Large Coupling Constant Research Articles

Isotope effect and the role of phonons in the iron-based superconductors

We studied the isotope effect of phonon in the Fe-based superconductors using a phenomenological two band model for the sign-changing $s$-wave ($\ifmmode\pm\else\textpm\fi{}s$-wave) state. Within this mean-field model, we showed that the large isotope effect is not inconsistent with the $\ifmmode\pm\else\textpm\fi{}s$-wave pairing state and its high transition temperature. In principle, a large phonon isotope coefficient $\ensuremath{\alpha}$ implies a large phonon coupling constant. However, the asymmetric density of states between two bands substantially enhances the value of $\ensuremath{\alpha}$, so that a moderate value of the phonon coupling constant $({\ensuremath{\lambda}}_{\text{ph}}\ensuremath{\approx}0.4)$ can produce a very large value of $\ensuremath{\alpha}(\ensuremath{\approx}0.4)$ as well as a high transition temperature together with an antiferromagnet-induced interaction.

Very Strongly Ferromagnetically Coupled Diradicals from Mixed Radical Centers: Nitronyl Nitroxide Coupled to Oxoverdazyl via Polyene Spacers

We predict extremely large and positive intramolecular magnetic exchange coupling constants (J) for coupled diradicals constructed from nitronyl nitroxide (NN) and oxoverdazyl (o-VER). These radicals have the general formula o-VER(N)-nC-NN where nC represents an olefinic spacer with n = 0, 2, 4, 6, and 8. Species like o-VER(C)-nC-NN have negative coupling constants. The atoms in the parentheses show the point of attachment of the coupler to the verdazyl moiety. Both the N-linked series and C-linked series have comparable stability. The triplet molecular geometries were optimized by the density functional (UB3LYP) method using the 6-311 g(d,p) basis set. This was followed by single-point UB3LYP calculations using 6-311++g(3df,3pd) basis. To calculate J, single-point broken-symmetry computations were performed on the optimized triplet geometries and using the same basis set. The N-linked diradicals coupled through conjugated polyenes are topologically different. These are found to have coupling constants of the order of 1000 cm(-1), whereas the C-linked diradicals show coupling constants of the order of -100 cm(-1). In general, for both cases, the absolute magnitude of the coupling constant decreases with the increase in the length of the spacer.

A Triad of Bis(orthometalated) d8-Complexes Containing Four-Membered Rings

Reaction of 2-LiC6F4PPh2 with [MCl2(SEt2)2] in diethyl ether gives the monomeric bis(chelate) complexes trans-[M(κ2-2-C6F4PPh2)2] [M = Pt (1), Pd (2)] or, in the case of platinum, a mixture of cis- and trans-isomers. Treatment of a mixture of NiCl2 and 2-BrC6F4PPh2 in THF with zinc dust gives trans-[Ni(κ2-2-C6F4PPh2)2] (3). The four-membered chelate rings in 1−3 are opened on addition of the bidentate ligand 1,2-bis(diphenylphosphino)ethane (dppe), and, in the case of 3, 2,2′-bipyridine (bipy) and 1,10-phenanthroline (phen), to give complexes of the type cis-[M(κC-C6F4-2-PPh2)2(L-L)] [L-L = dppe, M = Ni (6), Pd (7), Pt (8); M = Ni, L-L = bipy (9), phen (10)], in which the PPh2 groups are uncoordinated. Complexes 6−8 show unexpectedly large four-bond coupling constants (4JPF), in the range 75−95 Hz, between the fluorine atoms (F6) ortho to the metal−carbon σ-bond and the phosphorus atoms of the PPh2 groups, possibly because F6 and the lone pairs on phosphorus adopt a close to synperiplanar conformation. Treatment of 2 with [PdCl2(NCMe)2] gives the dinuclear complex [Pd2(μ-Cl)2(κ2-2-C6F4PPh2)2] (11), which dimerizes in solution to the tetranuclear complex [Pd4(μ-Cl)4(μ-2-C6F4PPh2)4] (12) as a result of opening of the chelate 2-C6F4PPh2 rings. Carbon monoxide inserts into a nickel−carbon σ-bond of 3 to give, after oxidation, bis-2,2′-(diphenylphosphinoyl)octafluorobenzophenone, {2,2′-C6F4P(O)Ph2}2CO (14). The molecular structures of complexes 1−3, 6, 8, 9, and 14 have been determined by single-crystal X-ray methods.

