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Horst-Holger Boltz

Publications and source records attributed to Horst-Holger Boltz.

18 recordsLinked to original sources
arXiv2026

Asymptotically exact scattering theory of the Kuramoto-Vicsek model

We consider the Kuramoto-Vicsek model of self-propelled particles with velocity-alignment interactions. Starting from the exact $N$-particle Liouville equation, a kinetic equation for the one-particle distribution function is obtained in a self-consistent manner. We show that the usual mean-field assumption of molecular chaos leads to qualitatively wrong predictions such as an infinite coefficient of self-diffusion. Going beyond mean-field and applying the refined assumption of \emph{one-sided molecular chaos} where the two-particle-correlations during binary interactions are explicitly taken into account, we analytically calculate the scattering of particles in the limit of low density and obtain explicit expressions for the dynamical noise of an effective one-particle Langevin-equation and the corresponding self-diffusion. The theory is developed in detail for anti-aligning couplings, where exact analytical results are obtainable. In this calculation, the superposition principle of traditional kinetic theory is modified to handle a system with non-Hamiltonian dynamics involving phase-space compression. The predicted theoretical expressions for the relaxation of hydrodynamic modes and the self-diffusion coefficient are in excellent, quantitative agreement with agent-based simulations. At large particle densities, a given particle is constantly approached and abandoned by different collision partners. Modeling this switching by a random telegraph process and exactly solving a self-consistent integral equation, we obtain explicit expressions for the noise correlations of the effective one-particle Langevin-equation. We also consider the effect of frozen disorder in the particle speeds and show how this can be used to calculate the exact Boltzmann collision operator for positive alignment strengths.

cond-mat.stat-mech↗
arXiv2026

Geometry-Induced Transport of Self-Aligning Chiral Bristlebots

Active matter systems characterized by the interplay of chirality and self-alignment offer a rich landscape for non-equilibrium collective behaviors and the development of autonomous materials. We present a versatile experimental platform for studying these dynamics using augmented commercial bristlebots, where custom-designed housings and elastic couplings induce a self-aligning torque and stable chiral drift. By mapping experimental trajectories to a Langevin-type model, we characterize the single-particle dynamics. In circular geometries, we show that the stability of edge currents is governed by the interaction between intrinsic particle chirality and handedness of the edge current. Furthermore, we demonstrate that transport can be geometrically rectified using a nautilus-shaped obstacle acting as a doubly chirality-sensitive ratchet. Finally, we explore the collective dynamics of rigidly linked assemblies, observing spontaneous mode-switching between translational and rotational states in active solids. Our results provide a robust framework for experimental studies in active gases and illustrate how geometric constraints can be used to program complex transport properties in active systems.

cond-mat.soft↗
arXiv2026

Dynamics of Aligning Active Matter: Mapping to a Schrödinger Equation and Exact Diagonalization

There has been recent interest in the relaxational modes of small-scale fully connected systems of aligning self-propelled particles (Spera et al., Phys. Rev. Lett. {\bf 132}: 078301 (2024)). We revisit the classical connection between Fokker-Planck and Schrödinger equations to address this by means of exact diagonalization, allowing for rigorous analytical insight into the full spectrum. This allows us to extract exact results which we compare to the existing result from linearized statistical field theory. We derive asymptotically correct analytical results that improve upon the prior approximations. We show that this methodology can fruitfully be extended to the case of non-reciprocal interactions which gives rise to a non-Hermitian Schrödinger problem akin to those in open quantum mechanics. While the non-reciprocity can be chosen such as not to alter the stationary distribution, it fundamentally changes the nature of the steady state which we quantify via the entropy production. We discuss the case of low particle numbers as well as the emergence of mean-field dynamics at large numbers.

cond-mat.stat-mech↗
arXiv2026

Spectral insights into active matter: Exceptional Points and the Mathieu equation

