arXiv subjects

A. Latz

Publications and source records attributed to A. Latz.

18 recordsLinked to original sources

arXiv2012

A three-dimensional self-learning kinetic Monte Carlo model: application to Ag(111)

The reliability of kinetic Monte Carlo (KMC) simulations depends on accurate transition rates. The self-learning KMC method (Trushin et al 2005 Phys. Rev. B 72 115401) combines the accuracy of rates calculated from a realistic potential with the efficiency of a rate catalog, using a pattern recognition scheme. This work expands the original two-dimensional method to three dimensions. The concomitant huge increase in the number of rate calculations on the fly needed can be avoided by setting up an initial database, containing exact activation energies calculated for processes gathered from a simpler KMC model. To provide two representative examples, the model is applied to the diffusion of Ag monolayer islands on Ag(111), and the homoepitaxial growth of Ag on Ag(111) at low temperatures.

cond-mat.mtrl-sci↗

arXiv2002

Light-Scattering by Longitudinal phonons in Molecular Supercooled Liquids I: Phenomenological Approach

We derive expressions for the intensity of the Brillouin polarized spectrum of a molecular liquid formed of axially symmetric molecules. These expressions take into account both the molecular dielectric anisotropy and the modulation of the local polarisability by density fluctuations. They also incorporate all the retardation effects which occur in such liquids. We show that the spectrum splits into a q-independent rotational contribution and q-dependent term, which reflects the propagation of longitudinal phonons. In the latter, the two light scattering mechanisms enter on an equal footing and generate three scattering channels. We study the influence of the two new channels and show that they may substantially modify the Brillouin line-shape when the relaxation time of the supercooled liquid and the phonon period are of the same order of magnitude.

cond-mat.stat-mech↗

arXiv2002

Light-Scattering by Longitudinal phonons in Supercooled Molecular Liquids II: Microscopic Derivation of the Phenomenological Equations

The constitutive equations for the orientational dynamics of a liquid formed of linear molecules are derived microscopically. The resulting generalised Langevin equations coincide with the phenomenological approach of Dreyfus et al. Formally exact expressions are given for the phenomenological coefficients and various constraints are shown to be consequences of this microscopic approach.

cond-mat.stat-mech↗

arXiv2001

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.

cond-mat.dis-nn↗

arXiv2001

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 $ϕ$ and aspect ratios $x_{0}$ we find an orientational peak in the center of mass spectra $χ_{000}^{''}(q,ω)$ and $ϕ_{000}^{''} (q,ω)$ about one decade below a high frequency peak. This orientational peak is the counterpart of a peak appearing in the quadrupolar spectra $χ_{22m}^{''}(q,ω)$ and $ϕ_{22m}^{''}(q,ω)$. The latter peak is almost insensitive on $ϕ$ 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.

cond-mat.dis-nn↗

arXiv2001

Universal properties of aging in structural glasse

A microscopic theory for equilibrium and non equilibrium relaxations in structural glasses is formulated. For all temperatures below the glass transition the dynamics can be asymptotically separated in a $β$ - relaxation regime, which connects a quasi equilibrium with the aging regime and the aging regime. In the $β$ - relaxation regime dynamic correlation are independent from spatial correlations. This is due to a self organized critical bifurcation scenario, which gives rise to one dynamic power law and a logarithmic law. It is shown that the fluctuation dissipation ratio in the aging regime is a universal property of the system independent from spatial scales.

cond-mat.dis-nn↗

arXiv2001

Microscopic dynamics of molecular liquids and glasses: Role of orientations and translation-rotation coupling

We investigate the dynamics of a fluid of dipolar hard spheres in its liquid and glassy phase, with emphasis on the microscopic time or frequency regime. This system shows rather different glass transition scenarios related to its rich equilibrium behavior which ranges from a simple hard sphere fluid to a long range ferroelectric orientational order. In the liquid phase close to the ideal glass transition line and in the glassy regime a medium range orientational order occurs leading to a softening of an orientational mode. To investigate the role of this mode we use the molecular mode-coupling equations to calculate the spectra $ϕ_{lm}^{\prime \prime}(q,ω)$ and $χ_{lm}''(q,ω)$. In the center of mass spectra $ ϕ_{00}''(q,ω)$ and $χ_{00}''(q,ω)$ we found besides a high frequency peak at $ω_{hf}$ a peak at $ω_{op}$, about one decade below $ω_{hf}$. $ω_{op}$ has almost no $q$-dependence and exhibits an ``isotope'' effect $ω_{op}\propto I^{-1/2}$, with $I$ the moment of inertia. We give evidence that the existence of this peak is related to the occurrence of the medium ranged orientational order. It is shown that some of these feature also exist for schematic mode coupling models.

