Coloring translates and homothets of a convex body

We obtain improved upper bounds and new lower bounds on the chromatic number as a linear function of the clique number, for the intersection graphs (and their complements) of finite families of translates and homothets of a convex body in \RR^n.Comment: 11 pages, 2 figure

Thermoelectric effects of an Aharonov-Bohm interferometer with an embedded quantum dot in the Kondo regime

Thermoelectric effects are studied in an Aharonov-Bohm (AB) interferometer with an embedded quantum dot in the Kondo regime. The AB flux-dependent transmission probability has an asymmetrical shape arising from the Fano interference between the direct tunneling path and the Kondo-resonant tunneling path through a quantum dot. The sign and magnitude of thermopower can be modulated by the AB flux and the direct tunneling amplitude. In addition, the thermopower is anomalously enhanced by the Kondo correlation in the quantum dot near the Kondo temperature ($T_K$). The Kondo correlation in the quantum dot also leads to crossover behavior in diagonal transport coefficients as a function of temperature. The amplitude of an AB oscillation in electric and thermal conductances is small at temperatures far above $T_K$, but becomes enhanced as the system is cooled below $T_K$. The AB oscillation is strong in the thermopower and Lorenz number within the crossover region near the Kondo temperature.Comment: 16 pages, 10 figure

Singularities in the Fermi liquid description of a partially filled Landau level and the energy gaps of fractional quantum Hall states

We consider a two dimensional electron system in an external magnetic field at and near an even denominator Landau level filling fraction. Using a fermionic Chern--Simons approach we study the description of the system's low energy excitations within an extension of Landau's Fermi liquid theory. We calculate perturbatively the effective mass and the quasi--particle interaction function characterizing this description. We find that at an even denominator filling fraction the fermion's effective mass diverges logarithmically at the Fermi level, and argue that this divergence allows for an {\it exact} calculation of the energy gaps of the fractional quantized Hall states asymptotically approaching these filling fractions. We find that the quasi--particle interaction function approaches a delta function. This singular behavior leads to a cancelation of the diverging effective mass from the long wavelength low frequency linear response functions at even denominator filling fractions.Comment: 46 pages, RevTeX, 5 figures included in a uuencoded postscript file. Minor revisions relative to the original version. The paper will be published in the Physical Review B, and can be retrieved from the World Wide Web, in http://cmtw.harvard.edu/~ster

Supersymmetry, Axions and Cosmology

Various authors have noted that in particular models, the upper bound on the axion decay constant may not hold. We point out that within supersymmetry, this is a generic issue. For large decay constants, the cosmological problems associated with the axion's scalar partner are far more severe than those of the axion. We survey a variety of models, both for the axion multiplet and for cosmology, and find that in many cases where the cosmological problems of the saxion are solved, the usual upper bound on the axion is significantly relaxed. We discuss, more generally, the cosmological issues raised by the pseudoscalar members of moduli multiplets, and find that they are potentially quite severe.Comment: 27 pages, published version, some discussions clarifie

Colossal magnetooptical conductivity in doped manganites

We show that the current carrier density collapse in doped manganites, which results from bipolaron formation in the paramagnetic phase, leads to a colossal change of the optical conductivity in an external magnetic field at temperatures close to the ferromagnetic transition. As with the colossal magnetoresistance (CMR) itself, the corresponding magnetooptical effect is explained by the dissociation of localized bipolarons into mobile polarons owing to the exchange interaction with the localized Mn spins in the ferromagnetic phase. The effect is positive at low frequencies and negative in the high-frequency region. The present results agree with available experimental observations.Comment: 4 pages, REVTeX 3.0, two eps-figures included in the tex

Constraints on diffuse neutrino background from primordial black holes

We calculated the energy spectra and the fluxes of electron neutrino emitted in the process of evaporation of primordial black holes (PBHs) in the early universe. It was assumed that PBHs are formed by a blue power-law spectrum of primordial density fluctuations. We obtained the bounds on the spectral index of density fluctuations assuming validity of the standard picture of gravitational collapse and using the available data of several experiments with atmospheric and solar neutrinos. The comparison of our results with the previous constraints (which had been obtained using diffuse photon background data) shows that such bounds are quite sensitive to an assumed form of the initial PBH mass function.Comment: 18 pages,(with 7 figures

