arXiv subjects

Esa Räsänen

Publications and source records attributed to Esa Räsänen.

At least 19 recordsLinked to original sources

arXiv2026

Pinning of a High-Energy Wavepacket by a Single Impurity

We demonstrate that a single repulsive impurity enhances directional confinement of a high-energy wavepacket in a finite two-dimensional lattice of quantum wells. At energies far above the interwell barriers, the impurity suppresses transverse dynamical tunneling while preserving propagation along a principal lattice axis, even as the corresponding classical regular region shrinks. Confinement is strongest at impurity amplitudes comparable to the barrier height and weakens for stronger perturbations. Spectral analysis links this nonmonotonic pinning to the wavepacket's overlap with eigenstates concentrated along the launch direction, consistent with impurity-induced variational scarring. These results show that a single local defect can control quantum propagation over distances far exceeding its own spatial extent.

quant-ph↗

arXiv2026

An active Lorentz gas: walking droplets in periodic media

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.

nlin.CD↗

arXiv2026

Coexistence of Anderson Localization and Quantum Scarring in Two Dimensions

We investigate finite two-dimensional disordered systems with periodic confinement. At low energies, eigenstates exhibit strong Anderson localization, while at higher energies a subset of states exhibits variational scarring with anisotropic intensity patterns that deviate from random-wave expectations. Scaling theory predicts that in two dimensions all eigenstates localize in the large-system-size limit, yet the energy-dependent localization length and finite-size effects allow these regimes to coexist. We demonstrate that this coexistence produces distinct, robust signatures in both spatial intensity patterns and spectral statistics that are directly observable in mesoscopic electronic, photonic, and cold-atom systems.

quant-ph↗

arXiv2025

Diffusion in the Inverted Triangular Soft Lorentz Gas

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 tongue-like structures in parameter space associated with quasiballistic transport. Furthermore, we develop an extension to the Machta-Zwanzig approximation that incorporates correlated multi-hop trajectories and correct for the influence of localized periodic orbits. Our findings highlight the qualitative and quantitative differences between inverted and repulsive soft Lorentz gases and offer new insights into transport phenomena in smooth periodic potentials.

nlin.CD↗

arXiv2025

Variational Scarring in Open Two-Dimensional Quantum Dots

Quantum scars have recently been directly visualized in graphene quantum dots (Nature 635, 841 (2024)), 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.

cond-mat.mes-hall↗

arXiv2025

Formation, prevalence, and stability of bouncing-ball quantum scars

Quantum scars correspond to enhanced probability densities along unstable classical periodic orbits. In recent years, research on quantum scars has extended to various systems including the many-body regime. In this work we focus on the formation, prevalence, and stability of linear "bouncing-ball" (BB) scars in two-dimensional (2D) quantum wells. These scars have relevance as effective and controllable channels in quantum transport. We utilize imaginary time propagation to solve the 2D Schrödinger equation within an arbitrary external confining potential, specifically the quantum well model with external perturbations. We show how BB scars begin to emerge with a single perturbative peak, such as a repulsive bump or attractive dip that simulates the effect of a charged nanotip in the system. We then identify the optimal size of the perturbative peak to maximize the prevalence of these scars. Finally, we investigate the stability of BB scars against external noise and find that some of them are remarkably robust. This suggests promising opportunities for further applications of BB scars in quantum transport.

cond-mat.mes-hall↗

arXiv2024

Chaotic dynamics creates and destroys branched flow

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 non-integrable 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.

nlin.PS↗

arXiv2024

Anomalous Diffusion in the Square Soft Lorentz Gas

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.