We show that recent numerical findings of universal scaling relations in systems of noisy, aligning self-propelled particles by Kürsten [Kürsten, arXiv:2402.18711v2 [cond-mat.soft] (2025)] can robustly be explained by perturbation theory and known results for the Mathieu equation with purely imaginary parameter. In particular, we highlight the significance of a cascade of exceptional points that leads to non-trivial fractional scaling exponents in the singular-perturbation limit of high activity. Crucially, these features are rooted in the Fokker-Planck operator corresponding to free self-propulsion. This can be viewed as a dynamical phase transition in the dynamics of noisy active matter. We also predict that these scaling relations depend on the symmetry of the alignment interactions and discuss the relevance of this structure in the free propagation for self-alignment and cohesion-type interactions.

cond-mat.stat-mech↗
arXiv2025

Reduced density fluctuations via anti-aligning in active matter

We highlight the importance of long-range correlations in active matter systems of self-propelling particles even in the absence of global order or steric interactions by demonstrating that long-range density fluctuations are reduced. We show this analytically for a one-dimensional lattice process employing a Poisson representation. Within this framework, we are able to derive the fluctuating hydrodynamics for the Poisson fields. The emergent imaginary noise indicates the non-Poissonian nature of the number fluctuations and manifests in a non-trivial structure factor $S(k)$ which we are computing analytically. Numerically, we corroborate the relevance of these findings for off-lattice Vicsek-type models with anti-aligning interactions for which we observe apparent non-universal hyperuniformity which we suggest to interpret as a reduction with integer power-law to a finite value.

cond-mat.soft↗
arXiv2020

Fluctuation Distributions of Energy Minima in Complex Landscapes

We discuss the properties of the distributions of energies of minima obtained by gradient descent in complex energy landscapes. We find strikingly similar phenomenology across several prototypical models. We particularly focus on the distribution of energies of minima in the analytically well-understood p-spin-interaction spin glass model. We numerically find non-Gaussian distributions that resemble the Tracy-Widom distributions often found in problems of random correlated variables, and non-trivial finite-size scaling. Based on this, we propose a picture of gradient descent dynamics that highlights the importance of a first-passage process in the eigenvalues of the Hessian. This picture provides a concrete link to problems in which the Tracy-Widom distribution is established. Aspects of this first-passage view of gradient-descent dynamics are generic for non-convex complex landscapes, rationalizing the commonality that we find across models.

cond-mat.stat-mech↗
arXiv2020

Quantitative spectroscopy of single molecule interaction times

Single molecule fluorescence tracking provides information at nm-scale and ms-temporal resolution about the dynamics and interaction of individual molecules in a biological environment. While the dynamic behavior of isolated molecules can be characterized well, the quantitative insight is more limited when interactions between two indistinguishable molecules occur. We address here this aspect by developing a solid theoretical foundation for a spectroscopy of interaction times, i.e. the inference of interaction constants from imaging data. The non trivial crossover between a power law to an exponential behavior of the distribution of the interaction times is highlighted here, together with the dependence of the exponential term upon the product of the microscopic reaction rates (affinity). Our approach is validated on simulated as well as experimental datasets.

cond-mat.stat-mech↗
arXiv2018

Elastic capsules at liquid-liquid interfaces

We investigate the deformation of elastic microcapsules adsorbed at liquid-liquid interfaces. An initially spherical elastic capsule at a liquid-liquid interface undergoes circumferential stretching due to the liquid-liquid surface tension and becomes lens- or discus-shaped, depending on its bending rigidity. The resulting elastic capsule deformation is qualitatively similar, but distinct from the deformation of a liquid droplet into a liquid lens at a liquid-liquid interface. We discuss the deformed shapes of droplets and capsules adsorbed at liquid-liquid interfaces for a whole range of different surface elasticities: from droplets (only surface tension) deforming into liquid lenses, droplets with a Hookean membrane (finite stretching modulus, zero bending modulus) deforming into elastic lenses, to microcapsules (finite stretching and bending modulus) deforming into rounded elastic lenses. We calculate capsule shapes at liquid-liquid interfaces numerically using shape equations from nonlinear elastic shell theory. Finally, we present theoretical results for the contact angle (or the capsule height) and the maximal capsule curvature at the three phase contact line. These results can be used to infer information about the elastic moduli from optical measurements. During capsule deformation into a lens-like shape, surface energy of the liquid-liquid interface is converted into elastic energy of the capsule shell giving rise to an overall adsorption energy gain by deformation. Soft hollow capsules exhibit a pronounced increase of the adsorption energy as compared to filled soft particles and, thus, are attractive candidates as foam and emulsion stabilizers.

