arXiv subjects

Sabine H. L. Klapp

Publications and source records attributed to Sabine H. L. Klapp.

At least 19 recordsLinked to original sources

arXiv2026

Non-stationary Statistics and Energetics of Brownian Motion under Stochastic Harmonic Confinement

We investigate the positional statistics and thermodynamic properties of a Brownian particle confined in a Harmonic trap. The stiffness of the particle fluctuates in time as the square of the Brownian process. First, in the absence of a thermal bath, we investigate the probability density function of the position of the particle at time $t$. Then, we provide an expression to compute the $n$th positional moment. We evaluate the first four positional moments and discuss their asymptotic behavior in the long-time limit. In contrast to previously studied models of fluctuating stiffness, the current model describes a non-stationary process. Furthermore, we provide the exact expression for the average work performed on the system and the average heat exchanged by the particle with the bath. Their long time behavior again reflects the non-stationary nature of the process. Our theoretical predictions are supported by numerical simulations.

cond-mat.stat-mech↗

arXiv2026

Quantum statistical enhancement of collective behaviour in a bosonic active Ising model

Collective behaviour such as flocking (the collective motion of a spontaneously formed group along a common direction) or aster formation (the binding of opposing flocks, inhibiting each others motion) are intriguing emergent phenomena in active systems with local alignment rules. Until recently, their occurrence was mainly studied for classical systems, a prime example being the active Ising model (AIM), which translates the main ingredients of flocking and aster formation (i.e., alignment and self-propulsion) to a lattice framework. Here we introduce and study a one-dimensional (1D) quantum lattice variant of the AIM, based on ideal bosons with a spin degree of freedom. We find that both the collective behaviours of the 1D classical model, flocking and aster formation, are markedly enhanced by the bosonic quantum statistics. This contrasts with a recent quantum generalization of the AIM based onto hard-core bosons [Khasseh et al., Phys. Rev. Lett. 135, 248302 (2025)], where flocking, but neither its quantum-statistical stabilization nor aster states were observed as a consequence of interactions. Moreover, we investigate the competition of this quantum statistical stabilization of collective phases with their suppression by the quantum fluctuations induced by a transverse external magnetic field.

quant-ph↗

arXiv2026

Entropy production in non-reciprocal polar active mixtures

The out-of-equilibrium character of active systems is often twofold, arising from both the activity itself and from non-reciprocal couplings between constituents. A well-established measure to quantify the system's distance from equilibrium is the informatic entropy production rate. Here, we ask the question whether and how the informatic entropy production rate reflects collective behaviors and transitions in an active mixture with non-reciprocal polar couplings. In such systems, non-reciprocal orientational couplings can induce chiral motion of particles. At the field-theoretical level, transitions to these time-dependent chiral states are marked by so-called critical exceptional points. Here, we show that at a particle level, the entropy production rate within the chiral states increases with the degree of non-reciprocity, provided it is sufficiently strong. Moreover, even at small degrees of non-reciprocity, the transitions via exceptional points leave clear signatures in the entropy production rate, which exhibits pronounced peaks at coupling strengths corresponding to the field-theoretical exceptional points. Overall, the increase and peaks of the entropy production rate mirror the susceptibility of the polarization vector at the particle level. This correspondence is supported by a field-theoretical analysis, which reveals that, in the long-wavelength limit, the entropy production rate scales with the susceptibilities of the polarization fields.

cond-mat.stat-mech↗

arXiv2025

Inference of a time delay in stochastic systems

Time delay is ubiquitous in many experimental and real-world situations. It is often unclear whether time delay plays a significant role in observed phenomena, and if it does, how long the time lag really is. This would be invaluable knowledge when analyzing and modeling such systems. Hitherto, no universal method is available by which the time delay can be inferred. To address this problem, we propose and demonstrate two different methods to infer time delay in overdamped Langevin systems with delayed feedback. In the first part, we focus on the power spectral density based on the positional data and use a characteristic signature of the time delay to infer the delay time. In limiting cases, we establish a direct relation of the observations made for nonlinear time-delayed feedback forces to analytical results obtained for the linear system. In other situations despite the absence of this direct relation, the characteristic signature remains and can be exploited by a semiautomatic method to infer the delay time. Furthermore, it may not always desirable or possible to observe a system for a long time to infer dependencies and parameters. Thus, in the second part, we propose for the first time a probing method combined with a neural network to infer the delay time, which requires only short observation time series. These proposed methods for inferring time delays in stochastic systems may prove to be valuable tools for gaining deeper insight into the role of delay across a wide range of applications -- from the behavior of individual colloidal particles under feedback control to emergent collective phenomena such as flocking and swarming.

