Esa Rasanen

The Lorentz gas is a paradigmatic model in dynamical systems theory for understanding the origin of nonequilibrium transport in terms of microscopic deterministic chaos. In the periodic setting, a point particle scatters elastically off disks arranged on a two-dimensional lattice. Here we replace the disks by smooth potentials and the particle by the widely studied walking droplet, which propels itself on a vertically vibrating fluid. In the low-memory limit, this droplet reduces to a particle with nonlinear active friction. We call this system an active Lorentz gas. Using extensive numerical simulations, we analyze how dissipation generated by the active deterministic dynamics alters the phase-space structure of the corresponding conservative Lorentz gas. We find that islands of stability collapse into attracting and repelling sets. To characterize these structures, we introduce an energy-variance filtering method that distinguishes localized periodic, quasi-ballistic periodic, and chaotic trajectories, enabling the construction of bifurcation diagrams in a non-conservative setting. We identify parameter regimes exhibiting strong bifurcation cascades, anomalous diffusion, and significant phase-space contraction. Our results establish the active Lorentz gas as a rich framework for studying transport in dissipative dynamical systems and provide a bridge between active matter and classical models of chaotic transport, with potential implications for hydrodynamic quantum analogs in periodic media.

Objective. Entropy-based heart rate variability (HRV) metrics are widely used to characterize heartbeat dynamics and distinguish physiological from pathological states, but their classification performance is highly sensitive to parameter selection. This study investigated a fixed-tolerance approach derived from a healthy reference population as an alternative to conventional subject-specific tolerance normalization and assessed how entropy-parameter selection influences classification performance. Approach. Approximate entropy (ApEn), sample entropy (SampEn), and multiscale entropy (MSE) were evaluated using both conventional and fixed-tolerance formulations in 24-h Holter recordings from 274 healthy subjects and 946 patients with congestive heart failure (CHF). Classification performance was quantified using the area under the receiver operating characteristic curve (AUC). Parameter sensitivity was assessed through systematic sweeps of the embedding dimension, tolerance coefficient, and MSE scale range. Main results. Classification performance varied substantially across the parameter space, and the embedding-dimension and tolerance values commonly used in the literature were generally suboptimal. The fixed-tolerance implementation consistently outperformed the conventional subject-specific approach, achieving AUC values of 0.78 (+0.03) for ApEn, 0.77 (+0.09) for SampEn, and 0.74 (+0.14) for MSE. For MSE, tolerance selection had a substantially larger influence on classification performance than scale-dependent parameterization. Significance. The results suggest that a substantial portion of the classification potential of entropy-based HRV analysis remains unexploited under conventional tolerance normalization and parameter selection. More generally, entropy-based HRV metrics appear to be more sensitive to methodological choices than is commonly assumed. The fixed-tolerance approach provides a simple and computationally inexpensive strategy for improving entropy-based CHF classification, although validation in independent datasets is needed to establish its broader applicability.

We investigate diffusion in a two-dimensional inverted soft Lorentz gas, where attractive Fermi-type potential wells are arranged in a triangular lattice. This configuration contrasts with earlier studies of soft Lorentz gases involving repulsive scatterers. By systematically varying the gap width and softness of the potential, we explore a rich landscape of diffusive behaviors. We present numerical simulations of the mean-squared displacement and compute diffusion coefficients, identifying tonguelike structures in parameter space associated with quasiballistic transport. Furthermore, we develop an extension to the Machta-Zwanzig approximation that incorporates correlated multihop trajectories, and we correct for the influence of localized periodic orbits. Our findings highlight the qualitative and quantitative differences between inverted and repulsive soft Lorentz gases, and they offer new insights into transport phenomena in smooth periodic potentials.

Quantum scars have recently been directly visualized in graphene quantum dots [], revealing their resilience and influence on electron dynamics in mesoscopic systems. Here, we examine variational scarring in two-dimensional quantum dots and demonstrate that these states remain robust even in an open system. We show that controlled perturbations enable modulation of electronic transmission via scarred states, presenting a viable approach to tuning quantum transport. These findings provide insights into the role of scarring in mesoscopic transport and open pathways for experimental realization in quantum devices.

We demonstrate and analyze anomalous diffusion properties of point-like particles in a two-dimensional system with circular scatterers arranged in a square lattice and governed by smooth potentials, referred to as the square soft Lorentz gas. Our numerical simulations reveal a rich interplay of normal and anomalous diffusion depending on the system parameters. To describe diffusion in normal regimes, we develop a unit cell hopping model that, in the single-hop limit, recovers the Machta-Zwanzig approximation and converges toward the numerical diffusion coefficient as the number of hops increases. Anomalous diffusion is characterized by quasiballistic orbits forming Kolmogorov-Arnold-Moser islands in phase space, alongside a complex tongue structure in parameter space defined by the interscatterer distance and potential softness. The distributions of the particle displacement vector show notable similarities to both analytical and numerical results for a hard-wall square Lorentz gas, exhibiting Gaussian behavior in normal diffusion and long tails due to quasiballistic orbits in anomalous regimes. Our work thus provides a catalog of key dynamical system properties that characterize the intricate changes in diffusion when transitioning from hard billiards to soft potentials.

The phenomenon of branched flow, visualized as a chaotic arborescent pattern of propagating particles, waves, or rays, has been identified in disparate physical systems ranging from electrons to tsunamis, with periodic systems only recently being added to this list. Here, we explore the laws governing the evolution of the branches in periodic potentials. On one hand, we observe that branch formation follows a similar pattern in all nonintegrable potentials, no matter whether the potentials are periodic or completely irregular. Chaotic dynamics ultimately drives the birth of the branches. On the other hand, our results reveal that for periodic potentials the decay of the branches exhibits new characteristics due to the presence of infinitely stable branches known as superwires. Again, the interplay between branched flow and superwires is deeply connected to Hamiltonian chaos. In this work, we explore the relationships between the laws of branched flow and the structures of phase space, providing extensive numerical and theoretical arguments to support our findings.