arXiv subjects

Philipp Maass

Publications and source records attributed to Philipp Maass.

At least 19 recordsLinked to original sources

arXiv2026

Hidden periodicities allow the prediction of locked particle motions on quasicrystalline surfaces

Motion of particles across quasicrystalline surfaces exhibits peculiar features due to the presence of long-range order without translational periodicity. Under time-periodic forcing, this motion can become locked in directions thatn deviate strongly from the mean driving direction. We show that for surface potentials with a quasicrystalline pattern of minima generated by a superposition of plane waves, particle trajectories are nonperiodic, yet their mean direction and speed are determined by hidden periodic potentials. The lattice vectors of these underlying potentials define characteristic velocities that dictate both directional and speed locking. The particle motion does not synchronize with the driving, and it is possible for the mean speed to remain nonlocked even in directionally locked states. These findings are demonstrated using a model directly amenable to experimental realization.

cond-mat.stat-mech↗

arXiv2026

Theory for the mixed alkali effect in glasses

The mixed alkali or mixed mobile ion effect in glasses manifests itself by strong nonlinear variations of ionic transport properties upon mixing of different types of mobile ions. We develop a theory for this effect based on thermally activated hopping transport in disordered site energy landscapes that consistently incorporates the statistical-mechanical and kinetic aspects of a mobile ion mixture. This includes a consideration of the joint probability density of site energy states, generalized Fermi distributions for mean site occupations, and cross-terms in the current response described by nondiagonal Onsager coefficients. The theory shows that a mixed alkali effect can arise even when the two ion species share identical site energy distributions. It suffices that sites have distinct energies when occupied by ions of different type. Taking into account that a mismatch energy is needed for ions of one type to occupy sites adapted to the other type, the mixed alkali effect becomes stronger. Spatial correlations between site energies are needed for the mobility of the majority ion to decrease stronger than exponential upon replacement by the minority ion. The theory agrees well with kinetic Monte Carlo simulations. Application to mixed alkali phosphate glasses yields good agreement with measured conductivity activation energies.

cond-mat.mtrl-sci↗

arXiv2026

Universal time-temperature scaling of conductivities in random site energy and associated random barrier model

Universal time-temperature scaling of conductivity spectra in disordered solids has been explained by thermally activated hopping of noninteracting particles over random energy barriers. An open problem is whether the random barrier model accounts for site energy disorder in real materials. Through mapping many-particle hopping in a disordered site energy landscape to that of independent particles in a barrier landscape, we show that time-temperature scaling is correctly described by the associated barrier model in the low temperature limit. However, the site energy model displays good scaling behavior at substantially higher temperatures than the barrier model, in agreement with experimental observations. Extending the mapping to different types of mobile charge carriers allows us to understand why time-temperature superposition can be absent in mixed alkali glasses.

cond-mat.dis-nn↗

arXiv2025

Current reversals in driven lattice gases and Brownian motion

Particle currents flowing against an external driving are a fascinating phenomenon in both single-particle and interacting many-particle systems. Underlying physical mechanisms of such current reversals are not fully understood yet. Predicting their appearance is difficult, in particular for interaction-induced ones that emerge upon changes of the particle density. We here derive conditions on external time-dependent drivings, under which current reversals occur in lattice gases with arbitrary pair interactions. Our derivation is based on particle-hole symmetry and shows that current reversals must emerge if the time-varying driving potential changes sign after a translation in time and/or space. Our treatment includes nonstationary dynamics and time-dependent spatially averaged currents in nonequilibrium steady states. It gives insight also into possible occurrences of current reversals in continuous-space dynamics, which we demonstrate for hardcore interacting particles driven across a periodic potential by a traveling wave.

cond-mat.stat-mech↗

arXiv2025

Nonequilibrium phase transition in single-file transport at high crowding

Driven particle transport in crowded and confining environments is fundamental to diverse phenomena across physics, chemistry, and biology. A main objective in studying such systems is to identify novel emergent states and phases of collective dynamics. Here, we report on a nonequilibrium phase transition occurring in periodic structures at high particle densities. This transition separates a weak-current phase of thermally activated transport from a high-current phase of solitary wave propagation. It is reflected also in a change of universality classes characterizing correlations of particle current fluctuations. Our findings demonstrate that sudden changes to high current states can occur when increasing particle densities beyond critical values.