physics.data-an↗

arXiv2025

Nonequilibrium fluctuations in a harmonic trap with annealed stochastic stiffness

We provide a comprehensive analysis of the positional dynamics and average thermodynamics of an overdamped Brownian particle subject to both, harmonic confinement and annealed disorder due to a temporarily fluctuating trap stiffness. We model this stiffness via a stationary Ornstein-Uhlenbeck (OU) process whose correlation time can be tuned from white noise to a quenched limit. We analytically calculate the positional distribution in these limits and provide exact expressions for the $n$th positional moments at finite correlation times, revealing important insights regarding stationarity. Further, we analyze the average work performed on the particle and the heat dissipated into the environment at all times, illustrating the nonequilibrium character of the system and its relaxation into a steady state. Our analytical results are validated by numerical Langevin simulations.

cond-mat.stat-mech↗

arXiv2025

Synchronization and exceptional points in nonreciprocal active polar mixtures

Many active matter systems consist of different particle types that interact via nonreciprocal couplings. Such nonreciprocal couplings can lead to the spontaneous emergence of time-dependent states that break parity-time symmetry. On the field-theoretical level, the transition to these states is marked by so-called exceptional points. However, their precise impact on observable particle dynamics remains poorly understood. In this study, we address this gap by providing a scale-bridging view of a minimal active mixture with nonreciprocal polar interactions. We find that nonreciprocity induces chiral motion on the particle level, yet no full, homogeneous synchronization. Instead, we observe various behaviors, ranging from fully synchronized clusters to chimera-like states. The nonreciprocity-induced spontaneous chirality increases with the degree of nonreciprocity and peaks at coupling strengths associated with exceptional points.

cond-mat.soft↗

arXiv2025

Nonreciprocal field theory for decision-making in multi-agent control systems

Field theories for complex systems traditionally focus on collective behaviors emerging from simple, reciprocal pairwise interaction rules. However, many natural and artificial systems exhibit behaviors driven by microscopic decision-making processes that introduce both nonreciprocity and many-body interactions, challenging these conventional approaches. We develop a theoretical framework to incorporate decision-making into field theories using the shepherding control problem as a paradigmatic example of a multi-agent control system, where agents (herders) must coordinate to confine another group of agents (targets) within a prescribed region. By introducing continuous approximations of two key decision-making elements - target selection and trajectory planning - we derive field equations that capture the essential features of this distributed control problem. Our theory reveals that different decision-making strategies emerge at the continuum level, from average attraction to highly selective choices, and from undirected to goal-oriented motion, driving transitions between homogeneous and confined configurations. The resulting nonreciprocal field theory not only describes the shepherding problem but provides a general framework for incorporating decision-making into continuum theories of collective behavior, with implications for applications ranging from robotic swarms to crowd management systems.

cond-mat.soft↗

arXiv2025

Self-assembly and time-dependent control of active and passive triblock Janus colloids

We perform Brownian Dynamics (BD) simulations to explore the self-assembly of a two-dimensional model system of triblock Janus colloids as an example of "patchy" colloids forming complex structures. Previous experiments and simulation studies have shown that such systems are capable of forming a two-dimensional Kagome lattice at room temperatures. However, it is well established that the crystallization is strongly hampered by the formation of long-living metastable aggregates. For this reason, recent studies have investigated activity, i.e., self-propulsion of the Janus particles as a mechanism to accelerate the formation of stable Kagome structures [Mallory and Cacciuto, JACS 141, 2500-2507 (2019)] at selected state points. Here we extend, first, the investigations of active Janus colloids for a broader range of densities and temperatures. We also characterize in detail the associated nucleation of Kagome clusters, as well as their structure in the steady state. Second, to make contact to the equilibrium case, we propose a simple activity time protocol where an initially chosen activity is switched off after a finite time. With this protocol, we not only find Kagome structures in a much broader range of densities than in the purely passive case, but also obtain a Kagome crystallization boundary very close to that proposed in earlier Monte Carlo simulations.

