown that the condition of detailed balance holds with a Hamiltonian which has infinite-ranged interactions, even though the initial model has only local dynamics. The long-ranged character of the interactions is responsible for phase separation, and for the fact that it persists at all temperatures. Possible experimental tests of the phenomenon are discussed.Comment: To appear in Phys Rev E (1 January 2000), 16 pages, RevTex, uses epsf, three ps figure

Nodal Quasiparticle Dispersion in Strongly Correlated d-wave Superconductors

We analyze the effects of a momentum-dependent self-energy on the photoemission momentum distribution curve (MDC) lineshape, dispersion and linewidth. We illustrate this general analysis by a detailed examination of nodal quasiparticles in high Tc cuprates. We use variational results for the nodal quasiparticle weight Z (which varies rapidly with hole doping x) and the low energy Fermi velocity $v_F^{low}$ (which is independent of x), to show that the high energy MDC dispersion $v_{high} = v_F^{low}/Z$, so that it is much larger than the bare (band structure) velocity and also increases strongly with underdoping. We also present arguments for why the low energy Fermi velocity and the high energy dispersion are independent of the bare band structure at small x. All of these results are in good agreement with earlier and recent photoemission data [Zhou et al, Nature 423, 398 (2003)].Comment: 4 pages, 3 eps fig

Exact Cover with light

We suggest a new optical solution for solving the YES/NO version of the Exact Cover problem by using the massive parallelism of light. The idea is to build an optical device which can generate all possible solutions of the problem and then to pick the correct one. In our case the device has a graph-like representation and the light is traversing it by following the routes given by the connections between nodes. The nodes are connected by arcs in a special way which lets us to generate all possible covers (exact or not) of the given set. For selecting the correct solution we assign to each item, from the set to be covered, a special integer number. These numbers will actually represent delays induced to light when it passes through arcs. The solution is represented as a subray arriving at a certain moment in the destination node. This will tell us if an exact cover does exist or not.Comment: 20 pages, 4 figures, New Generation Computing, accepted, 200

Enhanced Symmetries in Multiparameter Flux Vacua

We give a construction of type IIB flux vacua with discrete R-symmetries and vanishing superpotential for hypersurfaces in weighted projective space with any number of moduli. We find that the existence of such vacua for a given space depends on properties of the modular group, and for Fermat models can be determined solely by the weights of the projective space. The periods of the geometry do not in general have arithmetic properties, but live in a vector space whose properties are vital to the construction.Comment: 32 pages, LaTeX. v2: references adde

Pairing symmetry and long range pair potential in a weak coupling theory of superconductivity

We study the superconducting phase with two component order parameter scenario, such as, $d_{x^2-y^2} + e^{i\theta}s_{\alpha}$, where $\alpha = xy, x^2+y^2$. We show, that in absence of orthorhombocity, the usual $d_{x^2-y^2}$ does not mix with usual $s_{x^2+y^2}$ symmetry gap in an anisotropic band structure. But the $s_{xy}$ symmetry does mix with the usual d-wave for $\theta =0$. The d-wave symmetry with higher harmonics present in it also mixes with higher order extended $s$ wave symmetry. The required pair potential to obtain higher anisotropic $d_{x^2-y^2}$ and extended s-wave symmetries, is derived by considering longer ranged two-body attractive potential in the spirit of tight binding lattice. We demonstrate that the dominant pairing symmetry changes drastically from $d$ to $s$ like as the attractive pair potential is obtained from longer ranged interaction. More specifically, a typical length scale of interaction $\xi$, which could be even/odd multiples of lattice spacing leads to predominant $s/d$ wave symmetry. The role of long range interaction on pairing symmetry has further been emphasized by studying the typical interplay in the temperature dependencies of these higher order $d$ and $s$ wave pairing symmetries.Comment: Revtex 8 pages, 7 figures embeded in the text, To appear in PR

Phase fluctuations, dissipation and superfluid stiffness in d-wave superconductors

We study the effect of dissipation on quantum phase fluctuations in d-wave superconductors. Dissipation, arising from a nonzero low frequency optical conductivity which has been measured in experiments below $T_c$, has two effects: (1) a reduction of zero point phase fluctuations, and (2) a reduction of the temperature at which one crosses over to classical thermal fluctuations. For parameter values relevant to the cuprates, we show that the crossover temperature is still too large for classical phase fluctuations to play a significant role at low temperature. Quasiparticles are thus crucial in determining the linear temperature dependence of the in-plane superfluid stiffness. Thermal phase fluctuations become important at higher temperatures and play a role near $T_c$.Comment: Presentation improved, new references added (10 latex pages, 3 eps figures). submitted to PR

Non-linear electrical response in a charge/orbital ordered Pr⁡0.63\Pr_{0.63}Ca0.37_{0.37}MnO3_3 crystal : the charge density wave analogy

Non-linear conduction in a charge-ordered manganese oxide Pr$_{0.63}$Ca$_{0.37}$MnO$_3$ is reported. To interpret such a feature, it is usually proposed that a breakdown of the charge or orbitally ordered state is induced by the current. The system behaves in such a way that the bias current may generate metallic paths giving rise to resistivity drop. One can describe this feature by considering the coexistence of localized and delocalized electron states with independent paths of conduction. This situation is reminiscent of what occurs in charge density wave systems where a similar non-linear conduction is also observed. In the light of recent experimental results suggesting the development of charge density waves in charge and orbitally ordered manganese oxides, a phenomenological model for charge density waves motion is used to describe the non-linear conduction in Pr$_{0.63}$Ca$_{0.37}$MnO$_3$. In such a framework, the non-linear conduction arises from the motion of the charge density waves condensate which carries a net electrical current.Comment: 13 pages, 6 figure

Effective Actions and Phase Fluctuations in d-wave Superconductors

We study effective actions for order parameter fluctuations at low temperature in layered d-wave superconductors such as the cuprates. The order parameter lives on the bonds of a square lattice and has two amplitude and two phase modes associated with it. The low frequency spectral weights for amplitude and relative phase fluctuations is determined and found to be subdominant to quasiparticle contributions. The Goldstone phase mode and its coupling to density fluctuations in charged systems is treated in a gauge-invariant manner. The Gaussian phase action is used to study both the $c$-axis Josephson plasmon and the more conventional in-plane plasmon in the cuprates. We go beyond the Gaussian theory by deriving a coarse-grained quantum XY model, which incorporates important cutoff effects overlooked in previous studies. A variational analysis of this effective model shows that in the cuprates, quantum effects of phase fluctuations are important in reducing the zero temperature superfluid stiffness, but thermal effects are small for $T << T_c$.Comment: Some numerical estimates corrected and figures changed. to appear in PRB, Sept.1 (2000