Large scale numerical investigation of excited states in poly(phenylene)

A density matrix renormalisation group scheme is developed, allowing for the first time essentially exact numerical solutions for the important excited states of a realistic semi-empirical model for oligo-phenylenes. By monitoring the evolution of the energies with chain length and comparing them to the experimental absorption peaks of oligomers and thin films, we assign the four characteristic absorption peaks of phenyl-based polymers. We also determine the position and nature of the nonlinear optical states in this model.Comment: RevTeX, 10 pages, 4 eps figures included using eps

Effective theories of scattering with an attractive inverse-square potential and the three-body problem

A distorted-wave version of the renormalisation group is applied to scattering by an inverse-square potential and to three-body systems. In attractive three-body systems, the short-distance wave function satisfies a Schroedinger equation with an attractive inverse-square potential, as shown by Efimov. The resulting oscillatory behaviour controls the renormalisation of the three-body interactions, with the renormalisation-group flow tending to a limit cycle as the cut-off is lowered. The approach used here leads to single-valued potentials with discontinuities as the bound states are cut off. The perturbations around the cycle start with a marginal term whose effect is simply to change the phase of the short-distance oscillations, or the self-adjoint extension of the singular Hamiltonian. The full power counting in terms of the energy and two-body scattering length is constructed for short-range three-body forces.Comment: 19 pages (RevTeX), 2 figure

A theoretical investigation of the low lying electronic structure of poly(p-phenylene vinylene)

The two-state molecular orbital model of the one-dimensional phenyl-based semiconductors is applied to poly(p-phenylene vinylene). The energies of the low-lying excited states are calculated using the density matrix renormalization group method. Calculations of both the exciton size and the charge gap show that there are both Bu and Ag excitonic levels below the band threshold. The energy of the 1Bu exciton extrapolates to 2.60 eV in the limit of infinite polymers, while the energy of the 2Ag exciton extrapolates to 2.94 eV. The calculated binding energy of the 1Bu exciton is 0.9 eV for a 13 phenylene unit chain and 0.6 eV for an infinite polymer. This is expected to decrease due to solvation effects. The lowest triplet state is calculated to be at ca. 1.6 eV, with the triplet-triplet gap being ca. 1.6 eV. A comparison between theory, and two-photon absorption and electroabsorption is made, leading to a consistent picture of the essential states responsible for most of the third-order nonlinear optical properties. An interpretation of the experimental nonlinear optical spectroscopies suggests an energy difference of ca. 0.4 eV between the vertical energy and ca. 0.8 eV between the relaxed energy, of the 1Bu exciton and the band gap, respectively.Comment: LaTeX, 19 pages, 7 eps figures included using epsf. To appear in Physical Review B, 199

Renormalisation-group analysis of repulsive three-body systems

A coordinate space approach, based on that used by Efimov, is applied to three-body systems with contact interactions between pairs of particles. In systems with nonzero orbital angular momentum or with asymmetric spatial wave functions, the hyperradial equation contains a repulsive 1/r^2 potential. The resulting wave functions are used in a renormalisation group analysis. This confirms Griesshammer's power counting for short-range three-body forces in these systems. The only exceptions are ones like the 4S channel for three nucleons, where any derivatives needed in the interaction are found to be already counted by the scaling with the cut-off.Comment: 5 pages, RevTe

Effective field theory of 3He

3He and the triton are studied as three-body bound states in the effective field theory without pions. We study 3He using the set of integral equations developed by Kok et al. which includes the full off-shell T-matrix for the Coulomb interaction between the protons. To leading order, the theory contains: two-body contact interactions whose renormalized strengths are set by the NN scattering lengths, the Coulomb potential, and a three-body contact interaction. We solve the three coupled integral equations with a sharp momentum cutoff, Lambda, and find that a three-body interaction is required in 3He at leading order, as in the triton. It also exhibits the same limit-cycle behavior as a function of Lambda, showing that the Efimov effect remains in the presence of the Coulomb interaction. We also obtain the difference between the strengths of the three-body forces in 3He and the triton.Comment: 18 pages, 6 figures; further discussion and references adde

Effects of doping on thermally excited quasiparticles in the high-TcT_c superconducting state

The physical properties of low energy superconducting quasiparticles in high- $T_c$ superconductors are examined using magnetic penetration depth and specific heat experimental data. We find that the low energy density of states of quasiparticles of La$_{2-x}$Sr$_x$CuO$_4$ scales with $(x-x_c)/T_c$ to the leading order approximation, where $x_c$ is the critical doping concentration below which $T_c=0$. The linear temperature term of the superfluid density is renormalized by quasiparticle interactions and the renormalization factor times the Fermi velocity is found to be doping independent.Comment: 3 pages, 3 figures, minor change to the content, fig1 is reploted, to appear in Phys Rev