nlin.CD↗

arXiv2024

Timing and Dynamics of the Rosanna Shuffle

The Rosanna shuffle, the drum pattern from Toto's 1982 hit "Rosanna", is one of the most recognized drum beats in popular music. Recorded by Jeff Porcaro, this drum beat features a half-time shuffle with rapid triplets on the hi-hat and snare drum. In this analysis, we examine the timing and dynamics of the original drum track, focusing on rhythmic variations such as swing factor, microtiming deviations, tempo drift, and the overall dynamics of the hi-hat pattern. Our findings reveal that "Rosanna" exhibits a surprisingly pronounced swing for its genre, along with notable tempo drift typical of tracks recorded without a metronome. Additionally, we observe clear long-range correlations in the microtiming deviations, consistent with previous studies. Notably, the two-bar phrases of the song feature a distinctive repeating pattern in the timing and dynamics of the hi-hat beats, which enhances the song's phrasing. Overall, the Rosanna shuffle boasts a rich array of rhythmic characteristics that solidify its significant place in music history.

cs.SD↗

arXiv2024

Dynamical cross-correlations between RR and QT intervals in long-term electrocardiogram recordings

Understanding the dynamic relationship between RR and QT intervals is crucial for interpreting electrocardiograms (ECGs) and managing cardiac conditions. We investigated cross-correlation between RR and QT intervals in long-term ECG recordings from 202 healthy subjects using time-lagged cross-correlation analysis to explore how QT intervals correlate with both preceding and succeeding RR intervals across various time lags. Data was preprocessed with the smoothness priors method to remove long-term trends while preserving relevant short-term dynamics. Our results reveal that, as expected, the highest RR-QT cross-correlations occur when the intervals overlap the most. Notably, we also observed a strong cross-correlation between the present QT interval and the preceding RR interval, with the overall correlations skewed toward negative lags. This suggests that past RR intervals exert a stronger influence on current QT intervals. These findings align with previous research on RR-QT transfer entropy. We found no significant differences in RR-QT cross-correlations between sexes. However, aging was associated with significantly reduced cross-correlations across all lags. This effect is consistent with existing literature on age-related cardiac changes and provides further insight into the impact of aging on RR-QT coupling. Additionally, we observed a slight positive correlation between heart rate and cross-correlation at all lags, with cross-correlation decreasing as the lag increased. These findings enhance our understanding of the dynamic RR-QT relationship and may inform future studies on cardiac electrophysiology and diseases.

physics.med-ph↗

arXiv2022

Asymmetric Roughness of Elastic Interfaces at the Depinning Threshold

Roughness of driven elastic interfaces in random media is typically understood to be characterized by a single roughness exponent $ζ$. We show that at the depinning threshold, due to symmetry breaking caused by the direction of the driving force, elastic interfaces with local, long-range and mean-field elasticity exhibit asymmetric roughness. It is manifested as a skewed distribution of the local interface heights, and can be quantified by using detrended fluctuation analysis to compute a spectrum of local, segment-level scaling exponents. The asymmetry is observed as approximately linear dependence of the local scaling exponents on the difference of the segment height from the mean interface height.

cond-mat.stat-mech↗

arXiv2021

Density-functional approach to the band gaps of finite and periodic two-dimensional systems

We present an approach based on density-functional theory for the calculation of fundamental gaps of both finite and periodic two-dimensional (2D) electronic systems. The computational cost of our approach is comparable to that of total energy calculations performed via standard semi-local forms. We achieve this by replacing the 2D local density approximation with a more sophisticated -- yet computationally simple -- orbital-dependent modeling of the exchange potential within the procedure by Guandalini et al. [Phys. Rev. B 99, 125140 (2019)]. We showcase promising results for semiconductor 2D quantum dots and artificial graphene systems, where the band structure can be tuned through, e.g., Kekulé distortion.

cond-mat.mtrl-sci↗

arXiv2021

From Branched Flow to Superwires in Periodic Potentials

We report unexpected classical and quantum dynamics of a wave propagating in a periodic potential in high Brilloiun zones. Branched flow appears at wavelengths shorter than the typical length scale of the ordered periodic structure and for energies above the potential barrier. The strongest branches remain stable indefinitely and may create linear dynamical channels, wherein waves are not confined directly by potential walls as electrons in ordinary wires, but rather indirectly and more subtly by dynamical stability. We term these superwires, since they are associated with a superlattice.