cond-mat.soft↗
arXiv2017

Buckling of elastic filaments by discrete magnetic moments

We study the buckling of an idealized, semiflexible filament along whose contour magnetic moments are placed. {We give analytic expressions for the critical stiffness of the filament below which it buckles due to the magnetic compression. For this, we consider various scenarios of the attachment of the magnetic particles to the filament. One possible application for this model are the magnetosome chains of magnetotactic bacteria. An estimate of the critical bending stiffness indicates that buckling may occur within the range of biologically relevant parameters and suggests a role for the bending stiffness of the filament to stabilize the filament against buckling, which would compromise the functional relevance of the bending stiffness of the used filament.

cond-mat.soft↗
arXiv2015

Shapes of sedimenting soft elastic capsules in a viscous fluid

Soft elastic capsules which are driven through a viscous fluid undergo shape deformation coupled to their motion. We introduce an iterative solution scheme which couples hydrodynamic boundary integral methods and elastic shape equations to find the stationary axisymmetric shape and the velocity of an elastic capsule moving in a viscous fluid at low Reynolds numbers. We use this approach to systematically study dynamical shape transitions of capsules with Hookean stretching and bending energies and spherical rest shape sedimenting under the influence of gravity or centrifugal forces. We find three types of possible axisymmetric stationary shapes for sedimenting capsules with fixed volume: a pseudospherical state, a pear-shaped state, and buckled shapes. Capsule shapes are controlled by two dimensionless parameters, the Föppl-von-Kármán number characterizing the elastic properties and a Bond number characterizing the driving force. For increasing gravitational force the spherical shape transforms into a pear shape. For very large bending rigidity (very small Föppl-von-Kármán number) this transition is discontinuous with shape hysteresis. The corresponding transition line terminates, however, in a critical point, such that the discontinuous transition is not present at typical Föppl-von-Kármán numbers of synthetic capsules. In an additional bifurcation, buckled shapes occur upon increasing the gravitational force. This type of instability should be observable for generic synthetic capsules. All shape bifurcations can be resolved in the force-velocity relation of sedimenting capsules, where up to three capsule shapes with different velocities can occur for the same driving force. All three types of possible axisymmetric stationary shapes are stable with respect to rotation during sedimentation.

cond-mat.soft↗
arXiv2015

Controlling adsorption of semiflexible polymers on planar and curved substrates

We study the adsorption of semiflexible polymers such as polyelectrolytes or DNA on planar and curved substrates, e.g., spheres or washboard substrates via short-range potentials using extensive Monte-Carlo simulations, scaling arguments, and analytical transfer matrix techniques. We show that the adsorption threshold of stiff or semiflexible polymers on a planar substrate can be controlled by polymer stiffness: adsorption requires the highest potential strength if the persistence length of the polymer matches the range of the adsorption potential. On curved substrates, i.e., an adsorbing sphere or an adsorbing washboard surface, the adsorption can be additionally controlled by the curvature of the surface structure. The additional bending energy in the adsorbed state leads to an increase of the critical adsorption strength, which depends on the curvature radii of the substrate structure. For an adsorbing sphere, this gives rise to an optimal polymer stiffness for adsorption, i.e., a local minimum in the critical potential strength for adsorption, which can be controlled by curvature. For two- and three-dimensional washboard substrates, we identify the range of persistence lengths and the mechanisms for an effective control of the adsorption threshold by the substrate curvature.

cond-mat.soft↗
arXiv2015

Monte Carlo Simulation of Dense Polymer Melts Using Event Chain Algorithms

We propose an efficient Monte Carlo algorithm for the off-lattice simulation of dense hard sphere polymer melts using cluster moves, called event chains, which allow for a rejection-free treatment of the excluded volume. Event chains also allow for an efficient preparation of initial configurations in polymer melts. We parallelize the event chain Monte Carlo algorithm to further increase simulation speeds and suggest additional local topology-changing moves ("swap" moves) to accelerate equilibration. By comparison with other Monte Carlo and molecular dynamics simulations, we verify that the event chain algorithm reproduces the correct equilibrium behavior of polymer chains in the melt. By comparing intrapolymer diffusion time scales, we show that event chain Monte Carlo algorithms can achieve simulation speeds comparable to optimized molecular dynamics simulations. The event chain Monte Carlo algorithm exhibits Rouse dynamics on short time scales. In the absence of swap moves, we find reptation dynamics on intermediate time scales for long chains.

