Geodesic convexity of the relative entropy in reversible Markov chains

We consider finite-dimensional, time-continuous Markov chains satisfying the detailed balance condition as gradient systems with the relative entropy E as driving functional. The Riemannian metric is defined via its inverse matrix called the Onsager matrix K. We provide methods for establishing geodesic λ-convexity of the entropy and treat several examples including some discretizations of one-dimensional Fokker–Planck equations.     

Progress in metric-affine gauge theories of gravity with local scale invariance

Einstein's general relativity theory describes very well the gravitational phenomena in themacroscopic world. In themicroscopic domain of elementary particles, however, it does not exhibit gauge invariance or approximate Bjorken type scaling, properties which are believed to be indispensible for arenormalizable field theory. We argue that thelocal extension of space-time symmetries, such as of Lorentz and scale invariance, provides the clue for improvement. Eventually, this leads to aGL(4, R)-gauge approach to gravity in which the metric and the affine connection acquire the status ofindependent fields. The Yang-Mills type field equations, the Noether identities, and conformal models of gravity are discussed within this framework. After symmetry breaking, Einstein's GR surfaces as an effective low-energy theory.Based on a plenary talk given by one of us (EWM) at the 53rd annual meeting of the Deutsche Physikalische Gesellschaft in Bonn on March 14, 1989.Supported by the German-Israeli Foundation for Scientific Research and Development (GIF), Jerusalem and Munich.Supported by the Deutsche Forschungsgemeinschaft (DFG), Bonn, project He 528/12-1.Supported in part by DOE Grant DE-FG05-85-ER40200.     

The photoinduced isomerization and its implication in the photo-dynamical processes in two simple Schiff bases isolated in solid argon

Two Schiff bases: 2-(1-(methylimino)methyl)-phenol (SMA) and its chlorosubstituted derivative 2-(1-(methylimino)methyl)-6-chlorophenol (SMAC), and SMA complexes with water were studied by infrared matrix isolation spectroscopy and DFT/B3LYP/6-311G++(2d,2p) quantum chemical calculations. SMA and SMAC bases trapped in an argon matrix from the vapor above the liquid and solid samples have the most stable enol conformation with intramolecular O-H···N bonding. Irradiation (λ > 320 nm) leads in both bases to a rotational isomerization reaction in which the scission of the O-H···N bond occurs and the C(H)NCH(3) and OH groups are turned by 180° around the C-C and C-O bonds, respectively. In SMAC a competitive photoreaction channel yields the trans-keto tautomer. The identification of the two SMAC photoproducts evidences that in the excited enol form of this compound two processes compete with each other: the rotational isomerization and intramolecular proton transfer (ESIPT). In the argon matrices doped with SMA and H(2)O the SMA-water complexes were identified and characterized spectroscopically. Interaction of SMA with one or two water molecules does not affect the photochemistry of SMA.     

Photochemical and Photobiotogical Studies with Acridine and Phenanthridine Hydroperoxides in Cell-free DNA

Abstract— The acridine and phenanthridine hydroperoxides 3 and 7 were synthesized as photochemical hydroxyl radical sources for oxidative DNA damage studies. The generation of hydroxyl radicals upon UVA irradiation (Λ. = 350 nm) was verified by trapping experiments with 5,5-di-methyl-1-pyrroline N -oxide and benzene. The enzymatic assays of the damage in cell-free DNA from bacteriophage PM2 caused by the acridine and phenanthridine hydroperoxides 3 and 7 under near-UVA irradiation revealed a wide range of DNA modifications. Particularly, extensive single-strand break formation and DNA base modifications sensitive to formamidopyrimidine DNA glycosylase (Fpg protein) were observed. In the photooxida-tion of calf thymus DNA, up to 0.69±0.03% 8-oxo-7,8-dihydroguanine was formed by the hydroperoxides 3 and 7 on irradiation, whose yield was reduced up to 40% in the presence of the hydroxyl radical scavengers mannitol and fert-butanol. The acridine and phenanthridine hydroperoxides 3 and 7 also induce DNA damage through the type I photooxidation process, for which photoinduced electron transfer from 2'-deoxyguanosine to the singlet states of 3 and 7 was estimated by the Rehm-Weller equation to possess a negative Gibb's free energy of cα -5 kcal/ mol. Control experiments with the sensitizers acridine 1 and the acridine alcohol 4 in calf thymus and PM2 DNA confirmed the photosensitizing propensity of the UVA-ab-sorbing chromophores. The present study emphasizes that for the development of selective and efficient photochemical hydroxyl radical sources, chromophores with low photosensitizing ability must be chosen to avoid type I and type II photooxidation processes.     