cond-mat.stat-mech↗

arXiv2025

Cluster sizes, particle displacements and currents in transport mediated by solitary cluster waves

In overdamped particle motion across periodic landscapes, solitary cluster waves can occur at high particle densities and lead to particle transport even in the absence of thermal noise. Here we show that for driven motion under a constant drag, the sum of all particle displacements per soliton equals one wavelength of the periodic potential. This unit displacement law is used to determine particle currents mediated by the solitons. We furthermore derive properties of clusters involved in the wave propagation as well as relations between cluster sizes and soliton numbers.

cond-mat.stat-mech↗

arXiv2025

Engineering tunable fractional Shapiro steps in colloidal transport

Shapiro steps are quantized plateaus in the velocity-force or velocity-torque curve of a driven system, when its speed remains constant despite an increase in the driving force. For microscopic particles driven across a sinusoidal potential, integer Shapiro steps have been observed. By driving a single colloidal particle across a time-modulated, non-sinusoidal periodic optical landscape, we here demonstrate that fractional Shapiro steps emerge in addition to integer ones. Measuring the particle position via individual particle tracking, we reveal the underlying microscopic mechanisms that produce integer and fractional steps and demonstrate how these steps can be controlled by tuning the shape and driving protocol of the optical potential. The flexibility offered by optical engineering allows us to generate wide ranges of potential shapes and to study, at the single-particle level, synchronization behavior in driven soft condensed matter systems.

cond-mat.soft↗

arXiv2025

Phase locking and fractional Shapiro steps in collective dynamics of microparticles

In driven nonlinear systems, phase locking is an intriguing effect leading to robust stationary states that are stable over extended ranges of control parameters. Recent experiments allow for exploring microscopic mechanisms underlying such phenomena in collective dynamics of micro- and nanoparticles. Here we show that phase-locked dynamics of hardcore-interacting microparticles in a densely populated periodic potential under time-periodic driving arises from running solitary cluster waves. We explain how values of phase-locked currents are related to soliton velocities and why collective particle dynamics synchronize with the driving for certain particle diameters only. Our analysis is based on an effective potential for the solitary wave propagation and a unit displacement law, saying that the total average shift of all particle positions per soliton period equals one wavelength of the periodic potential.

cond-mat.stat-mech↗

arXiv2025

Correlations of density and current fluctuations in single-file motion of hard spheres and in driven lattice gas with nearest-neighbor interaction

We analyze correlations between density fluctuations and between current fluctuations in a one-dimensional driven lattice gas with repulsive nearest-neighbor interaction and in single-file Brownian motion of hard spheres dragged across a cosine potential with constant force. By extensive kinetic Monte Carlo and Brownian dynamics simulations we show that density and current correlation functions in nonequilibrium steady states follow the scaling behavior of the Kardar-Parisi-Zhang (KPZ) universality class. In a coordinate frame comoving with the collective particle velocity, the current correlation function decays as $\sim -t^{-4/3}$ with time $t$. Density fluctuations spread superdiffusively as $\sim t^{2/3}$ at long times and their spatio-temporal behavior is well described by the KPZ scaling function. In the absence of the cosine potential, the correlation functions in the system of dragged hard spheres show scaling behavior according to the Edwards-Wilkinson universality class. In the coordinate frame comoving with the mean particle velocity, they behave as in equilibrium, with current correlations decaying as $\sim -t^{-3/2}$ and density fluctuations spreading diffusively as $\sim t^{1/2}$.

cond-mat.stat-mech↗

arXiv2024

Distributions and correlation properties of offshore wind speeds and wind speed increments