Magnetoelastic coupling inDyMn2O5via infrared spectroscopy

We investigated the infrared-active phonons in ${\text{DyMn}}_{2}{\text{O}}_{5}$ as a function of temperature and magnetic field in order to elucidate the magnetic ordering-induced lattice distortions. Spin-lattice coupling in this geometrically frustrated multiferroic is evidenced by small frequency shifts of several phonon modes at various magnetic ordering temperatures, vibrational frequency shifts between 60 and 65 K from which we extract large coupling constants, and magnetic-field dependence of numerous phonons. We analyze these results in terms of local lattice distortions and discuss the consequences for the ferroelectric polarization and magnetodielectric effect.

Spin identification of the Randall-Sundrum resonance in lepton-pair production at the CERN LHC

The determination of the spin of the quantum states exchanged in the various nonstandard interactions is a relevant aspect in the identification of the corresponding scenarios. We discuss the identification reach at the CERN LHC on the spin-2 of the lowest-lying Randall-Sundrum (RS) resonance, predicted by gravity with one warped extra dimension, against spin-1 and spin-0 nonstandard exchanges with the same mass and producing the same number of events in the cross section. We focus on the angular distributions of leptons produced in the Drell-Yan process at the LHC; in particular, we use as a basic observable a 'normalized' integrated angular asymmetry A{sub CE}. Our finding is that the 95% C.L. identification reach on the spin-2 of the RS resonance (equivalently, the exclusion reach on both the spin-1 and spin-0 hypotheses for the peak) is up to a resonance mass scale of the order of 1.0 or 1.6 TeV in the case of weak coupling between graviton excitations and SM particles (k/M{sub Pl}=0.01) and 2.4 or 3.2 TeV for a larger coupling constant (k/M{sub Pl}=0.1) for a time-integrated LHC luminosity of 10 or 100 fb{sup -1}, respectively. Also, some comments are given on the complementary roles of the angular analysismore » and the eventual discovery of the predicted second graviton excitation in the identification of the RS scenario.« less

Impact of bound states on similarity renormalization group transformations

We study a simple class of unitary renormalization group (RG) transformations governed by a parameter f in the range [0; 1]. For f = 0, the transformation is one introduced by Wegner in condensed matter physics, and for f = 1 it is a simpler transformation that is being used in nuclear theory. The transformation with f = 0 diagonalizes the Hamiltonian but in the transformations withf near 1 divergent couplings arise as bound state thresholds emerge. To illustrate and diagnose this behavior, we numerically study Hamiltonian ows in two simple models with bound states: one with asymptotic freedom and a related one with a limit cycle. The f = 0 transformation places bound-state eigenvalues on the diagonal at their natural scale, after which the bound states decouple from the dynamics at much smaller momentum scales. At the other extreme, the f = 1 transformation tries to move bound-state eigenvalues to the part of the diagonal corresponding to the lowest momentum scales available and inevitably diverges when this scale is taken to zero. Intermediate values of f cause intermediate shifts of bound state eigenvalues down the diagonal and produce increasingly large coupling constants to do this. In discrete models, there is a critical value, fc, below which bound state eigenvalues appear at their natural scale and the entire ow to the diagonal is well-behaved. We analyze the shift mechanism analytically in a 3x3 matrix model,

Is X(3872) really a molecular state?

