Polaron formation and hopping conductivity in the Holstein-Hubbard model

On the basis of the Holstein-Hubbard model the formation of polarons at finite densities is investigated by means of a variational approach appropriate for describing squeezing and correlation effects. An effective Hubbard model for the polarons is derived, where the correlations are treated within the slave-boson saddlepoint approximation. For low enough phonon frequencies, with increasing coupling an abrupt self-trapping transition from light to heavy polarons is found. With increasing density the squeezing effect increases, and the transition is shifted to higher couplings. In the case of an effective Coulomb repulsion, the self-trapping transition is shifted to lower couplings with increasing Hubbard interaction, and the effective polaron mass below the transition is enhanced. In the heavy polaron regime, the frequency-dependent polaron hopping conductivity is calculated. There occur qualitative finite-density and correlation effects on the zero-temperature absorption spectrum which are discussed with respect to their possible relevance to the midinfrared absorption in high-T _c superconductors.     

Non-Planar Structures of Sterically Overcrowded Trialkylamines

Several amines with three bulky alkyl groups at the nitrogen atom, which exceed the steric crowding of triisopropylamine significantly, were synthesized, mainly by treating N-chlorodialkylamines with Grignard reagents. In six cases, namely tert-butyldiisopropylamine, 1-adamantyl-tert-butylisopropylamine, di-1-adamantylamines with an additional N-cyclohexyl or N-exo-2-norbonyl substituent, as well as 2,2,6,6-tetramethylpiperidine derivatives with N-cyclohexyl or N-neopentyl groups, appropriate single crystals were generated that enabled X-ray diffraction studies and analysis of the molecular structures. The four noncyclic amines adopt triskele-like conformations, and the sum of the three C−N−C angles is always in the range of 351.1° to 352.4°. Consequently, these amines proved to be structurally significantly flatter than trialkylamines without steric congestion, which is also signalized by the smaller heights of the NC₃ pyramids (0.241–0.259 Å). There is no clear correlation between the heights of these pyramids and the degree of the steric crowding in the new amines, presumably because steric repulsion is partly compensated by dispersion interaction. In the cases of the two heterocyclic amines, the steric stress is smaller, and the molecular structures include quite different conformations. Quantum chemical calculations led to precise gas-phase structures of the sterically overcrowded trialkylamines exhibiting heights of the NC₃ pyramids and preferred molecular conformers which are similar to those resulting from the X-ray studies.     

Towards a quantitative kinetic theory of polar active matter

A recent kinetic approach for Vicsek-like models of active particles is reviewed. The theory is based on an exact Chapman- Kolmogorov equation in phase space. It can handle discrete time dynamics and “exotic” multi-particle interactions. A nonlocal mean-field theory for the one-particle distribution function is obtained by assuming molecular chaos. The Boltzmann approach of Bertin, et al., Phys. Rev. E 74, 022101 (2006) and J. Phys. A 42, 445001 (2009), is critically assessed and compared to the current approach. In Boltzmann theory, a collision starts when two particles enter each others action spheres and is finished when their distance exceeds the interaction radius. The average duration of such a collision, τ₀, is measured for the Vicsek model with continuous time-evolution. If the noise is chosen to be close to the flocking threshold, the average time between collisions is found to be roughly equal to τ₀ at low densities. Thus, the continuous-time Vicsek-model near the flocking threshold cannot be accurately described by a Boltzmann equation, even at very small density because collisions take so long that typically other particles join in, rendering Boltzmann’s binary collision assumption invalid. Hydrodynamic equations for the phase space approach are derived by means of a Chapman-Enskog expansion. The equations are compared to the Toner-Tu theory of polar active matter. New terms, absent in the Toner-Tu theory, are highlighted. Convergence problems of Chapman-Enskog and similar gradient expansions are discussed.     

Spin excitations and thermodynamics of the antiferromagnetic Heisenberg model on the layered honeycomb lattice

We present a spin-rotation-invariant Green-function theory for the dynamic spin susceptibility in the spin-1/2 antiferromagnetic Heisenberg model on a stacked honeycomb lattice. Employing a generalized mean-field approximation for arbitrary temperatures, the thermodynamic quantities (two-spin correlation functions, internal energy, magnetic susceptibility, staggered magnetization, Néel temperature, correlation length) and the spin-excitation spectrum are calculated by solving a coupled system of self-consistency equations for the correlation functions. The temperature dependence of the magnetic (uniform static) susceptibility is ascribed to antiferromagnetic short-range order. The Néel temperature is calculated for arbitrary interlayer couplings. Our results are in a good agreement with numerical computations for finite clusters and with available experimental data on the β-Cu₂V₂O₂ compound.     

Sodium borohydride mediated reduction of N-Boc protected purines and applications in the synthesis of 7-alkyladenines and tetrahydro[1,4]diazepino-[1,2,3-gh]purines

Electron deficient purines can be reduced to 7,8-dihydropurines when treated with cheap and easy-to-handle sodium borohydride in methanol. The dihydropurine formed by reduction of tris-Boc-protected adenine is a useful intermediate in efficient syntheses of 7-alkyladenines and tetrahydro[1,4]diazepino[1,2,3-gh]purines.     

Zur elektrolytischen Bestimmung der Metalle

Ohne Zusammenfassung     

Discussion on Peshkov et al., “Boltzmann-Ginzburg-Landau approach for continuous descriptions of generic Vicsek-like models”

A discussion on the contribution of Peshkov, Bertin, Ginelli and Chaté [1] in this special issue.     

Reply to comment on “Towards a quantitative kinetic theory of polar active matter” by Bertin et al.

A reply to the comment of Bertin, Chaté, Ginelli, Grégoire, Léonard and Peshkov [1] in this special issue.