Recent advances in hypertension and cardiovascular toxicities with vascular endothelial growth factor inhibition

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Carnot-Caratheodory metric and gauge fluctuation in Noncommutative Geometry

Gauge fields have a natural metric interpretation in terms of horizontal distance. The latest, also called Carnot-Caratheodory or subriemannian distance, is by definition the length of the shortest horizontal path between points, that is to say the shortest path whose tangent vector is everywhere horizontal with respect to the gauge connection. In noncommutative geometry all the metric information is encoded within the Dirac operator D. In the classical case, i.e. commutative, Connes's distance formula allows to extract from D the geodesic distance on a riemannian spin manifold. In the case of a gauge theory with a gauge field A, the geometry of the associated U(n)-vector bundle is described by the covariant Dirac operator D+A. What is the distance encoded within this operator ? It was expected that the noncommutative geometry distance d defined by a covariant Dirac operator was intimately linked to the Carnot-Caratheodory distance dh defined by A. In this paper we precise this link, showing that the equality of d and dh strongly depends on the holonomy of the connection. Quite interestingly we exhibit an elementary example, based on a 2 torus, in which the noncommutative distance has a very simple expression and simultaneously avoids the main drawbacks of the riemannian metric (no discontinuity of the derivative of the distance function at the cut-locus) and of the subriemannian one (memory of the structure of the fiber).Comment: published version with additional figures to make the proof more readable. Typos corrected in this ultimate versio

Ideal Stars and General Relativity

We study a system of differential equations that governs the distribution of matter in the theory of General Relativity. The new element in this paper is the use of a dynamical action principle that includes all the degrees of freedom, matter as well as metric. The matter lagrangian defines a relativistic version of non-viscous, isentropic hydrodynamics. The matter fields are a scalar density and a velocity potential; the conventional, four-vector velocity field is replaced by the gradient of the potential and its scale is fixed by one of the eulerian equations of motion, an innovation that significantly affects the imposition of boundary conditions. If the density is integrable at infinity, then the metric approaches the Schwarzschild metric at large distances. There are stars without boundary and with finite total mass; the metric shows rapid variation in the neighbourhood of the Schwarzschild radius and there is a very small core where a singularity indicates that the gas laws break down. For stars with boundary there emerges a new, critical relation between the radius and the gravitational mass, a consequence of the stronger boundary conditions. Tentative applications are suggested, to certain Red Giants, and to neutron stars, but the investigation reported here was limited to polytropic equations of state. Comparison with the results of Oppenheimer and Volkoff on neutron cores shows a close agreement of numerical results. However, in the model the boundary of the star is fixed uniquely by the required matching of the interior metric to the external Schwarzschild metric, which is not the case in the traditional approach.Comment: 26 pages, 7 figure

Mass Renormalization in the Su-Schrieffer-Heeger Model

This study of the one dimensional Su-Schrieffer-Heeger model in a weak coupling perturbative regime points out the effective mass behavior as a function of the adiabatic parameter $\omega_{\pi}/J$, $\omega_{\pi}$ is the zone boundary phonon energy and $J$ is the electron band hopping integral. Computation of low order diagrams shows that two phonons scattering processes become appreciable in the intermediate regime in which zone boundary phonons energetically compete with band electrons. Consistently, in the intermediate (and also moderately antiadiabatic) range the relevant mass renormalization signals the onset of a polaronic crossover whereas the electrons are essentially undressed in the fully adiabatic and antiadiabatic systems. The effective mass is roughly twice as much the bare band value in the intermediate regime while an abrupt increase (mainly related to the peculiar 1D dispersion relations) is obtained at $\omega_{\pi}\sim \sqrt{2}J$.Comment: To be published in Phys.Rev.B - 3 figure

Shot Noise in Nanoscale Conductors From First Principles

We describe a field-theoretic approach to calculate quantum shot noise in nanoscale conductors from first principles. Our starting point is the second-quantization field operator to calculate shot noise in terms of single quasi-particle wavefunctions obtained self-consistently within density functional theory. The approach is valid in both linear and nonlinear response and is particularly suitable in studying shot noise in atomic-scale conductors. As an example we study shot noise in Si atomic wires between metal electrodes. We find that shot noise is strongly nonlinear as a function of bias and it is enhanced for one- and two-Si wires due to the large contribution from the metal electrodes. For longer wires it shows an oscillatory behavior for even and odd number of atoms with opposite trend with respect to the conductance, indicating that current fluctuations persist with increasing wire length.Comment: 4 pages, 4 figure

