Dielectric properties of multiband electron systems: I - Tight-binding formulation

The screened electron-electron interaction in a multi-band electron system is calculated within the random phase approximation and in the tight-binding representation. The obtained dielectric matrix contains, beside the usual site-site correlations, also the site-bond and bond-bond correlations, and thus includes all physically relevant polarization processes. The arguments are given that the bond contributions are negligible in the long wavelength limit. We analyse the system with two non-overlapping bands in this limit, and show that the corresponding dielectric matrix reduces to a $2\times2$ form. The intra-band and inter-band contributions are represented by diagonal matrix elements, while the off-diagonal elements contain the mixing between them. The latter is absent in insulators but may be finite in conductors. Performing the multipole expansion of the bare long-range interaction, we show that this mixing is directly related to the symmetry of the atomic orbitals participating in the tight-binding electronic states. In systems with forbidden atomic dipolar transitions, the intra-band and inter-band polarizations are separated. However, when the dipolar transitions are allowed, the off-diagonal elements of the dielectric matrix are of the same order as diagonal ones, due to a finite monopole-dipole interaction between the intra-band and inter-band charge fluctuations.Comment: 32 pages, LaTeX, to appear in Z.Phys.

Dielectric properties of multiband electron systems: II - Collective modes

Starting from the tight-binding dielectric matrix in the random phase approximation we examine the collective modes and electron-hole excitations in a two-band electronic system. For long wavelengths (${\bf q}\rightarrow0$), for which most of the analysis is carried out, the properties of the collective modes are closely related to the symmetry of the atomic orbitals involved in the tight-binding states. In insulators there are only inter-band charge oscillations. If atomic dipolar transitions are allowed, the corresponding collective modes reduce in the asymptotic limit of vanishing bandwidths to Frenkel excitons for an atomic insulator with weak on-site interactions. The finite bandwidths renormalize the dispersion of these modes and introduce a continuum of incoherent inter-band electron-hole excitations. The possible Landau damping of collective modes due to the presence of this continuum is discussed in detail.Comment: 25 pages, LaTeX, to appear in Z.Phys.

Photo-emission properties of quasi-one-dimensional conductors

We calculate the self-energy of one-dimensional electron band with the three-dimensional long range Coulomb interaction within the random phase approximation, paying particular attention to the contribution coming from the electron scatterings on the collective plasmon mode. It is shown that the spectral density has a form of wide feature at thr frequency scale of the plasmon frequency, without the presence of quasi-particle delta-peaks. The relevance of this result with respect to experimental findings and to the theory of Luttinger liquids is discussed.Comment: 4 pages, 2 figure

Photo-emission properties of quasi-one-dimensional conductors

We calculate the self-energy of the one-dimensional electron band with the three-dimensional long-range Coulomb interaction within the random phase approximation, paying particular attention to the contribution coming from the electron scatterings on the collective plasmon mode. It is shown that the spectral density has a form of wide feature at the frequency scale of the plasmon frequency, without the presence of quasi-particle $\delta$-peaks. The relevance of this result with respect to experimental findings and to the theory of Luttinger liquids is discussed

The functional design of the rotary enzyme ATP synthase is consistent with maximum entropy production

We show that the molecular motor ATP synthase has evolved in accordance with the statistical selection principle of Maximum Shannon Entropy and one of its corollaries, Maximum Entropy Production. These principles predict an optimal angular position for the ATP-binding transition close to the experimental value; an inverse relation between the optimal gearing ratio and the proton motive force (pmf); optimal operation at an inflection point in the curve of ATP synthesis rate versus pmf, enabling rapid metabolic control; and a high optimal free energy conversion efficiency. Our results suggest a statistical interpretation for the evolutionary optimization of ATP synthase function

Fractal analysis of Hopf bifurcation for a class of completely integrable nonlinear Schrödinger Cauchy problems

We study the complexity of solutions for a class of completely integrable, nonlinear integro-differential Schrödinger initial-boundary value problems on a bounded domain, depending on a real bifurcation parameter. The considered Schrödinger problem is a natural extension of the classical Hopf bifurcation model for planar systems into an infinite-dimensional phase space. Namely, the change in the sign of the bifurcation parameter has a consequence that an attracting (or repelling) invariant subset of the sphere in $L^2(\Omega)$ is born. We measure the complexity of trajectories near the origin by considering the Minkowski content and the box dimension of their finite-dimensional projections. Moreover we consider the compactness and rectifiability of trajectories, and box dimension of multiple spirals and spiral chirps. Finally, we are able to obtain the box dimension of trajectories of some nonintegrable Schrödinger evolution problems using their reformulation in terms of the corresponding (not explicitly solvable) dynamical systems in $\mathbb{R}^n$

Plasmon spectra and cohesion of the mixed stack organic conductors

Plasmon dispersion relations for quasi one-dimensional charge transfer crystals with two inequivalent conducting stacks are found in the Tomonaga model. The relationship between the Tomonaga model and the perturbation scheme is established for the evaluation of the ground state energy. The plasmon spectrum and the corresponding energy are calculated numerically for the configurations of chains, which correspond to the stacking patterns observed in the TTF-TCNQ and HMTTF-TCNQ crystals. It is found that the change of the zero point plasmon energy on going from one to the other lattice is considerably smaller than the change of the Madelung energy.Nous déterminons les relations de dispersion pour les plasmons dans les complexes de transfert de charge à deux chaînes non équivalentes. Nous utilisons le modèle de Tomonaga et établissons la correspondance entre cette approche et le calcul perturbatif de l'énergie de cohésion. Les spectres de plasmons et les énergies de cohésion correspondantes sont calculés numériquement pour les deux configurations des chaines, observées dans le TTF-TCNQ et HMTTF-TCNQ. Il apparaît que la variation de l'énergie de cohésion due aux plasmons lors du passage d'un réseau à l'autre est beaucoup plus faible que la variation de l'énergie de Madelung