cond-mat.soft↗

arXiv2025

Persistent motion of a Brownian particle subject to repulsive feedback with time delay

Based on analytical and numerical calculations we study the dynamics of an overdamped colloidal particle moving in two dimensions under time-delayed, non-linear feedback control. Specifically, the particle is subject to a force derived from a repulsive Gaussian potential depending on the difference between its instantaneous position, $\mathbf{r}(t)$, and its earlier position $\mathbf{r}(t-τ)$, where $τ$ is the delay time. Considering first the deterministic case, we provide analytical results for both, the case of small displacements and the dynamics at long times. In particular, at appropriate values of the feedback parameters, the particle approaches a steady state with a constant, non-zero velocity whose direction is constant as well. In the presence of noise, the direction of motion becomes randomized at long times, but the (numerically obtained) velocity autocorrelation still reveals some persistence of motion. Moreover, the mean-squared displacement (MSD) reveals a mixed regime at intermediate times with contributions of both, ballistic motion and diffusive translational motion, allowing us to extract an estimate for the effective propulsion velocity in presence of noise. We then analyze the data in terms of exact, known results for the MSD of active Brownian particles. The comparison indeed indicates a strong similarity between the dynamics of the particle under repulsive delayed feedback and active motion. This relation carries over to the behavior of the long-time diffusion coefficient $D_\mathrm{eff}$ which, similarly to active motion, is strongly enhanced compared to the free case. Finally we show that, for small delays, $D_\mathrm{eff}$ can be estimated analytically.

cond-mat.soft↗

arXiv2025

Heat production in a stochastic system with nonlinear time-delayed feedback

Using the framework of stochastic thermodynamics we study heat production related to the stochastic motion of a particle driven by repulsive, nonlinear, time-delayed feedback. Recently it has been shown that this type of feedback can lead to persistent motion above a threshold in parameter space [Physical Review E 107, 024611 (2023)]. Here we investigate, numerically and by analytical methods, the rate of heat production in the different regimes around the threshold to persistent motion. We find a nonzero average heat production rate, $\langle \dot{q}\rangle$, already below the threshold, indicating the nonequilibrium character of the system even at small feedback. In this regime, we compare to analytical results for a corresponding linearized delayed system and a small-delay approximation which provides a reasonable description of $\langle \dot{q}\rangle$ at small repulsion (or delay time). Beyond the threshold, the rate of heat production is much larger and shows a maximum as function of the delay time. In this regime, $\langle \dot{q}\rangle$ can be approximated by that of a system subject to a constant force stemming from the long-time velocity in the deterministic limit. The distribution of dissipated heat, however, is non-Gaussian, contrary to the constant-force case.

cond-mat.soft↗

arXiv2025

Exponential Change of Relaxation Rate by Quenched Disorder

We determine the asymptotic relaxation rate of a Brownian particle in a harmonic potential perturbed by quenched Gaussian disorder, a simplified model for rugged energy landscapes in complex systems. Depending on the properties of the disorder, we show that the mean and variance of the asymptotic relaxation rate are non-monotonous functions of the parameters for a broad class of disorders. In particular, the rate of relaxation may either increase or decrease exponentially compared to the unperturbed case. This implies that disorder may, depending on its properties, both significantly speed up \textit{and} slow down relaxation. In the limit of weak disorder, we derive the probability distribution of the asymptotic relaxation rate and show that it is Gaussian, with analytic expressions for the mean and variance that feature universal limits. Our findings indicate that controlled disorder may serve to tune the relaxation speed in complex systems.