After taking into account both the pion and sigma meson exchange potential, we have performed a dynamical calculation of the D-0(D) over bar*(0) system. The s meson exchange potential is repulsive from heavy quark symmetry and numerically important for a loosely bound system. Our analysis disfavors the interpretation of X(3872) as a loosely bound molecular state if we use the experimental D*D pi coupling constant g = 0.59 and a reasonable cutoff around 1 GeV, which is the typical hadronic scale. Bound state solutions with negative eigenvalues for the D-0(D) over bar* system exist only with either a very large coupling constant (twice the experimental value) or a large cutoff (Lambda similar to 6GeV or beta similar to 6GeV(2)). In contrast, there probably exists a loosely bound S-wave B (B) over bar* molecular state. Once produced, such a molecular state would be rather stable, since its dominant decay mode is the radiative decay through B* -> B gamma. Experimental search of these states will be very interesting.

Photophysics of Soret-Excited Tetrapyrroles in Solution. I. Metalloporphyrins: MgTPP, ZnTPP, and CdTPP

The photophysical behavior of three Soret-excited diamagnetic meso-substituted tetraphenylmetalloporphyrins, MgTPP, ZnTPP, and CdTPP, have been examined in a wide variety of solvents using both steady-state and femtosecond fluorescence upconversion methods. The S 2 population of MgTPP decays to S 1 on the time scale of a few picoseconds with unit S 2-S 1 internal conversion efficiency, and the decay rates conform to the weak coupling case of radiationless transition theory. The energy gap law parameters characterizing the coupling of the S 2 and S 1 states of MgTPP have been obtained. The most important accepting vibrational modes in the S 1 state are multiple in-plane C-C and C-N stretches in the 1200-1500 cm (-1) range. Net S 2-S 1 decay is the dominant decay path for ZnTPP and CdTPP as well, but the process occurs at rates that exceed (in the case of CdTPP, they vastly exceed) those predicted by weak interstate coupling. Alternate mechanisms for the radiationless decay of the S 2 states of ZnTPP and CdTPP have been explored. Large spin-orbit coupling constants and the presence of multiple, near-equiergic triplet states suggest that S 2-T n intersystem crossing might occur at rates competitive with internal conversion. However, the measured efficiencies of S 2-S 1 internal conversion show that, at most, only a few percent of the S 2 population of ZnTPP and no more than about 30% of the S 2 population of CdTPP can decay by a "dark" path such as intersystem crossing.

Coupling constant behavior of eigenvalues of Zakharov-Shabat systems

We consider the eigenvalues of the non-self-adjoint Zakharov-Shabat systems as the coupling constant of the potential is varied. In particular, we are interested in eigenvalue collisions and eigenvalue trajectories in the complex plane. We identify shape features in the potential that are responsible for the occurrence of collisions and we prove asymptotic formulas for large coupling constants that tell us where eigenvalues collide or where they emerge from the continuous spectrum. Some examples are provided which show that the asymptotic methods yield results that compare well with exact numerical computations.

ON CONVERGENCE TO EQUILIBRIUM IN STRONGLY COUPLED BOGOLIUBOV'S OSCILLATOR MODEL

We examine classical Bogoliubov's model of a particle coupled to a heat bath which consists of infinitely many stochastic oscillators. Bogoliubov's result1 suggests that, in the stochastic limit, the model exhibits convergence to thermodynamical equilibrium. It has recently been shown that the system does attain the equilibrium if the coupling constant is small enough.12 We show that in the case of the large coupling constant, the distribution function ρS (q, p, t) → 0 pointwise as t → ∞. This implies that if there is convergence to equilibrium, then the limit measure has no finite momenta. Besides, the probability to find the particle in any finite domain of phase space tends to zero. This is also true for domains in the coordinate space and in the momentum space.

Dimension of the spectrum of one-dimensional discrete Schrödinger operators with Sturmian potentials

Damanik and collaborators (2007) gave the behavior for large coupling constant of the box dimension of the spectrum of a one-dimensional discrete Schrödinger operator whose potential is a Sturm sequence associated with the golden ratio. They also show that in this case the Hausdorff and box dimensions coincide (i.e. the spectrum is dimension-regular). This Note aims at giving a simpler proof of the asymptotic property result and to generalize it to the case of any Sturm potential associated with an irrational frequency whose continued fraction expansion has bounded partial quotients. Moreover, we determine the upper box dimension of the spectrum, with large coupling constant, and show that it is not dimension-regular in general. To cite this article: Q.-H. Liu et al., C. R. Acad. Sci. Paris, Ser. I 345 (2007).