We determine distributions and correlation properties of offshore wind speeds and wind speed increments by analyzing wind data sampled with a resolution of one second for 20 months at different heights above sea level in the North Sea. Distributions of horizontal wind speeds can be fitted to Weibull distributions with shape and scale parameters varying weakly with the vertical height separation. Kullback-Leibler divergences between distributions at different heights change with the squared logarithm of the height ratio. Cross-correlations between time derivatives of wind speeds are long-term anticorrelated, and the even parts of their correlation functions satisfy sum rules. Distributions of horizontal wind speed increments change from a tent-like shape to a Gaussian with rising increment lag. A surprising peak occurs in the left tail of the increment distributions for lags in a range $10-200\,{\rm km}$ after applying the Taylor's hypothesis locally to transform time lags into distances. The peak is decisive in order to obtain an expected and observed linear scaling of third-order structure functions with distance. This suggests that it is an intrinsic feature of atmospheric turbulence.

physics.ao-ph↗

arXiv2024

Fast Brownian cluster dynamics

We present an efficient method to perform overdamped Brownian dynamics simulations in external force fields and for particle interactions that include a hardcore part. The method applies to particle motion in one dimension, where it is possible to update particle positions by repositioning particle clusters as a whole. These clusters consist of several particles in contact. They form because particle collisions are treated as completely inelastic rather than elastic ones. Updating of cluster positions in time steps is carried out by cluster fragmentation and merging procedures. The presented method is particularly powerful at high collision rates in densely crowded systems, where collective movements of particle assemblies is governing the dynamics. As an application, we simulate the single-file diffusion of sticky hard spheres in a periodic potential.

cond-mat.stat-mech↗

arXiv2024

Solitary cluster waves in periodic potentials: Formation, propagation, and soliton-mediated particle transport

Transport processes in crowded periodic structures are often mediated by cooperative movements of particles forming clusters. Recent theoretical and experimental studies of driven Brownian motion of hard spheres showed that cluster-mediated transport in one-dimensional periodic potentials can proceed in form of solitary waves. We here give a comprehensive description of these solitons. Fundamental for our analysis is a static presoliton state, which is formed by a periodic arrangement of basic stable clusters. Their size follows from a geometric principle of minimum free space. Adding one particle to the presoliton state gives rise to solitons. We derive the minimal number of particles needed for soliton formation, number of solitons at larger particle numbers, soliton velocities and soliton-mediated particle currents. Incomplete relaxations of the basic clusters are responsible for an effective repulsive soliton-soliton interaction seen in measurements. A dynamical phase transition is predicted to occur in current-density relations at low temperatures. Our results provide a theoretical basis for describing experiments on cluster-mediated particle transport in periodic potentials.

cond-mat.stat-mech↗

arXiv2023

Weak pinning and long-range anticorrelated motion of phase boundaries in driven diffusive systems

We show that domain walls separating coexisting extremal current phases in driven diffusive systems exhibit complex stochastic dynamics, with a subdiffusive temporal growth of position fluctuations due to long-range anticorrelated current fluctuations and a weak pinning at long times. This weak pinning manifests itself in a saturated width of the domain wall position fluctuations that increases sublinearly with the system size. As a function of time $t$ and system size $L$, the width $w(t,L)$ exhibits a scaling behavior $w(t,L)=L^{3/4}f(t/L^{9/4})$, with $f(u)$ constant for $u\gg1$ and $f(u)\sim u^{1/3}$ for $u\ll1$. An Orstein-Uhlenbeck process with long-range anticorrelated noise is shown to capture this scaling behavior. Results for the drift coefficient of the domain wall motion point to memory effects in its dynamics.