cond-mat.stat-mech↗

arXiv2025

Breakdown of stochastic resonance in complex networks

In networked systems, stochastic resonance occurs as a collective phenomenon where the entire stochastic network resonates with a weak applied periodic signal. Beyond the interplay among the network coupling, the amplitude of the external periodic signal, and the intensity of stochastic fluctuations, the maintenance of stochastic resonance also crucially depends on the resonance capacity of each oscillator composing the network. This scenario raises the question: Can local defects in the ability of oscillators to resonate break down the stochastic resonance phenomenon in the entire network? Here, we investigate this possibility in complex networks of prototypical bistable oscillators in a double-well potential. We test the sustainability of stochastic resonance by considering a fraction of network oscillators with nonresonant potential landscapes. We find that the number of nonresonant oscillators depends nonlinearly on their dissimilarity from the rest of the network oscillators. In addition, we unravel the role of the network topology and coupling strength in maintaining, or suppressing, the stochastic resonance for different noise levels and number of nonresonant oscillators. Finally, we obtain a low-dimensional deterministic model confirming the results observed for the networks.

nlin.AO↗

arXiv2024

Discrete state model of a self-aggregating colloidal system with directional interactions

The construction of coarse-grained descriptions of a system's kinetics is well established in biophysics. One prominent example is Markov state models in protein folding dynamics. In this paper, we develop a coarse-grained, discrete state model of a self-aggregating colloidal particle system inspired by the concepts of Markov state modelling. The specific self-aggregating system studied here involves field-responsive colloidal particles in orthogonal electric and magnetic fields. Starting from particle-resolved (Brownian dynamics) simulations, we define the discrete states by categorizing each particle according to it's local structure. We then describe the kinetics between these states as a series of stochastic, memoryless jumps. In contrast to other works on colloidal self-assembly, our coarse-grained approach describes the simultaneous formation and evolution of multiple aggregates from single particles. Our discrete model also takes into account the changes in transition dynamics between the discrete states as the size of the largest cluster grows. We validate the coarse-grained model by comparing the predicted population fraction in each of the discrete states with those calculated directly from the particle-resolved simulations as a function of the largest cluster size. We then predict population fractions in presence of noise-averaging and in a situation where a model parameter is changed instantaneously after a certain time. Finally, we explore the validity of the detailed balance condition in the various stages of aggregation.

cond-mat.soft↗

arXiv2024

Dynamical structures in phase-separating non-reciprocal polar active mixtures

Non-reciprocal systems exhibit diverse dynamical phases whose character depends on the type and degree of non-reciprocity. In this study, we theoretically investigate dynamical structures in a mixture of non-reciprocally aligning polar active particles with repulsion, focusing on the performance on (and connection between) different levels of description. Linear stability analyses of the associated continuum model predict a profound influence of non-reciprocity, leading to phase separation, (anti-)flocking and asymmetric clustering behavior. On the microscopic level, particle simulations confirm the emergence of these dynamical phases and allow for a more in-depth investigation of (microscopic) properties, including orientational correlations and susceptibilities. The drastic impact of orientational couplings alone on the density dynamics is demonstrated in particle simulations without repulsion, where non-reciprocal alignment leads to the asymmetric formation of single-species polarized clumps. Overall, our findings demonstrate that certain dynamical properties, like a chase-and-run behavior in the asymmetrical clustering phase, are overlooked in mean-field continuum theory, making microscopic simulations an indispensable tool for studying the effects of non-reciprocal alignment couplings.

cond-mat.soft↗

arXiv2024

Non-reciprocal alignment induces asymmetric clustering in active mixtures

Heterogeneity is ubiquitous in biological and synthetic active matter systems that are inherently out of equilibrium. Typically, such active mixtures involve not only conservative interactions between the constituents, but also non-reciprocal couplings, whose full consequences for the collective behavior still remain elusive. Here, we study a minimal active non-reciprocal mixture with both, symmetric isotropic and non-reciprocal polar interactions. By combining a hydrodynamic theory derived from microscopic equations and particle-based simulations, we provide a scale-bridging view on the rich dynamics that occur even in absence of oscillatory instabilities. We show, in particular, that non-reciprocal alignment alone induces asymmetrical clustering at otherwise fully symmetric parameters. These density inhomogeneities go beyond the typical band formation in Vicsek-like systems. Within the asymmetric clustering state, single-species clusters chase more dilute accumulations of the other species.

cond-mat.soft↗

arXiv2024

Impact of non-reciprocal interactions on colloidal self-assembly with tunable anisotropy

