Field Theory And Second Renormalization Group For Multifractals In Percolation

The field-theory for multifractals in percolation is reformulated in such a way that multifractal exponents clearly appear as eigenvalues of a second renormalization group. The first renormalization group describes geometrical properties of percolation clusters, while the second-one describes electrical properties, including noise cumulants. In this context, multifractal exponents are associated with symmetry-breaking fields in replica space. This provides an explanation for their observability. It is suggested that multifractal exponents are ''dominant'' instead of ''relevant'' since there exists an arbitrary scale factor which can change their sign from positive to negative without changing the Physics of the problem.Comment: RevTex, 10 page

Mechanism of CDW-SDW Transition in One Dimension

The phase transition between charge- and spin-density-wave (CDW, SDW) phases is studied in the one-dimensional extended Hubbard model at half-filling. We discuss whether the transition can be described by the Gaussian and the spin-gap transitions under charge-spin separation, or by a direct CDW-SDW transition. We determine these phase boundaries by level crossings of excitation spectra which are identified according to discrete symmetries of wave functions. We conclude that the Gaussian and the spin-gap transitions take place separately from weak- to intermediate-coupling region. This means that the third phase exists between the CDW and the SDW states. Our results are also consistent with those of the strong-coupling perturbative expansion and of the direct evaluation of order parameters.Comment: 5 pages(REVTeX), 5 figures(EPS), 1 table, also available from http://wwwsoc.nacsis.ac.jp/jps/jpsj/1999/p68a/p68a42/p68a42h/p68a42h.htm

In-situ surface technique analyses and ex-situ characterization of Si1-xGex epilayers grown on Si(001)-2 ×1 by molecular beam epitaxy

Si1-xGex epilayers grown by Molecular Beam Epitaxy on Si(001) at 400 ○C have been analyzed in-situ by surface techniques such as X-ray and Ultraviolet Photoelectron Spectroscopies (XPS and UPS), Low Energy Electron Diffraction (LEED) and photoelectron diffraction (XPD). The Ge surface concentrations (x) obtained from the ratios of Ge and Si core level intensities are systematically higher than those obtained by the respective evaporation fluxes. This indicates a Ge enrichment in the first overlayers confirmed by Ge-like UPS valence band spectra. The structured crystallographic character of the epilayers is ascertained by LEED and XPD polar scans in the (100) plane since the Ge Auger LMM and the Si 2p XPD intensity patterns from the Si1-xGex epilayers are identical to those of the Si substrate. The residual stress in the epilayer is determined by ex-situ X-ray diffraction (XRD) which also allows, as Rutherford Back Scattering (RBS), Ge concentration determinations

Impermeability effects in three-dimensional vesicles

We analyse the effects that the impermeability constraint induces on the equilibrium shapes of a three-dimensional vesicle hosting a rigid inclusion. A given alteration of the inclusion and/or vesicle parameters leads to shape modifications of different orders of magnitude, when applied to permeable or impermeable vesicles. Moreover, the enclosed-volume constraint wrecks the uniqueness of stationary equilibrium shapes, and gives rise to pear-shaped or stomatocyte-like vesicles.Comment: 16 pages, 7 figure

Bond-charge Interaction in the extended Hubbard chain

We study the effects of bond-charge interaction (or correlated hopping) on the properties of the extended ({\it i.e.,} with both on-site ($U$) and nearest-neighbor ($V$) repulsions) Hubbard model in one dimension at half-filling. Energy gaps and correlation functions are calculated by Lanczos diagonalization on finite systems. We find that, irrespective of the sign of the bond-charge interaction, $X$, the charge--density-wave (CDW) state is more robust than the spin--density-wave (SDW) state. A small bond-charge interaction term is enough to make the differences between the CDW and SDW correlation functions much less dramatic than when $X=0$. For $X=t$ and fixed $V<2t$ ($t$ is the uncorrelated hopping integral), there is an intermediate phase between a charge ordered phase and a phase corresponding to singly-occupied sites, the nature of which we clarify: it is characterized by a succession of critical points, each of which corresponding to a different density of doubly-occupied sites. We also find an unusual slowly decaying staggered spin-density correlation function, which is suggestive of some degree of ordering. No enhancement of pairing correlations was found for any $X$ in the range examined.Comment: 10 pages, 7 PostScript figures, RevTeX 3; to appear in Phys Rev