quant-ph↗

arXiv2020

Dynamical Heart Beat Correlations during Running

Fluctuations of the human heart beat constitute a complex system that has been studied mostly under resting conditions using conventional time series analysis methods. During physical exercise, the variability of the fluctuations is reduced, and the time series of beat-to-beat RR intervals (RRIs) become highly non-stationary. Here we develop a dynamical approach to analyze the time evolution of RRI correlations in running across various training and racing events under real-world conditions. In particular, we introduce dynamical detrended fluctuation analysis and dynamical partial autocorrelation functions, which are able to detect real-time changes in the scaling and correlations of the RRIs as functions of the scale and the lag. We relate these changes to the exercise intensity quantified by the heart rate (HR). Beyond subject-specific HR thresholds the RRIs show multiscale anticorrelations with both universal and individual scale-dependent structure that is potentially affected by the stride frequency. These preliminary results are encouraging for future applications of the dynamical statistical analysis in exercise physiology and cardiology, and the presented methodology is also applicable across various disciplines.

physics.data-an↗

arXiv2019

Fiend -- Finite Element Quantum Dynamics

We present Fiend - a simulation package for three-dimensional single-particle time-dependent Schrödinger equation for cylindrically symmetric systems. Fiend has been designed for the simulation of electron dynamics under inhomogeneus vector potentials such as in nanostructures, but it can also be used to study, e.g., nonlinear light-matter interaction in atoms and linear molecules. The light-matter interaction can be included via the minimal coupling principle in its full rigour, beyond the conventional dipole approximation. The underlying spatial discretization is based on the finite element method (FEM), and time-stepping is provided either via the generalized-α or Crank-Nicolson methods. The software is written in Python 3.6, and it utilizes state-of-the-art linear algebra and FEM backends for performance-critical tasks. Fiend comes along with an extensive API documentation, a user guide, simulation examples, and allows for easy installation via Docker or the Python Package Index.

physics.comp-ph↗

arXiv2019

Fundamental gaps of quantum dots on the cheap

We show that the fundamental gaps of quantum dots can be accurately estimated at the computational effort of a standard ground-state calculation supplemented with a non self-consistent step of negligible cost, all performed within density-functional theory at the level of the local-density approximation.

physics.comp-ph↗

arXiv2016

Optimal control of photoelectron emission by realistic waveforms

Recent experimental techniques in multicolor waveform synthesis allow the temporal shaping of strong femtosecond laser pulses with applications in the control of quantum mechanical processes in atoms, molecules, and nanostructures. Prediction of the shapes of the optimal waveforms can be done computationally using quantum optimal control theory (QOCT). In this work we demonstrate the control of above-threshold photoemission of one-dimensional hydrogen model with pulses feasible for experimental waveform synthesis.By mixing different spectral channels and thus lowering the intensity requirements for individual channels, the resulting optimal pulses can extend the cutoff energies by at least up to 50\% and bring up the electron yield by several orders of magnitude. Insights into the electron dynamics for optimized photoelectron emission are obtained with a semiclassical two-step model.

physics.atom-ph↗

arXiv2016

Strong quantum scarring by local impurities

We discover and characterize strong quantum scars, or eigenstates resembling classical periodic orbits, in two-dimensional quantum wells perturbed by local impurities. These scars are not explained by ordinary scar theory, which would require the existence of short, moderately unstable periodic orbits in the perturbed system. Instead, they are supported by classical resonances in the unperturbed system and the resulting quantum near-degeneracy. Even in the case of a large number of randomly scattered impurities, the scars prefer distinct orientations that extremize the overlap with the impurities. We demonstrate that these preferred orientations can be used for highly efficient transport of quantum wave packets across the perturbed potential landscape. Assisted by the scars, wave-packet recurrences are significantly stronger than in the unperturbed system. Together with the controllability of the preferred orientations, this property may be very useful for quantum transport applications.

quant-ph↗