cond-mat.soft↗
arXiv2014

Parallelized event chain algorithm for dense hard sphere and polymer systems

We combine parallelization and cluster Monte Carlo for hard sphere systems and present a parallelized event chain algorithm for the hard disk system in two dimensions. For parallelization we use a spatial partitioning approach into simulation cells. We find that it is crucial for correctness to ensure detailed balance on the level of Monte Carlo sweeps by drawing the starting sphere of event chains within each simulation cell with replacement. We analyze the performance gains for the parallelized event chain and find a criterion for an optimal degree of parallelization. Because of the cluster nature of event chain moves massive parallelization will not be optimal. Finally, we discuss first applications of the event chain algorithm to dense polymer systems, i.e., bundle-forming solutions of attractive semiflexible polymers.

cond-mat.stat-mech↗
arXiv2014

Depinning of stiff directed lines in random media

Driven elastic manifolds in random media exhibit a depinning transition to a state with non-vanishing velocity at a critical driving force. We study the depinning of stiff directed lines, which are governed by a bending rigidity rather than line tension. Their equation of motion is the (quenched) Herring-Mullins equation, which also describes surface growth governed by surface diffusion. Stiff directed lines are particularly interesting as there is a localization transition in the static problem at a finite temperature and the commonly exploited time ordering of states by means of Middleton's theorems (A. Middleton, Phys. Rev. Lett. 68, 670 (1992)) is not applicable. We employ analytical arguments and numerical simulations to determine the critical exponents and compare our findings with previous works and functional renormalization group results, which we extend to the different line elasticity. We see evidence for two distinct correlation length exponents.

cond-mat.stat-mech↗
arXiv2013

Stiff directed lines in random media

We investigate the localization of stiff directed lines with bending energy by a short-range random potential. We apply perturbative arguments, Flory scaling arguments, a variational replica calculation, and functional renormalization to show that a stiff directed line in 1+d dimensions undergoes a localization transition with increasing disorder for d > 2=3. We demonstrate that this transition is accessible by numerical transfer matrix calculations in 1+1 dimensions and analyze the properties of the disorder dominated phase in detail. On the basis of the two-replica problem, we propose a relation between the localization of stiff directed lines in 1+d dimensions and of directed lines under tension in 1+3d dimensions, which is strongly supported by identical free energy distributions. This shows that pair interactions in the replicated Hamiltonian determine the nature of directed line localization transitions with consequences for the critical behavior of the Kardar-Parisi-Zhang (KPZ) equation. We support the proposed relation to directed lines via multifractal analysis revealing an analogous Anderson transition-like scenario and a matching correlation length exponent. Furthermore, we quantify how the persistence length of the stiff directed line is reduced by disorder.

cond-mat.stat-mech↗
arXiv2012

Localization transition of stiff directed lines in random media

We investigate the localization of stiff directed lines with bending energy by a short-range random potential. Using perturbative arguments, Flory arguments, and a replica calculation, we show that a stiff directed line in 1+d dimensions undergoes a localization transition with increasing disorder for $d>2/3$. We demonstrate that this transition is accessible by numerical transfer matrix calculations in 1+1 dimensions and analyze the properties of the disorder-dominated phase. On the basis of the two-replica problem, we propose a relation between the localization of stiff directed lines in 1+d dimensions and of directed lines under tension in 1+3d dimensions, which is strongly supported by identical free energy distributions. This shows that pair interactions in the replicated Hamiltonian determine the nature of directed line localization transitions with consequences for the critical behavior of the Kardar-Parisi-Zhang (KPZ) equation. Furthermore, we quantify how the persistence length of the stiff directed line is reduced by disorder.

cond-mat.stat-mech↗