Direct fiber comb stabilization to a gas-filled hollow-core photonic crystal fiber

We have isolated a single tooth from a fiber laser-based optical frequency comb for nonlinear spectroscopy and thereby directly referenced the comb. An 89 MHz erbium fiber laser frequency comb is directly stabilized to the P(23) (1539.43 nm) overtone transition of [superscript]12C[subscript]2H[subscript]2 inside a hollow-core photonic crystal fiber. To do this, a single comb tooth is isolated and amplified from 20 nW to 40 mW with sufficient fidelity to perform saturated absorption spectroscopy. The fractional stability of the comb, ~7 nm away from the stabilized tooth, is shown to be 6 × 10[superscript]−12 at 100 ms gate time, which is over an order of magnitude better than that of a comb referenced to a GPS-disciplined Rb oscillator

Elastic deformation of a fluid membrane upon colloid binding

When a colloidal particle adheres to a fluid membrane, it induces elastic deformations in the membrane which oppose its own binding. The structural and energetic aspects of this balance are theoretically studied within the framework of a Helfrich Hamiltonian. Based on the full nonlinear shape equations for the membrane profile, a line of continuous binding transitions and a second line of discontinuous envelopment transitions are found, which meet at an unusual triple point. The regime of low tension is studied analytically using a small gradient expansion, while in the limit of large tension scaling arguments are derived which quantify the asymptotic behavior of phase boundary, degree of wrapping, and energy barrier. The maturation of animal viruses by budding is discussed as a biological example of such colloid-membrane interaction events.Comment: 14 pages, 9 figures, REVTeX style, follow-up on cond-mat/021242

Self-Dual Bending Theory for Vesicles

We present a self-dual bending theory that may enable a better understanding of highly nonlinear global behavior observed in biological vesicles. Adopting this topological approach for spherical vesicles of revolution allows us to describe them as frustrated sine-Gordon kinks. Finally, to illustrate an application of our results, we consider a spherical vesicle globally distorted by two polar latex beads.Comment: 10 pages, 3 figures, LaTeX2e+IOPar

Tricritical Behavior in the Extended Hubbard Chains

Phase diagrams of the one-dimensional extended Hubbard model (including nearest-neighbor interaction $V$) at half- and quarter-filling are studied by observing level crossings of excitation spectra using the exact diagonalization. This method is based on the Tomonaga-Luttinger liquid theory including logarithmic corrections which stem from the renormalization of the Umklapp- and the backward-scattering effects. Using this approach, the phase boundaries are determined with high accuracy, and then the structure of the phase diagram is clarified. At half-filling, the phase diagram consists of two Berezinskii-Kosterlitz-Thouless (BKT) transition lines and one Gaussian transition line in the charge sector, and one spin-gap transition line. This structure reflects the U(1) $\otimes$ SU(2) symmetry of the electron system. Near the $U=2V$ line, the Gaussian and the spin-gap transitions take place independently from the weak- to the intermediate-coupling region, but these two transition lines are coupled in the strong-coupling region. This result demonstrates existence of a tricritical point and a bond-charge-density-wave (BCDW) phase between charge- and spin-density-wave (CDW, SDW) phases. To clarify this mechanism of the transition, we also investigate effect of a correlated hopping term which plays a role to enlarge BCDW and bond-spin-density-wave (BSDW) phases. At quarter-filling, a similar crossover phenomenon also takes place in the large-$V$ region involving spin-gap and BKT-type metal-insulator transitions.Comment: 18 pages(REVTeX), 17 figures(EPS(color)), 3 tables, Detailed paper of JPSJ 68 (1999) 3123 (cond-mat/9903227), see also cond-mat/000341

Noisy random resistor networks: renormalized field theory for the multifractal moments of the current distribution

We study the multifractal moments of the current distribution in randomly diluted resistor networks near the percolation treshold. When an external current is applied between to terminals $x$ and $x^\prime$ of the network, the $l$th multifractal moment scales as $M_I^{(l)} (x, x^\prime) \sim | x - x^\prime |^{\psi_l /\nu}$, where $\nu$ is the correlation length exponent of the isotropic percolation universality class. By applying our concept of master operators [Europhys. Lett. {\bf 51}, 539 (2000)] we calculate the family of multifractal exponents $\{\psi_l \}$ for $l \geq 0$ to two-loop order. We find that our result is in good agreement with numerical data for three dimensions.Comment: 30 pages, 6 figure