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Thomas Ihle

Publications and source records attributed to Thomas Ihle.

At least 19 recordsLinked to original sources
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 Schr\"odinger 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 Schr\"odinger 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 Schr\"odinger 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 K\"ursten [K\"ursten, 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

Non-reciprocal anti-aligning active mixtures: deriving the exact Boltzmann collision operator

We consider the effect of non-reciprocity in a binary mixture of self-propelled particles with anti-aligning interactions, where a particle of type A reacts differently to a particle of type B than vice versa. Starting from a well-known microscopic Langevin-model for the particles, setting up the corresponding exact N-particle Fokker-Planck equation and making Boltzmann's assumptions of low density and one-sided molecular chaos, the non-linear active Boltzmann equation with the exact collision operator is derived. In this derivation, the effect of phase-space compression and the build-up of pair-correlations during binary interactions is explicitly taken into account, leading to a theoretical description beyond mean-field. This extends previous results for reciprocal interactions, where it was found that orientational order can emerge in a system with purely anti-aligning interactions. Although the equations of motion are more complex than in the reciprocal system, the theory still leads to analytical expressions and predictions. Comparisons with agent-based simulations show excellent quantitative agreement of the dynamic and static behavior in the low density and/or small coupling limit.

cond-mat.stat-mech↗
arXiv2024

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↗
arXiv2023

Flocking in Binary Mixtures of Anti-aligning Self-propelled Particles

We consider two species of self-propelled point particles: A-particles and B-particles. The orientations between nearby particles are subject to pair interactions of different strength for A-A-, A-B-(=B-A-) and B-B-interactions, respectively. Even if all interactions involved are repelling, that is, if they locally favor anti-alignment between each pair of particles, we find global polar order of both A-particles and B-particles We find qualitative agreement between agent-based simulations and mean field theory. Beyond mean field, we develop a Boltzmann-scattering theory based on one-sided molecular chaos that yields excellent quantitative agreement with simulations for dilute systems. For large systems, we find, depending on parameters, either micro-phase-separation or static patterns with either patches or stripes that carry different polarization orientations.

cond-mat.soft↗
arXiv2023

Scattering theory of Non-Brownian active particles with social distancing

We consider deterministic self-propelled particles with anti-alignment interactions. An asymptotically exact kinetic theory for particle scattering at low densities is constructed by a non-local closure of the BBGKY-hierarchy, involving pair correlations. We show that the mean-field assumption of molecular chaos yields unphysical predictions, whereas the scattering theory shows excellent agreement with agent-based simulations. To extend the theory to high densities, a self-consistent mapping to a random-telegraph process is performed. The approach is used to derive a one-particle Langevin-equation and leads to analytical expressions for the correlations of its effective noise.

cond-mat.stat-mech↗
arXiv2023

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↗
arXiv2021

Phases and homogeneous ordered states in alignment-based self-propelled particle models

We study a set of models of self-propelled particles that achieve collective motion through similar alignment-based dynamics, considering versions with and without repulsive interactions that do not affect the heading directions. We explore their phase space within a broad range of values of two nondimensional parameters (coupling strength and Peclet number), characterizing their polarization and degree of clustering. The resulting phase diagrams display equivalent, similarly distributed regions for all models with repulsion. The diagrams without repulsion exhibit differences, in particular for high coupling strengths. We compare the boundaries and representative states of all regions, identifying various regimes that had not been previously characterized. We analyze in detail three types of homogeneous polarized states, comparing them to existing theoretical and numerical results by computing their velocity and density correlations, giant number fluctuations, and local order-density coupling. We find that they all deviate in one way or another from the theoretical predictions, attributing these differences either to the remaining inhomogeneities or to finite-size effects. We discuss our results in terms of the universal or specific features of each model, their thermodynamic limit, and the high mixing and low mixing regimes. Our study provides a broad, overarching perspective on the multiple phases and states found in alignment-based self-propelled particle models.

cond-mat.soft↗
arXiv2021

A Quantitative Kinetic Theory of Flocking with Three-Particle-Closure

We consider aligning self-propelled particles in two dimensions. Their motion is given by generalized Langevin equations and includes non-additive N-particle interactions. The qualitative behavior is as for the famous Vicsek model. We develop a kinetic theory of flocking beyond mean field. In particular, we self-consistently take into account the full pair correlation function. We find excellent quantitative agreement of the pair correlations with direct agent-based simulations within the disordered regime. Furthermore we use a closure relation to incorporate spatial correlations of three particles. In that way we achieve good quantitative agreement of the onset of flocking with direct simulations. Compared to mean field theory, the flocking transition is shifted significantly towards lower noise because directional correlations favor disorder. We compare our theory with a recently developed Landau-kinetic theory.

cond-mat.soft↗
arXiv2020

Dry Active Matter exhibits a self-organized 'Cross Sea' Phase

The Vicsek model of self-propelled particles is known in three different phases: (i) a polar ordered homogeneous phase also called Toner-Tu phase, (iii) a phase of polar ordered regularly arranged high density bands (waves) with surrounding low density regions without polar order and (iv) a homogeneous phase without polar order. It has been questioned whether the band phase (iii) should be divided into two parts [Chaté2020]: one with periodically arranged and one with strongly interacting but not ordered bands. We answer this question by showing that the standard Vicsek model has a fourth phase for large system sizes: (ii) a polar ordered cross sea phase. Close to the transition towards (i) this phase becomes unstable and looks like strongly interacting bands. We demonstrate that the cross sea phase is not just a superposition of two waves, but it is an independent complex pattern. Furthermore we show that there is a non-zero mass flow through the structure of the cross sea pattern within its co-moving frame.