Non-reciprocal (NR) effective interactions violating Newton's third law occur in many biological systems, but can also be engineered in synthetic, colloidal systems. Recent research has shown that such NR interactions can have tremendous effects on the overall collective behaviour and pattern formation, but can also influence aggregation processes on the particle scale. Here we focus on the impact of non-reciprocity on the self-assembly of an (originally passive) colloidal system with anisotropic interactions whose character is tunable by external fields. In the absence of non-reciprocity, that is, under equilibrium conditions, the colloids form aggregates with extremely long life times [Kogler et al., Soft Matter 11, 7356 (2015)], indicating kinetic trapping. Here we study, based on Brownian Dynamics (BD) simulations in 2D, a NR version of this model consisting of two species with reciprocal isotropic, but NR anisotropic interactions. We find that NR induces an effective propulsion of particle pairs and small aggregates forming at initial stages of self-assembly, an indication of the NR-induced non-equilibrium. The shape and stability of these initial clusters strongly depends on the degree of anisotropy. At longer times we find, for weak NR interactions, large (even system-spanning) clusters where single particles can escape and enter at the boundaries, in stark contrast to the small rigid aggregates appearing at the same time in the passive case. In this sense, weak NR shortcuts the aggregation. Increasing the degree of NR (and thus, propulsion), we even observe large-scale phase separation if the interactions are weakly anisotropic. In contrast, system with strong NR and anisotropy remain essentially disordered. Overall, NR interactions are shown to destabilize the rigid aggregates interrupting self-assembly in the passive case, helping the system to overcome kinetic barriers.

cond-mat.soft↗

arXiv2024

Pattern selection and the route to turbulence in incompressible polar active fluids

Active fluids, such as suspensions of microswimmers, are known to self-organize into complex spatio-temporal flow patterns. An intriguing example is mesoscale turbulence, a state of dynamic vortex structures exhibiting a characteristic length scale. Here, we employ a minimal model for the effective microswimmer velocity field to explore how the turbulent state develops from regular vortex patterns when the strength of activity resp. related parameters such as nonlinear advection or polar alignment strength - is increased. First, we demonstrate analytically that the system, without any spatial constraints, develops a stationary square vortex lattice in the absence of nonlinear advection. Subsequently, we perform an extended stability analysis of this nonuniform "ground state" and uncover a linear instability, which follows from the mutual excitement and simultaneous growth of multiple perturbative modes. This extended analysis is based on linearization around an approximation of the analytical vortex lattice solution and allows us to calculate critical activity parameters. Above these critical values, the vortex lattice develops into mesoscale turbulence in numerical simulations. Utilizing the numerical approach, we uncover an extended region of hysteresis where both patterns are possible depending on the initial condition. Here, we find that turbulence persists below the instability of the vortex lattice. We further determine the stability of square vortex patterns as a function of their wavenumber and represent the results analogous to the well-known Busse balloons known from classical pattern-forming systems. Here, the region of stable periodic patterns shrinks and eventually disappears with increasing activity parameters. Our results show that the strength of activity plays a similar role for active turbulence as the Reynolds number does in driven flow exhibiting inertial turbulence.

cond-mat.soft↗

arXiv2024

Nonequilibrium dynamics and entropy production of a trapped colloidal particle in a complex nonreciprocal medium

We discuss the two-dimensional motion of a Brownian particle that is confined to a harmonic trap and driven by a shear flow. The surrounding medium induces memory effects modelled by a linear, typically nonreciprocal coupling of the particle coordinates to an auxiliary (hidden) variable. The system's behavior resulting from the microscopic Langevin equations for the three variables is analyzed by means of exact moment equations derived from the Fokker-Planck representation, and numerical Brownian Dynamics (BD) simulations. Increasing the shear rate beyond a critical value we observe, for suitable coupling scenarios with nonreciprocal elements, a transition from a stationary to an instationary state, corresponding to an escape from the trap. We analyze this behavior, analytically and numerically, in terms of the associated moments of the probability distribution, and from the perspective of nonequilibrium thermodynamics. Intriguingly, the entropy production rate remains finite when crossing the stability threshold.

cond-mat.stat-mech↗