Classical Nambu-Goldstone fields

It is shown that a Nambu-Goldstone (NG) field may be coherently produced by a large number of particles in spite of the fact that the NG bosons do not couple to flavor conserving scalar densities like $\bar{\psi}\psi$. If a flavor oscillation process takes place the phases of the pseudo-scalar or flavor violating densities of different particles do not necessarily cancel each other. The NG boson gets a macroscopic source whenever the total (spontaneously broken) quantum number carried by the source particles suffers a net increase or decrease in time. If the lepton numbers are spontaneously broken such classical NG (majoron) fields may significantly change the neutrino oscillation processes in stars pushing the observational capabilities of neutrino-majoron couplings down to $m_{\nu}/300$ GeV.Comment: 11 pages, updated, to appear in PR

Fully supersymmetric CP violations in the kaon system

We show that, on the contrary to the usual claims, fully supersymmetric CP violations in the kaon system are possible through the gluino mediated flavor changing interactions. Both $\epsilon_K$ and ${\rm Re} (\epsilon' / \epsilon_K)$ can be accommodated for relatively large $\tan\beta$ without any fine tunings or contradictions to the FCNC and EDM constraints.Comment: Contribution to the Proceedings of ICHEP2000, Osaka, 200

Coherent Phonons in Carbon Nanotubes and Graphene

We review recent studies of coherent phonons (CPs) corresponding to the radial breathing mode (RBM) and G-mode in single-wall carbon nanotubes (SWCNTs) and graphene. Because of the bandgap-diameter relationship, RBM-CPs cause bandgap oscillations in SWCNTs, modulating interband transitions at terahertz frequencies. Interband resonances enhance CP signals, allowing for chirality determination. Using pulse shaping, one can selectively excite speci!c-chirality SWCNTs within an ensemble. G-mode CPs exhibit temperature-dependent dephasing via interaction with RBM phonons. Our microscopic theory derives a driven oscillator equation with a density-dependent driving term, which correctly predicts CP trends within and between (2n+m) families. We also find that the diameter can initially increase or decrease. Finally, we theoretically study the radial breathing like mode in graphene nanoribbons. For excitation near the absorption edge, the driving term is much larger for zigzag nanoribbons. We also explain how the armchair nanoribbon width changes in response to laser excitation.Comment: 48 pages, 41 figure

Viability of primordial black holes as short period gamma-ray bursts

It has been proposed that the short period gamma-ray bursts, which occur at a rate of $\sim 10 {\rm yr^{-1}}$, may be evaporating primordial black holes (PBHs). Calculations of the present PBH evaporation rate have traditionally assumed that the PBH mass function varies as $M_{{\rm BH}}^{-5/2}$. This mass function only arises if the density perturbations from which the PBHs form have a scale invariant power spectrum. It is now known that for a scale invariant power spectrum, normalised to COBE on large scales, the PBH density is completely negligible, so that this mass function is cosmologically irrelevant. For non-scale-invariant power spectra, if all PBHs which form at given epoch have a fixed mass then the PBH mass function is sharply peaked around that mass, whilst if the PBH mass depends on the size of the density perturbation from which it forms, as is expected when critical phenomena are taken into account, then the PBH mass function will be far broader than $M_{{\rm BH}}^{-5/2}$. In this paper we calculate the present day PBH evaporation rate, using constraints from the diffuse gamma-ray background, for both of these mass functions. If the PBH mass function has significant finite width, as recent numerical simulations suggest, then it is not possible to produce a present day PBH evaporation rate comparable with the observed short period gamma-ray burst rate. This could also have implications for other attempts to detect evaporating PBHs.Comment: 5 pages, 2 figures, version to appear in Phys. Rev. D with additional reference