cond-mat.dis-nn↗

arXiv2000

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 $ρ_{lm}(q)$ 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.

cond-mat.soft↗

arXiv2000

Molecular mode-coupling theory applied to a liquid of diatomic molecules

We study the molecular mode coupling theory for a liquid of diatomic molecules. The equations for the critical tensorial nonergodicity parameters ${\bf F}_{ll'}^m(q)$ and the critical amplitudes of the $β$ - relaxation ${\bf H}_{ll'}^m(q)$ are solved up to a cut off $l_{co}$ = 2 without any further approximations. Here $l,m$ are indices of spherical harmonics. Contrary to previous studies, where additional approximations were applied, we find in agreement with simulations, that all molecular degrees of freedom vitrify at a single temperature $T_c$. The theoretical results for the non ergodicity parameters and the critical amplitudes are compared with those from simulations. The qualitative agreement is good for all molecular degrees of freedom. To study the influence of the cut off on the non ergodicity parameter, we also calculate the non ergodicity parameters for an upper cut off $l_{co}=4$. In addition we also propose a new method for the calculation of the critical nonergodicity parameter

cond-mat.dis-nn↗

arXiv2000

Ideal glass transitions for hard ellipsoids

For hard ellipsoids of revolution we calculate the phase diagram for the idealized glass transition. Our equations cover the glass physics in the full phase space, for all packing fractions and all aspect ratios X$_0$. With increasing aspect ratio we find the idealized glass transition to become primarily be driven by orientational degrees of freedom. For needle or plate like systems the transition is strongly influenced by a precursor of a nematic instability. We obtain three types of glass transition lines. The first one ($ϕ_c^{(B)}$) corresponds to the conventional glass transition for spherical particles which is driven by the cage effect. At the second one ($ϕ_c^{(B')}$) which occurs for rather non-spherical particles a glass phase is formed which consists of domains. Within each domain there is a nematic order where the center of mass motion is quasi--ergodic, whereas the inter--domain orientations build an orientational glass. The third glass transition line ($ϕ_c^{(A)}$) occurs for nearly spherical ellipsoids where the orientational degrees of freedom with odd parity, e.g. 180$^o$ flips, freeze independently from the positions.

cond-mat.soft↗

arXiv2000

Light scattering spectra of supercooled molecular liquids

The light scattering spectra of molecular liquids are derived within a generalized hydrodynamics. The wave vector and scattering angle dependences are given in the most general case and the change of the spectral features from liquid to solidlike is discussed without phenomenological model assumptions for (general) dielectric systems without long-ranged order. Exact microscopic expressions are derived for the frequency-dependent transport kernels, generalized thermodynamic derivatives and the background spectra.

cond-mat.stat-mech↗

arXiv2000

The dynamics of the spherical p-spin model: from microscopic to asymptotics

We have numerically investigated the mean-field dynamics of the the $p$-spin interaction spin glass model with p=3 using an efficient method of integrating the dynamic equations. We find a new time scale associated with the onset of the breakdown of the fluctuation-dissipation theorem in the intermediate time regime. We also find that the off-equilibrium relaxation exhibits a sub-aging behavior in the intermediate times and crosses over to a simple aging in the asymptotic regime.

cond-mat.dis-nn↗

arXiv2000

Test of molecular mode coupling theory: A first resume

We report recent progress on the test of mode coupling theory for molecular liquids (MMCT) for molecules of arbitrary shape. The MMCT equations in the long time limit are solved for supercooled water including all molecular degrees of freedom. In contrast to our earlier treatment of water as a linear molecule, we find that the glass transition temperature $T_c$ is overestimated by the theory as was found in the case of simple liquids. The nonergodicity parameters are calculated from the "full" set of MMCT-equations truncated at $l_{co}=2$. These results are compared $(i)$ with the nonergodicity parameters from MMCT with $l_{co}=2$ in the "dipole" approximation $n=n'=0$ and the diagonalization approximation $n=n'=0$,$l=l'$ and $(ii)$ with the corresponding results from a MD-simulation. This work supports the possibility that a reduction to the most prominent correlators may constitute a valid approximation for solving the MMCT equations for rigid molecules.