cond-mat.soft↗
arXiv2019

Multiple Particle Correlation Analysis of Many-Particle Systems: Formalism and Application to Active Matter

We introduce a fast spatial point pattern analysis technique which is suitable for systems of many identical particles giving rise to multi-particle correlations up to arbitrary order. The obtained correlation parameters allow to quantify the quality of mean field assumptions or theories that incorporate correlations of limited order. We study the Vicsek model of self-propelled particles and create a correlation map marking the required correlation order for each point in phase space incorporating up to ten-particle correlations. We find that multi-particle correlations are important even in a large part of the disordered phase. Furthermore, the two-particle correlation parameter serves as an excellent order parameter to locate both phase transitions of the system, whereas two different order parameters were required before.

cond-mat.soft↗
arXiv2019

Transport coefficients of self-propelled particles: Reverse perturbations and transverse current correlations

The reverse perturbation method [Phys. Rev. E 59, 4894 (1999)] for shearing simple liquids and measuring their viscosity is extended to the Vicsek-model (VM) of active particles [Phys. Rev. Lett. 75, 1226 (1995)] and its metric-free version. The sheared systems exhibit a phenomenon that is similar to the skin effect of an alternating electric current: momentum that is fed into the boundaries of a layer decays mostly exponentially towards the center of the layer. It is shown how two transport coefficients, i.e. the shear viscosity $ν$ and the momentum amplification coefficient $λ$, can be obtained by fitting this decay with an analytical solution of the hydrodynamic equations for the VM. The viscosity of the VM consists of two parts, a kinetic and a collisional contribution. While analytical predictions already exist for the former, a novel expression for the collisional part is derived by an Enskog-like kinetic theory. To verify the predictions for the transport coefficients, Green-Kubo relations were evaluated and transverse current correlations were measured in independent simulations. Not too far to the transition to collective motion, we find excellent agreement between the different measurements of the transport coefficients. However, the measured values of $ν$ and $1-λ$ are always slightly higher than the mean-field predictions, even at large mean free paths and at state points quite far from the threshold to collective motion, that is, far in the disordered phase. These findings seem to indicate that the mean-field assumption of molecular chaos is much less reliable in systems with velocity-alignment rules such as the VM, compared to models obeying detailed balance such as Multi-Particle Collision Dynamics.

cond-mat.soft↗
arXiv2018

Polarized Ukraine 2014: Opinion and Territorial Split Demonstrated with the Bounded Confidence XY Model, Parameterized by Twitter Data

Multiple countries have recently experienced extreme political polarization, which in some cases led to escalation of hate crime, violence and political instability. Beside the much discussed presidential elections in the United States and France, Britain's Brexit vote and Turkish constitutional referendum, showed signs of extreme polarization. Among the countries affected, Ukraine faced some of the gravest consequences. In an attempt to understand the mechanisms of these phenomena, we here combine social media analysis with agent-based modeling of opinion dynamics, targeting Ukraine's crisis of 2014. We use Twitter data to quantify changes in the opinion divide and parameterize an extended Bounded-Confidence XY Model, which provides a spatiotemporal description of the polarization dynamics. We demonstrate that the level of emotional intensity is a major driving force for polarization that can lead to a spontaneous onset of collective behavior at a certain degree of homophily and conformity. We find that the critical level of emotional intensity corresponds to a polarization transition, marked by a sudden increase in the degree of involvement and in the opinion bimodality.

physics.soc-ph↗
arXiv2018

Influence of Sensorial Delay on Clustering and Swarming

We show that sensorial delay alters the collective motion of self-propelling agents with aligning interactions: In a two-dimensional Vicsek model, short delays enhance the emergence of clusters and swarms, while long or negative delays prevent their formation. In order to quantify this phenomenon, we introduce a global clustering parameter based on the Voronoi tessellation, which permits us to efficiently measure the formation of clusters. Thanks to its simplicity, sensorial delay might already play a role in the organization of living organisms and can provide a powerful tool to engineer and dynamically tune the behavior of large ensembles of autonomous robots.

cond-mat.soft↗
arXiv2017

Giant Kovacs-Like Memory Effect for Active Particles

Dynamical properties of a Vicsek-like gas of self-propelled particles are investigated by means of kinetic theory and agent based simulations. While memory effects have been observed in disordered systems, we show that they also occur in active matter systems. In particular, we find that the system exhibits a giant Kovacs-like memory effect that is much larger than predicted by a generic linear theory. Based on a separation of time scales we develop a nonlinear theory to explain this effect. We apply this theory to driven granular gases and propose further applications to spin glasses.

cond-mat.stat-mech↗
arXiv2016

Critical assessment of von Mises distribution and an infinite series ansatz for self-propelled particles

We consider a Vicsek model of self-propelled particles with bounded confidence, where each particle interacts only with neighbors that have a similar direction. Depending on parameters, the system exhibits a continuous or discontinuous polar phase transition from the isotropic phase to a phase with a preferred direction. In a recent paper [1] the von Mises distribution was proposed as an ansatz for polar ordering. In the present system the time evolution of the angular distribution can be solved in Fourier space. We compare the results of the Fourier analysis with the ones obtained by using the von Mises distribution ansatz. In the latter case the qualitative behavior of the system is recovered correctly. However, quantitatively there are serious deviations. We introduce an extended von Mises distribution ansatz such that a second term takes care of the next two Fourier modes. With the extended ansatz we find much better quantitative agreement. As an alternative approach we also use a Gaussian and a geometric series ansatz in Fourier space. The geometric series ansatz is analytically handable but fails for very weak noise, the Gaussian ansatz yields better results but it is not analytically treatable.

cond-mat.stat-mech↗