arXiv subjects

Philipp Maass

Publications and source records attributed to Philipp Maass.

77 records · Page 5Linked to original sources

arXiv2001

Hopping in the Glass Configuration Space: Subaging and Generalized Scaling Laws

Aging dynamics in glassy systems is investigated by considering the hopping motion in a rugged energy landscape whose deep minima are characterized by an exponential density of states. In particular we explore the behavior of a generic two-time correlation function Pi(t_w+t,t_w) below the glass transition temperature T_g when both the observation time t and the waiting time t_w become large. We show the occurrence of ordinary scaling behavior, which includes normal aging and subaging, and the possible simultaneous occurrence of generalized scaling behavior. Which situation occurs depends on the form of the effective transition rates between the low lying states. Employing a ``Partial Equilibrium Concept'', the exponents of the aging and the asymptotic form of the scaling functions are obtained both by simple scaling arguments and by analytical calculations. The predicted scaling properties compare well with Monte-Carlo simulations in dimensions d = 1-1000 and it is argued that a mean-field type treatment of the hopping motion fails to describe the aging dynamics in any dimension. Implications for more general situations involving different forms of transition rates and the occurrence of many scaling regimes in the t-t_w plane are pointed out.

cond-mat.stat-mech↗

arXiv2000

Soft Ellipsoid Model for Gaussian Polymer Chains

A soft ellipsoid model for Gaussian polymer chains is studied, following an idea proposed by Murat and Kremer [J. Chem. Phys. 108, 4340 (1998)]. In this model chain molecules are mapped onto ellipsoids with certain shapes, and to each shape a monomer density is assigned. In the first part of the work, the probabilities for the shapes and the associated monomer densities are studied in detail for Gaussian chains. Both quantities are expressed in terms of simple approximate formulae. The free energy of a system composed of many ellipsoids is given by an intramolecular part accounting for the internal degrees of freedom and an intermolecular part following from pair interactions between the monomer densities. Structural and kinetic properties of both homogeneous systems and binary mixtures are subsequently studied by Monte-Carlo simulations. It is shown that the model provides a powerful phenomenological approach for investigating polymeric systems on semi-macroscopic time and length scales.

cond-mat.soft↗

arXiv2000

Multiple scaling regimes in simple aging models

We investigate aging in glassy systems based on a simple model, where a point in configuration space performs thermally activated jumps between the minima of a random energy landscape. The model allows us to show explicitly a subaging behavior and multiple scaling regimes for the correlation function. Both the exponents characterizing the scaling of the different relaxation times with the waiting time and those characterizing the asymptotic decay of the scaling functions are obtained analytically by invoking a `partial equilibrium' concept.

cond-mat.stat-mech↗

arXiv1999

Exact Density Functionals in One Dimension

We propose a new and general method for deriving exact density functionals in one dimension for lattice gases with finite-range pairwise interactions. Corresponding continuum functionals are derived by applying a proper limiting procedure. The method is based on a generalised Markov property, which allows us to set up a rather transparent scheme that covers all previously known exact functionals for one-dimensional lattice gas or fluid systems. Implications for a systematic construction of approximate density functionals in higher dimensions are pointed out.

cond-mat.stat-mech↗

arXiv1999

Wall induced density profiles and density correlations in confined Takahashi lattice gases

We propose a general formalism to study the static properties of a system composed of particles with nearest neighbor interactions that are located on the sites of a one-dimensional lattice confined by walls (``confined Takahashi lattice gas''). Linear recursion relations for generalized partition functions are derived, from which thermodynamic quantities, as well as density distributions and correlation functions of arbitrary order can be determined in the presence of an external potential. Explicit results for density profiles and pair correlations near a wall are presented for various situations. As a special case of the Takahashi model we consider in particular the hard rod lattice gas, for which a system of nonlinear coupled difference equations for the occupation probabilities has been presented previously by Robledo and Varea. A solution of these equations is given in terms of the solution of a system of independent linear equations. Moreover, for zero external potential in the hard rod system we specify various central regions between the confining walls, where the occupation probabilities are constant and the correlation functions are translationally invariant in the canonical ensemble. In the grand canonical ensemble such regions do not exist.

cond-mat.stat-mech↗