Analyzing molecular properties calculated with two-component relativistic methods using spin-free natural bond orbitals: NMR spin-spin coupling constants

An analysis method for static linear response properties employing two-component (spin-orbit) relativistic density functional theory along with scalar relativistic "natural localized molecular orbitals" (NLMOs) and "natural bond orbitals" (NBOs) has been developed. The spin-orbit NLMO/NBO analysis has been applied to study the indirect spin-spin coupling (J-coupling) constants in Tl-I, PbH(4), and a dinuclear Pt-Tl bonded complex with a very large Pt-Tl coupling constant (expt.: 146.8 kHz). For Tl-I it is shown that the analysis scheme based on scalar relativistic NLMOs is applicable even if spin-orbit coupling is responsible for most of the coupling's magnitude. For PbH(4) it is shown that electron delocalization plays a much larger role for the Pb-H coupling than it is the case for the C-H coupling in methane. For the Pt-Tl complex the analysis clearly demonstrates the strong influence of the ligands on the Pt-Tl coupling constant and quantifies the effect of the delocalization of the Pt-Tl bond on the Pt-Tl coupling constant.

Homoclinic orbits and localized solutions in nonlinear Schrödinger lattices

By using the symmetry properties of the reversible planar maps, instead of the Melnikov analysis, we improve the homoclinic orbit approach without assuming small perturbations to prove rigorously the existence of bright and dark soliton solutions of the discrete nonlinear Schrödinger equations with various nonlinearities in one-dimensional lattices. Our approach is valid both for small and large coupling constants. The latter case is inaccessible to the anti-integrability method.

Roles of inter- and intramolecular vibrations and band-hopping crossover in the charge transport in naphthalene crystal

We calculate the hole and electron mobilities in naphthalene crystal from 10 to 300 K within the framework of the Holstein-Peierls model coupled with first-principles density-functional-theory-projected tight-binding band structures. All the electron-phonon coupling constants, including both local and nonlocal parts for inter- and intramolecular vibrations, have been taken into considerations through density functional theory. The band-hopping crossover transition temperature for the electron transport in the c' axis is calculated to be around 23 K. We have identified a few high frequency intramolecular vibrations which are very important to the charge transport in naphthalene crystal due to their comparatively large electron-phonon coupling constants. However, their contributions to the temperature dependence of mobility are minor because of the small phonon occupations and small nonlocal coupling strengths. The low frequency intermolecular modes (longitudinal optical modes) are found to be the major contributions to the temperature dependent charge transfer properties in naphthalene crystal. Even though the calculated qualitative temperature dependence is in agreement with experiment, the predicted absolute mobility is about one to two orders of magnitude larger.

Positive Lyapunov Exponent and Minimality for the Continuous 1-d Quasi-Periodic Schrödinger Equation with Two Basic Frequencies

We consider the time-independent quasi-periodic Schrodinger equation $$-u^{\prime\prime}(x) + K^{2}V (x, \theta + \omega x)u(x) = Eu(x), \,\,\,\, x \in {\mathbb{R}}$$ , with a potential function \(V : {\mathbb{T}}^{2} \rightarrow {\mathbb{R}}\) of class C2 with a unique non-degenerate global minimum, large coupling constants K2 and energies E in the bottom of the spectrum of the associated Schrodinger operator. We obtain estimates on the Lyapunov exponents and the Lebesgue measure of the spectrum, as well as localization results. Moreover, we show that the projective flow on \({\mathbb{T}}^{2} \times {\mathbb{P}}^{1}\) induced by the Schrodinger equation often is minimal.

Square-Pyramidal/Triangular Framework Oxide: Synthesis and Structure of PKU-6

PKU-6, a new aluminoborate (HAl2B3O8), has been synthesized in a closed system at 400 degrees C. The structure of PKU-6, characterized by using powder and single-crystal X-ray diffraction, consists of AlO5 square-pyramidal chains and B3O7 groups, which are interconnected and form a three-dimensional framework. The 27Al NMR study indicates that the isotropic chemical shift of pyramidal Al is 34.6 ppm with a large quadrupolar coupling constant (CQ=4.2 MHz), mainly due to a nonspherical coordination environment.