Einstein-Weyl Gravity from a Topological {{\rm SL}(5, \mathbb{R})} Gauge Invariant Action

A topological field theory of gravity in four-dimension is proposed which is finite after quantization. Since such ‘minimal’ BF type models for the high energy limit are physically not quite realistic, a tiny symmetry breaking is needed to recover standard Einsteinian gravity for the macroscopic metrical background.     

The complexes between CH3OH and CF4. Infrared matrix isolation and theoretical studies

The complex formed between methanol and tetrafluoromethane has been identified in argon and neon matrixes by help of FTIR spectroscopy. Three fundamentals (nu(OH), nu(FCF), and nu(CO)) were observed for the complex isolated in the two matrixes, and the OH stretch was red shifted in a neon matrix and blue shifted in an argon matrix with respect to the corresponding vibration of the methanol monomer. The theoretical studies of the structure and spectral characteristics of the complexes formed between CH(3)OH and CF(4) were carried out at the MP2 level of theory with the 6-311+G(2df,2pd) basis set. The calculations resulted in three stationary points from which two (I-1, I-2) corresponded to structures involving the O-H...F hydrogen bond and the third one (I-3) to the non-hydrogen-bonded structure. The topological analysis of the distribution of the charge density (AIM theory) confirmed the existence of the hydrogen bond in I-1, I-2 complexes and indicated weak interaction between the oxygen atom of CH(3)OH and three fluorine atoms of CF(4) in the I-3 complex. The comparison of the experimental and theoretical data suggests that in the matrixes only the non-hydrogen-bonded complex I-3 is trapped. The blue/red shift of the complex OH stretching vibration with respect to the corresponding vibration of CH(3)OH in argon/neon matrixes is explained by the different sensitivity of the complex and monomer vibrations to matrix material. The ab initio calculations performed for the ternary CH(3)OH-CF(4)-Ar systems indicated a negligible effect of an argon atom on the binary complex frequencies.     

Accurate vibrational-rotational partition functions and standard-state free energy values for H2O2 from Monte Carlo path-integral calculations

Accurate quantum mechanical partition functions and absolute free energies of H(2)O(2) are determined using a realistic potential energy surface [J. Koput, S. Carter, and N. C. Handy, J. Phys. Chem. A 102, 6325 (1998)] for temperatures ranging from 300 to 2,400 K by using Monte Carlo path integral calculations with new, efficient polyatomic importance sampling methods. The path centroids are sampled in Jacobi coordinates via a set of independent ziggurat schemes. The calculations employed enhanced-same-path extrapolation of trapezoidal Trotter Fourier path integrals, and the paths were constructed using fast Fourier sine transforms. Importance sampling was also used in Fourier coefficient space, and adaptively optimized stratified sampling was used in configuration space. The free energy values obtained from the path-integral calculations are compared to separable-mode approximations, to the Pitzer-Gwinn approximation, and to values in thermodynamic tables. Our calculations support the recently proposed revisions to the JANAF tables.     

Two dimensional interacting electrons on a torus in a strong magnetic field: Symmetry properties and the effect of disorder

We discuss the symmetry properties of two dimensional interacting electrons on a torus in a strong magnetic field. Invariance under magnetic translations of the center of mass leads to a decomposition of the Hilbert space into a direct sum of subspaces. The degenerate ground states are out of one of these subspaces. This is used to calculate the energy splitting of the ground state energy due to a disordered background potential. The energy splitting is small and vanishes in thermodynamic limit if the denominator of the filling factor is odd and small. Numerical calculations confirm our results.