Path integrals approach to resisitivity anomalies in anharmonic systems

Different classes of physical systems with sizeable electron-phonon coupling and lattice distortions present anomalous resistivity behaviors versus temperature. We study a molecular lattice Hamiltonian in which polaronic charge carriers interact with non linear potentials provided by local atomic fluctuations between two equilibrium sites. We study a molecular lattice Hamiltonian in which polaronic charge carriers interact with non linear potentials provided by local atomic fluctuations between two equilibrium sites. A path integral model is developed to select the class of atomic oscillations which mainly contributes to the partition function and the electrical resistivity is computed in a number of representative cases. We argue that the common origin of the observed resistivity anomalies lies in the time retarded nature of the polaronic interactions in the local structural instabilities.Comment: 4 figures, to appear in Phys.Rev.B, May 1st (2001

Polaron features of the one-dimensional Holstein Molecular Crystal Model

The polaron features of the one-dimensional Holstein Molecular Crystal Model are investigated by improving a variational method introduced recently and based on a linear superposition of Bloch states that describe large and small polaron wave functions. The mean number of phonons, the polaron kinetic energy, the electron-phonon local correlation function, and the ground state spectral weight are calculated and discussed. A crossover regime between large and small polaron for any value of the adiabatic parameter $\omega_0/t$ is found and a polaron phase diagram is proposed.Comment: 12 pages, 2 figure

Quantum Monte Carlo and variational approaches to the Holstein model

Based on the canonical Lang-Firsov transformation of the Hamiltonian we develop a very efficient quantum Monte Carlo algorithm for the Holstein model with one electron. Separation of the fermionic degrees of freedom by a reweighting of the probability distribution leads to a dramatic reduction in computational effort. A principal component representation of the phonon degrees of freedom allows to sample completely uncorrelated phonon configurations. The combination of these elements enables us to perform efficient simulations for a wide range of temperature, phonon frequency and electron-phonon coupling on clusters large enough to avoid finite-size effects. The algorithm is tested in one dimension and the data are compared with exact-diagonalization results and with existing work. Moreover, the ideas presented here can also be applied to the many-electron case. In the one-electron case considered here, the physics of the Holstein model can be described by a simple variational approach.Comment: 18 pages, 11 Figures, v2: one typo correcte

Polaron Effective Mass, Band Distortion, and Self-Trapping in the Holstein Molecular Crystal Model

We present polaron effective masses and selected polaron band structures of the Holstein molecular crystal model in 1-D as computed by the Global-Local variational method over a wide range of parameters. These results are augmented and supported by leading orders of both weak- and strong-coupling perturbation theory. The description of the polaron effective mass and polaron band distortion that emerges from this work is comprehensive, spanning weak, intermediate, and strong electron-phonon coupling, and non-adiabatic, weakly adiabatic, and strongly adiabatic regimes. Using the effective mass as the primary criterion, the self-trapping transition is precisely defined and located. Using related band-shape criteria at the Brillouin zone edge, the onset of band narrowing is also precisely defined and located. These two lines divide the polaron parameter space into three regimes of distinct polaron structure, essentially constituting a polaron phase diagram. Though the self-trapping transition is thusly shown to be a broad and smooth phenomenon at finite parameter values, consistency with notion of self-trapping as a critical phenomenon in the adiabatic limit is demonstrated. Generalizations to higher dimensions are considered, and resolutions of apparent conflicts with well-known expectations of adiabatic theory are suggested.Comment: 28 pages, 15 figure

Lattice dynamics effects on small polaron properties

This study details the conditions under which strong-coupling perturbation theory can be applied to the molecular crystal model, a fundamental theoretical tool for analysis of the polaron properties. I show that lattice dimensionality and intermolecular forces play a key role in imposing constraints on the applicability of the perturbative approach. The polaron effective mass has been computed in different regimes ranging from the fully antiadiabatic to the fully adiabatic. The polaron masses become essentially dimension independent for sufficiently strong intermolecular coupling strengths and converge to much lower values than those tradition-ally obtained in small-polaron theory. I find evidence for a self-trapping transition in a moderately adiabatic regime at an electron-phonon coupling value of .3. Our results point to a substantial independence of the self-trapping event on dimensionality.Comment: 8 pages, 5 figure