cond-mat.soft↗

arXiv2000

Molecular Correlations in a Supercooled Liquid

We present static and dynamic properties of molecular correlation functions S_{lmn,l'm'n'}(q,t) in a simulated supercooled liquid of water molecules, as a preliminary effort in the direction of solving the molecular mode coupling theory (MMCT) equations for supercooled molecular liquids. The temperature and time dependence of various molecular correlation functions, calculated from 250 ns long molecular dynamics simulations, show the characteristic patterns predicted by MMCT and shed light on the driving mechanism responsible for the slowing down of the molecular dynamics. We also discuss the symmetry properties of the molecular correlation functions which can be predicted on the basis of the C_{2v}-symmetry of the molecule. The analysis of the MD--results for the static correlators S_{lmn,l'm'n'}(q) reveals that additional relationships between correlators with different signs of n and n' exist. We prove that for molecules with C_{rv}-symmetry this unexpected result becomes exact at least for high temperatures.

cond-mat.stat-mech↗

arXiv1999

Non equilibrium mode coupling theory for supercooled liquids and glasses

A formally exact set of equations is derived for the description of nonequilibrium phenomena in classical liquids and glasses. With the help of a non equilibrium projection operator formalism, the correlation functions and fluctuation propagators are expressed in terms of memory functions and time dependent collective frequencies. This formally exact set of equations is approximated by applying mode coupling approximations to the memory functions. The resulting set of equations for wavevector dependent correlation functions, fluctuation propagators and one-time structure factors $S_q(t)$ generalizes the well known mode coupling theory of the glass transition to situations far away from equilibrium.

cond-mat.dis-nn↗

arXiv1999

Molecular mode-coupling theory for supercooled liquids: Application to water

We present mode-coupling equations for the description of the slow dynamics observed in supercooled molecular liquids close to the glass transition. The mode-coupling theory (MCT) originally formulated to study the slow relaxation in simple atomic liquids, and then extended to the analysis of liquids composed by linear molecules, is here generalized to systems of arbitrarily shaped, rigid molecules. We compare the predictions of the theory for the $q$-vector dependence of the molecular nonergodicity parameters, calculated by solving numerically the molecular MCT equations in two different approximation schemes, with ``exact'' results calculated from a molecular dynamics simulation of supercooled water. The agreement between theory and simulation data supports the view that MCT succeeds in describing the dynamics of supercooled molecular liquids, even for network forming ones.

cond-mat.soft↗

arXiv1999

Fluids of hard ellipsoids: Phase diagram including a nematic instability from Percus-Yevick theory

An important aspect of molecular fluids is the relation between orientation and translation parts of the two-particle correlations. Especially the detailed knowledge of the influence of orientation correlations is needed to explain and calculate in detail the occurrence of a nematic phase. The simplest model system which shows both orientation and translation correlations is a system of hard ellipsoids. We investigate an isotropic fluid formed of hard ellipsoids with Percus-Yevick theory. Solving the Percus-Yevick equations self-consistently in the high density regime gives a clear criterion for a nematic instability. We calculate in detail the equilibrium phase diagram for a fluid of hard ellipsoids of revolution. Our results compare well with Monte Carlo Simulations and density functional theory.

cond-mat.soft↗

arXiv1997

Chaotic Properties of Dilute Two and Three Dimensional Random Lorentz Gases I: Equilibrium Systems

We compute the Lyapunov spectrum and the Kolmogorov-Sinai entropy for a moving particle placed in a dilute, random array of hard disk or hard sphere scatterers - i.e. the dilute Lorentz gas model. This is carried out in two ways: First we use simple kinetic theory arguments to compute the Lyapunov spectrum for both two and three dimensional systems. In order to provide a method that can easily be generalized to non-uniform systems we then use a method based upon extensions of the Lorentz-Boltzmann (LB) equation to include variables that characterize the chaotic behavior of the system. The extended LB equations depend upon the number of dimensions and on whether one is computing positive or negative Lyapunov exponents. In the latter case the extended LB equation is closely related to an "anti-Lorentz-Boltzmann equation" where the collision operator has the opposite sign from the ordinary LB equation. Finally we compare our results with computer simulations of Dellago and Posch and find very good agreement.

chao-dyn↗