Inward and Outward Integral Equations and the KKR Method for Photons

In the case of electromagnetic waves it is necessary to distinguish between inward and outward on-shell integral equations. Both kinds of equation are derived. A correct implementation of the photonic KKR method then requires the inward equations and it follows directly from them. A derivation of the KKR method from a variational principle is also outlined. Rather surprisingly, the variational KKR method cannot be entirely written in terms of surface integrals unless permeabilities are piecewise constant. Both kinds of photonic KKR method use the standard structure constants of the electronic KKR method and hence allow for a direct numerical application. As a by-product, matching rules are obtained for derivatives of fields on different sides of the discontinuity of permeabilities. Key words: The Maxwell equations, photonic band gap calculationsComment: (to appear in J. Phys. : Cond. Matter), Latex 17 pp, PRA-HEP 93/10 (exclusively English and unimportant misprints corrected

Pulling hairpinned polynucleotide chains: Does base-pair stacking interaction matter?

Force-induced structural transitions both in relatively random and in designed single-stranded DNA (ssDNA) chains are studied theoretically. At high salt conditions, ssDNA forms compacted hairpin patterns stabilized by base-pairing and base-pair stacking interactions, and a threshold external force is needed to pull the hairpinned structure into a random coiled one. The base-pair stacking interaction in the ssDNA chain makes this hairpin-coil conversion a discontinuous (first-order) phase transition process characterized by a force plateau in the force-extension curve, while lowering this potential below some critical level turns this transition into continuous (second-order) type, no matter how strong the base-pairing interaction is. The phase diagram (including hairpin-I, -II, and random coil) is discussed as a function of stacking potential and external force. These results are in quantitative agreement with recent experimental observations of different ssDNA sequences, and they reveal the necessity to consider the base-pair stacking interactions in order to understand the structural formation of RNA, a polymer designed by nature itself. The theoretical method used may be extended to study the long-range interaction along double-stranded DNA caused by the topological constraint of fixed linking number.Comment: 8 pages using Revte

Correlation functions for 1d interacting fermions with spin-orbit coupling

We compute correlation functions for one-dimensional electron systems which spin and charge degrees of freedom are coupled through spin-orbit coupling. Charge density waves, spin density waves, singlet- triplet- superconducting fluctuations are studied. We show that the spin-orbit interaction modify the exponents and the phase diagram of the system, changing the dominant fluctuations and making new susceptibilities diverge for low temperature.Comment: 5 pages, 3 figures. Accepted for publication in Phys. Rev.

Quantum phase transition in Bose-Fermi mixtures

We study a quantum Bose-Fermi mixture near a broad Feshbach resonance at zero temperature. Within a quantum field theoretical model a two-step Gaussian approximation allows to capture the main features of the quantum phase diagram. We show that a repulsive boson-boson interaction is necessary for thermodynamic stability. The quantum phase diagram is mapped in chemical potential and density space, and both first and second order quantum phase transitions are found. We discuss typical characteristics of the first order transition, such as hysteresis or a droplet formation of the condensate which may be searched for experimentally.Comment: 16 pages, 17 figures; typos corrected, one figure adde

Rashba effect in 2D mesoscopic systems with transverse magnetic field

We present semiclassical and quantum mechanical results for the effects of a strong magnetic field in Quantum Wires in the presence of Rashba Spin Orbit coupling. Analytical and numerical results show how the perturbation acts in the presence of a transverse magnetic field in the ballistic regime and we assume a strong reduction of the backward scattering interaction which could have some consequences for the Tomonaga-Luttinger transport. We analyze the spin texture due to the action of Spin Orbit coupling and magnetic field often referring to the semiclassical solutions that magnify the singular spin polarization: results are obtained for free electrons in a twodimensional electron gas and for electrons in a Quantum Wire. We propose the systems as possible devices for the spin filtering at various regimes.Comment: 12 pages, 12 figures, to appear in Phys. Rev.

A superconvergent representation of the Gersten-Nitzan and Ford-Webber nonradiative rates

An alternative representation of the quasistatic nonradiative rates of Gersten and Nitzan [J. Chem. Phys. 1981, 75, 1139] and Ford and Weber [Phys. Rep. 1984, 113, 195] is derived for the respective parallel and perpendicular dipole orientations. Given the distance d of a dipole from a sphere surface of radius a, the representations comprise four elementary analytic functions and a modified multipole series taking into account residual multipole contributions. The analytic functions could be arranged hierarchically according to decreasing singularity at the short distance limit d ---> 0, ranging from d^{-3} over d^{-1} to ln (d/a). The alternative representations exhibit drastically improved convergence properties. On keeping mere residual dipole contribution of the modified multipole series, the representations agree with the converged rates on at least 99.9% for all distances, arbitrary particle sizes and emission wavelengths, and for a broad range of dielectric constants. The analytic terms of the representations reveal a complex distance dependence and could be used to interpolate between the familiar d^{-3} short-distance and d^{-6} long-distance behaviors with an unprecedented accuracy. Therefore, the representations could be especially useful for the qualitative and quantitative understanding of the distance behavior of nonradiative rates of fluorophores and semiconductor quantum dots involving nanometal surface energy transfer in the presence of metallic nanoparticles or nanoantennas. As a byproduct, a complete short-distance asymptotic of the quasistatic nonradiative rates is derived. The above results for the nonradiative rates translate straightforwardly to the so-called image enhancement factors Delta, which are of relevance for the surface-enhanced Raman scattering.Comment: 30 pages including 6 figure

Torsional Directed Walks, Entropic Elasticity, and DNA Twist Stiffness

DNA and other biopolymers differ from classical polymers due to their torsional stiffness. This property changes the statistical character of their conformations under tension from a classical random walk to a problem we call the `torsional directed walk'. Motivated by a recent experiment on single lambda-DNA molecules [Strick et al., Science 271 (1996) 1835], we formulate the torsional directed walk problem and solve it analytically in the appropriate force regime. Our technique affords a direct physical determination of the microscopic twist stiffness C and twist-stretch coupling D relevant for DNA functionality. The theory quantitatively fits existing experimental data for relative extension as a function of overtwist over a wide range of applied force; fitting to the experimental data yields the numerical values C=120nm and D=50nm. Future experiments will refine these values. We also predict that the phenomenon of reduction of effective twist stiffness by bend fluctuations should be testable in future single-molecule experiments, and we give its analytic form.Comment: Plain TeX, harvmac, epsf; postscript available at http://dept.physics.upenn.edu/~nelson/index.shtm