Simultaneous and extensive removal of the East Asian lithospheric root

Much evidence points to a dramatic thinning of East Asian lithosphere during the Mesozoic, but with little precision on when, or over what time scale. Using geochemical constraints, we examine an extensive compilation of dated volcanic samples from Russia, Mongolia and North China to determine when the lithosphere thinned and how long that process took. Geochemical results suggest that magmatism before 107 Ma derived from metasomatised subcontinental lithospheric mantle (SCLM), whereas after 107 Ma, melt predominantly derived from an asthenospheric source. The switch to an asthenospheric magma source at ~107 Ma occurred in both Mongolia and North China (>1600 km apart), whereas in eastern Russia the switch occurred a little later (~85 Ma). Such a dramatic change to an asthenospheric contribution appears to have taken, from beginning to end, just ~30 Myrs, suggesting this is the duration for lithospheric mantle weakening and removal. Subsequent volcanism, through the Cenozoic in Mongolia and North China does not appear to include any contribution from the removed SCLM, despite melts predominantly deriving from the asthenosphere

Evidence for southward subduction of the Mongol-Okhotsk oceanic plate: Implications from Mesozoic adakitic lavas from Mongolia

A combination of new 40Ar/39Ar dating results, major- and trace-element data, plus Sr-Nd-Pb-Hf isotope data, are used to investigate the petrogenesis of Triassic high-Si adakite (HSA), Cretaceous low-Si adakite-like (LSA) lavas, and Cretaceous high-K and shoshonitic trachyandesite lavas, from eastern and south-central Mongolia. All samples are light rare-earth element and large-ion lithophile element enriched but depleted in some high-field strength elements (notably Nb, Ta and Ti). Two alternative models are proposed to explain the petrogenesis of the HSA samples. (1) A southward-subducting Mongol-Okhotsk slab underwent partial melting in the Triassic during the closure of the Mongol-Okhotsk Ocean, with the resultant melts assimilating mantle and crustal material. Alternatively (2), a basaltic underplate of thickened (>50 km; >1.5 GPa), eclogitic lower crust foundered into the underlying mantle, and underwent partial melting with minor contamination from mantle material and some shallow-level crustal contamination. The LSA samples are interpreted as melts derived from a lithospheric mantle wedge that was previously metasomatised by slab melts. Similarly, the trachyandesite lavas are interpreted as melts deriving from a subduction-enriched subcontinental lithospheric mantle. The spatial distribution of these samples implies that metasomatism likely occurred due to a southward-subducting Mongol-Okhotsk slab associated with the closure of the Mongol-Okhotsk Ocean. When this interpretation is combined with previous evidence for a northward-subducting Mongol-Okhotsk slab it advocates that the Mongol-Okhotsk Ocean closed with double-sided subduction

Beating the standard quantum limit: Phase super-sensitivity of N-photon interferometers

Quantum metrology promises greater sensitivity for optical phase measurements than could ever be achieved classically. Here we present a theory of the phase sensitivity for the general case where the detection probability is given by an $N$ photon interference fringe. We find that the phase sensitivity has a complex dependence on both the intrinsic efficiency of detection $\eta$ and the interference fringe visibility $V$. Most importantly, the phase that gives maximum phase sensitivity is in general not the same as the phase at which the slope of the interference fringe is a maximum, as has previously been assumed. We determine the parameter range where quantum enhanced sensitivity can be achieved. In order to illustrate these theoretical results, we perform a four photon experiment with $\eta=3/4$ and $V=82\pm6$% (an extension of our previous work [Science \textbf{316}, 726 (2007)]) and find a phase sensitivity 1.3 times greater than the standard quantum limit at a phase different to that which gives maximum slope of the interference fringe.Comment: submitted for publication Oct 2007, 5pages, 3figure

Irreversibility and Polymer Adsorption

Physisorption or chemisorption from dilute polymer solutions often entails irreversible polymer-surface bonding. We present a theory of the non-equilibrium layers which result. While the density profile and loop distribution are the same as for equilibrium layers, the final layer comprises a tightly bound inner part plus an outer part whose chains make only fN surface contacts where N is chain length. The contact fractions f follow a broad distribution, P(f) ~ f^{-4/5}, in rather close agreement with strong physisorption experiments [H. M. Schneider et al, Langmuir v.12, p.994 (1996)].Comment: 4 pages, submitted to Phys. Rev. Let