arXiv subjects

Thomas Franosch

Publications and source records attributed to Thomas Franosch.

100 records · Page 6Linked to original sources

arXiv2008

Exclusion Processes with Internal States

We introduce driven exclusion processes with internal states that serve as generic transport models in various contexts, ranging from molecular or vehicular traffic on parallel lanes to spintronics. The ensuing non-equilibrium steady states are controllable by boundary as well as bulk rates. A striking polarization phenomenon accompanied by domain wall motion and delocalization is discovered within a mesoscopic scaling. We quantify this observation within an analytic description providing exact phase diagrams. Our results are confirmed by stochastic simulations.

cond-mat.stat-mech↗

arXiv2008

Domain wall delocalization, dynamics and fluctuations in an exclusion process with two internal states

We investigate the delocalization transition appearing in an exclusion process with two internal states resp. on two parallel lanes. At the transition, delocalized domain walls form in the density profiles of both internal states, in agreement with a mean-field approach. Remarkably, the topology of the system's phase diagram allows for the delocalization of a (localized) domain wall when approaching the transition. We quantify the domain wall's delocalization close to the transition by analytic results obtained within the framework of the domain wall picture. Power-law dependences of the domain wall width on the distance to the delocalization transition as well as on the system size are uncovered, they agree with numerical results.

cond-mat.stat-mech↗

arXiv2007

Critical dynamics of ballistic and Brownian particles in a heterogeneous environment

The dynamic properties of a classical tracer particle in a random, disordered medium are investigated close to the localization transition. For Lorentz models obeying Newtonian and diffusive motion at the microscale, we have performed large-scale computer simulations, demonstrating that universality holds at long times in the immediate vicinity of the transition. The scaling function describing the crossover from anomalous transport to diffusive motion is found to vary extremely slowly and spans at least 5 decades in time. To extract the scaling function, one has to allow for the leading universal corrections to scaling. Our findings suggest that apparent power laws with varying exponents generically occur and dominate experimentally accessible time windows as soon as the heterogeneities cover a decade in length scale. We extract the divergent length scales, quantify the spatial heterogeneities in terms of the non-Gaussian parameter, and corroborate our results by a thorough finite-size analysis.

cond-mat.soft↗

arXiv2007

Traffic jams induced by rare switching events in two-lane transport

We investigate a model for driven exclusion processes where internal states are assigned to the particles. The latter account for diverse situations, ranging from spin states in spintronics to parallel lanes in intracellular or vehicular traffic. Introducing a coupling between the internal states by allowing particles to switch from one to another induces an intriguing polarization phenomenon. In a mesoscopic scaling, a rich stationary regime for the density profiles is discovered, with localized domain walls in the density profile of one of the internal states being feasible. We derive the shape of the density profiles as well as resulting phase diagrams analytically by a mean-field approximation and a continuum limit. Continuous as well as discontinuous lines of phase transition emerge, their intersections induce multicritical behavior.

cond-mat.stat-mech↗

arXiv2007

Crossover in the Slow Decay of Dynamic Correlations in the Lorentz Model

The long-time behavior of transport coefficients in a model for spatially heterogeneous media in two and three dimensions is investigated by Molecular Dynamics simulations. The behavior of the velocity auto-correlation function is rationalized in terms of a competition of the critical relaxation due to the underlying percolation transition and the hydrodynamic power-law anomalies. In two dimensions and in the absence of a diffusive mode, another power law anomaly due to trapping is found with an exponent -3 instead of -2. Further, the logarithmic divergence of the Burnett coefficient is corroborated in the dilute limit; at finite density, however, it is dominated by stronger divergences.

cond-mat.soft↗

arXiv2006

Generic principles of active transport

Nonequilibrium collective motion is ubiquitous in nature and often results in a rich collection of intringuing phenomena, such as the formation of shocks or patterns, subdiffusive kinetics, traffic jams, and nonequilibrium phase transitions. These stochastic many-body features characterize transport processes in biology, soft condensed matter and, possibly, also in nanoscience. Inspired by these applications, a wide class of lattice-gas models has recently been considered. Building on the celebrated {\it totally asymmetric simple exclusion process} (TASEP) and a generalization accounting for the exchanges with a reservoir, we discuss the qualitative and quantitative nonequilibrium properties of these model systems. We specifically analyze the case of a dimeric lattice gas, the transport in the presence of pointwise disorder and along coupled tracks.

cond-mat.stat-mech↗

arXiv2006

Spin models for orientational ordering of colloidal molecular crystals

Two-dimensional colloidal suspensions exposed to periodic external fields exhibit a variety of molecular crystalline phases. There two or more colloids assemble at lattice sites of potential minima to build new structural entities, referred to as molecules. Using the strength of the potential and the filling fraction as control parameter, phase transition to unconventional orientationally ordered states can be induced. We introduce an approach that focuses at the discrete set of orientational states relevant for the phase ordering. The orientationally ordered states are mapped to classical spin systems. We construct effective hamiltonians for dimeric and trimeric molecules on triangular lattices suitable for a statistical mechanics discussion. A mean-field analysis produces a rich phase behavior which is substantiated by Monte Carlo simulations.

cond-mat.soft↗

arXiv2006

Localization Transition of the Three-Dimensional Lorentz Model and Continuum Percolation

The localization transition and the critical properties of the Lorentz model in three dimensions are investigated by computer simulations. We give a coherent and quantitative explanation of the dynamics in terms of continuum percolation theory, an excellent matching of both the critical density and exponents is obtained. Upon exploiting a dynamic scaling Ansatz employing two divergent length scales we find data collapse for the mean-square displacements and identify the leading-order corrections to scaling. The non-Gaussian parameter is predicted to diverge at the transition.

cond-mat.soft↗

arXiv2005

Renewal processes and fluctuation analysis of molecular motor stepping

We model the dynamics of a processive or rotary molecular motor using a renewal processes, in line with the work initiated by Svoboda, Mitra and Block. We apply a functional technique to compute different types of multiple-time correlation functions of the renewal process, which have applications to bead-assay experiments performed both with processive molecular motors, such as myosin V and kinesin, and rotary motors, such as F1-ATPase.

cond-mat.stat-mech↗

arXiv2004

Rotational Dynamics and Light-scattering in Super-cooled Molecular Liquids

Constitutive equations for the long-wavelength behaviour of the orientational dynamics of a super-cooled liquid are derived using a projection-operator technique and resulting expressions for light-scattering spectra are formulated. We thus extend recent studies for axially symmetric molecules to the general case of arbitrarily shaped rigid molecules. The second part of the discussion considers hydrodynamic energy-fluctuations and thus arrives at expressions for light-scattering spectra which also include a Rayleigh-line. The role of the memory-kernels in the theory is treated in detail. In particular, the derivation of a theory that formally resembles earlier approaches to the problem is presented using a mathematically rigorous description of the Laplace-transforms of correlation-functions.

cond-mat.soft↗