Dynamics of the Quasi-Periodic Schrödinger Cocycle at the Lowest Energy in the Spectrum

In this paper we consider the quasi-periodic Schrodinger cocycle over \(\mathbb{T}^d\) (d ≥ 1) and, in particular, its projectivization. In the regime of large coupling constants and Diophantine frequencies, we give an affirmative answer to a question posed by M. Herman [21, p.482] concerning the geometric structure of certain Strange Non-chaotic Attractors which appear in the projective dynamical system. We also show that for some phase, the lowest energy in the spectrum of the associated Schrodinger operator is an eigenvalue with an exponentially decaying eigenfunction. This generalizes [39] to the multi-frequency case (d > 1).

Neutrino scattering rates in neutron star matter with Δ isobars

We take the \ensuremath{\Delta}-isobar degrees of freedom into account in neutron star matter and evaluate their contributions to neutrino scattering cross sections and mean free paths. The neutron star matter is described by means of an effective hadronic model in the relativistic mean-field approximation. It is found that \ensuremath{\Delta} isobars may be present in neutron stars. The electron chemical potential does not decrease and the neutrino abundance does not increase with the increase of the density when neutrinos are trapped in the matter with \ensuremath{\Delta} isobars. The large vector coupling constant between the ${\ensuremath{\Delta}}^{\ensuremath{-}}$ and neutrino and the high spin of the \ensuremath{\Delta} influence significantly the neutrino scattering cross section and lead the contribution of the ${\ensuremath{\Delta}}^{\ensuremath{-}}$ to the dominance of the scattering rates. In neutrino-trapped case, the presence of \ensuremath{\Delta}s causes the neutrino mean free path to decrease drastically compared to that in the matter in which baryons are only nucleons.

On the highest transcendentality in [formula omitted] SUSY

We investigate the Eden–Staudacher equation for the anomalous dimension of the twist-2 operators at the large spin s in the N = 4 super-symmetric gauge theory. This equation is reduced to a set of linear algebraic equations with the kernel calculated analytically. We prove that in perturbation theory the anomalous dimension is a sum of products of the Euler functions ζ ( k ) having the property of the maximal transcendentality with the coefficients being integer numbers. The radius of convergency of the perturbation theory is found. It is shown, that at g = ∞ the kernel has an essential singularity. The analytic properties of the solution of the Eden–Staudacher equation are investigated. In particular for the case of the strong coupling constant the solution has an essential singularity on the second sheet of the variable j appearing in its Laplace transformation. Similar results are derived also for the Beisert–Eden–Staudacher equation which includes the contribution from the phase related to the crossing symmetry of the underlying S-matrix. We show, that its singular solution at large coupling constants reproduces the anomalous dimension predicted from the string side of the AdS/CFT correspondence.

Vibronic Interaction in Metalloporphyrin π-Anion Radicals

The vibronic (vibrational-electronic) interactions in the pi-anion radicals of the metalloporphyrins (M=Cr, Mn, Fe, Co, Ni, Cu, and Zn), which show delocalized D4h structures in the neutral states, are discussed using B3LYP density-functional-theory calculations. The B1g and B2g modes of vibration can remove the degenerate 2Eg state of the pi-anion radicals in the D4h symmetric structures to lead to rectangular and diamond D2h distortions, respectively. Calculated vibronic coupling constants demonstrate that the B1g modes of vibration better couple with the degenerate electronic state, leading to the rectangular D2h distortion. In particular, the B1g modes of nu10 and nu11, which have dominant contributions from Calpha-Cm and Cbeta-Cbeta stretching, give large vibronic coupling constants in the pi-anion radicals. The vibronic coupling constant can be viewed as the Jahn-Teller distortion force, and therefore these C-C stretching B1g modes will play a central role in the Jahn-Teller effect of the pi-anion radicals of the metalloporphyrins.