On the theory of light scattering in molecular liquids

The theory of light scattering for a system of linear molecules with anisotropic polarizabilities is considered. As a starting point for our theory, we express the result of a scattering experiment in VV and VH symmetry as dynamic correlation functions of tensorial densities $\rho_{lm}(q)$ with $l=0$ and $l=2$. $l$, $m$ denote indices of spherical harmonics. To account for all observed hydrodynamic singularities, a generalization of the theory of Schilling and Scheidsteger \cite{schilling97} for these correlation functions is presented, which is capable to describe the light scattering experiments from the liquid regime to the glassy state. As a microscopic theory it fulfills all sum rules contrary to previous {\em phenomenological} theories. We emphasize the importance of the helicity index $m$ for the microscopic theory by showing, that only the existence of $m=1$ components lead to the well known Rytov dip in liquids and to the appearance of transversal sound waves in VH symmetry in the deeply supercooled liquid and the glass. Exact expressions for the phenomenological frequency dependent rotation translation coupling coefficients of previous theories are derived.Comment: 30 pages including 15 figures, submitted to EPJ B, revised version a detailed discussion on the depolarization ratio is added and the discussion on the hydrodynamic analysis is enlarge

Microscopic Dynamics of Hard Ellipsoids in their Liquid and Glassy Phase

To investigate the influence of orientational degrees of freedom onto the dynamics of molecular systems in its supercooled and glassy regime we have solved numerically the mode-coupling equations for hard ellipsoids of revolution. For a wide range of volume fractions $\phi$ and aspect ratios $x_{0}$ we find an orientational peak in the center of mass spectra $\chi_{000}^{''}(q,\omega)$ and $\phi_{000}^{''} (q,\omega)$ about one decade below a high frequency peak. This orientational peak is the counterpart of a peak appearing in the quadrupolar spectra $\chi_{22m}^{''}(q,\omega)$ and $\phi_{22m}^{''}(q,\omega)$. The latter peak is almost insensitive on $\phi$ for $x_{0}$ close to one, i.e. for weak steric hindrance, and broadens strongly with increasing $x_{0}$. Deep in the glass we find an additional peak between the orientational and the high frequency peak. We have evidence that this intermediate peak is the result of a coupling between modes with $l=0$ and $l=2$, due to the nondiagonality of the static correlators.Comment: 6 figures, 12 page

A Tableaux Calculus for Reducing Proof Size

A tableau calculus is proposed, based on a compressed representation of clauses, where literals sharing a similar shape may be merged. The inferences applied on these literals are fused when possible, which reduces the size of the proof. It is shown that the obtained proof procedure is sound, refutationally complete and allows to reduce the size of the tableau by an exponential factor. The approach is compatible with all usual refinements of tableaux.Comment: Technical Repor

Dynamical precursor of nematic order in a dense fluid of hard ellipsoids of revolution

We investigate hard ellipsoids of revolution in a parameter regime where no long range nematic order is present but already finite size domains are formed which show orientational order. Domain formation leads to a substantial slowing down of a collective rotational mode which separates well from the usual microscopic frequency regime. A dynamic coupling of this particular mode into all other modes provides a general mechanism which explains an excess peak in spectra of molecular fluids. Using molecular dynamics simulation on up to 4096 particles and on solving the molecular mode coupling equation we investigate dynamic properties of the peak and prove its orientational origin.Comment: RevTeX4 style, 7 figure

Pseudogap and photoemission spectra in the attractive Hubbard model

Angle-resolved photoemission spectra are calculated microscopically for the two-dimensional attractive Hubbard model. A system of self-consistent T-matrix equations are solved numerically in the real-time domain. The single-particle spectral function has a two-peak structure resulting from the presense of bound states. The spectral function is suppressed at the chemical potential, leading to a pseudogap-like behavior. At high temperatures and densities the pseudogap diminishes and finally disappears; these findings are similar to experimental observations for the cuprates.Comment: 5 pages, 4 figures, published versio

Diffusion and localization in quantum random resistor networks

The theoretical description of transport in a wide class of novel materials is based upon quantum percolation and related random resistor network (RRN) models. We examine the localization properties of electronic states of diverse two-dimensional quantum percolation models using exact diagonalization in combination with kernel polynomial expansion techniques. Employing the local distribution approach we determine the arithmetically and geometrically averaged densities of states in order to distinguish extended, current carrying states from localized ones. To get further insight into the nature of eigenstates of RRN models we analyze the probability distribution of the local density of states in the whole parameter and energy range. For a recently proposed RRN representation of graphene sheets we discuss leakage effects.Comment: 6 pages, 4 figure