cond-mat.stat-mech↗

arXiv2023

Single-file transport of binary hard-sphere mixtures through periodic potentials

Single-file transport occurs in various scientific fields, including diffusion through nanopores, nanofluidic devices, and cellular processes. We here investigate the impact of polydispersity on particle currents for single-file Brownian motion of hard spheres, when they are driven through periodic potentials by a constant drag force. Through theoretical analysis and extensive Brownian dynamics simulations, we unveil the behavior of particle currents for random binary mixtures. The particle currents show a recurring pattern in dependence of the hard-sphere diameters and mixing ratio. We explain this recurrent behavior by showing that a basic unit cell exists in the space of the two hard-sphere diameters. Once the behavior of an observable inside the unit cell is determined, it can be inferred for any diameter. The overall variation of particle currents with the mixing ratio and hard-sphere diameters is reflected by their variation in the limit where the system is fully covered by hard spheres. In this limit, the currents can be predicted analytically. Our analysis explains the occurrence of pronounced maxima and minima of the currents by changes of an effective potential barrier for the center-of-mass motion.

cond-mat.stat-mech↗

arXiv2023

Scaling laws for single-file diffusion of adhesive particles

Single-file diffusion refers to the Brownian motion in narrow channels where particles cannot pass each other. In such processes, the diffusion of a tagged particle is typically normal at short times and becomes subdiffusive at long times. For hard-sphere interparticle interaction, the time-dependent mean squared displacement of a tracer is well understood. Here we develop a scaling theory for adhesive particles. It provides a full description of the time-dependent diffusive behavior with a scaling function that depends on an effective strength of adhesive interaction. Particle clustering induced by the adhesive interaction slows down the diffusion at short times, while it enhances subdiffusion at long times. The enhancement effect can be quantified in measurements irrespective of how tagged particles are injected into the system. Combined effects of pore structure and particle adhesiveness should speed up translocation of molecules through narrow pores.

cond-mat.stat-mech↗

arXiv2022

Brownian dynamics simulations of hard rods in external fields and with contact interactions

We propose a simulation method for Brownian dynamics of hard rods in one dimension for arbitrary continuous external force fields. It is an event-driven procedure based on the fragmentation and mergers of clusters formed by particles in contact. It allows one to treat particle interactions in addition to the hard-sphere exclusion as long as the corresponding interaction forces are continuous functions of the particle coordinates. We furthermore develop a treatment of sticky hard spheres as described by Baxter's contact interaction potential.

cond-mat.stat-mech↗

arXiv2022

Hydrodynamic interactions hinder transport of flow-driven colloidal particles

The flow-driven transport of interacting micron-sized particles occurs in many soft matter systems spanning from the translocation of proteins to moving emulsions in microfluidic devices. Here we combine experiments and theory to investigate the collective transport properties of colloidal particles along a rotating ring of optical traps. In the co-rotating reference frame, the particles are driven by a vortex flow of the surrounding fluid. When increasing the depth of the optical potential, we observe a jamming behavior that manifests itself in a strong reduction of the current with increasing particle density. We show that this jamming is caused by hydrodynamic interactions that enhance the energetic barriers between the optical traps. This leads to a transition from an over- to an under-critical tilting of the potential in the corotating frame. Based on analytical considerations, the enhancement effect is estimated to increase with increasing particle size or decreasing radius of the ring of traps. Measurements for different ring radii and Stokesian dynamics simulations for corresponding particle sizes confirm this. The enhancement of potential barriers in the flow-driven system is contrasted to the reduction of barriers in a force-driven one. This diverse behavior demonstrates that hydrodynamic interactions can have a very different impact on the collective dynamics of many-body systems. Applications to soft matter and biological systems require careful consideration of the driving mechanism and of the role of hydrodynamic interactions.

cond-mat.soft↗

arXiv2022

On the possibility of exploring tip-molecule interactions with STM experiments

We present a theory for analyzing residence times of single molecules in a fixed detection area of a scanning tunneling microscope (STM). The approach is developed for one-dimensional molecule diffusion and can be extended to two dimensions by using the same methodology. Explicit results are derived for an harmonic attractive and repulsive tip-molecule interaction. Applications of the theory allows one to estimate the type and strength of interactions between the STM tip and the molecule. This includes the possibility of an estimation of molecule-molecule interaction when the tip is decorated by a molecule. Despite our focus on STM, this theory can analogously be applied to other experimental probes that monitor single molecules.

cond-mat.mes-hall↗