Equilibria and dynamics of two coupled chains of interacting dipoles.

We explore the energy transfer dynamics in an array of two chains of identical rigid interacting dipoles. Varying the distance b between the two chains of the array, a crossover between two different ground-state (GS) equilibrium configurations is observed. Linearizing around the GS configurations, we verify that interactions up to third nearest neighbors should be accounted to accurately describe the resulting dynamics.

Characterizing a transition from limited to unlimited diffusion in energy for a time-dependent stochastic billiard.

We explore Fermi acceleration in a stochastic oval billiard which shows unlimited to limited diffusion in energy when passing from the free to the dissipative case. We provide evidence for a transition from limited to unlimited energy growth taking place while detuning the corresponding restitution coefficient responsible for the degree of dissipation. A corresponding order parameter is suggested, and its susceptibility is shown to diverge at the critical point.

Quantum Phases from Competing Van der Waals and Dipole-Dipole Interactions of Rydberg Atoms.

Competing short- and long-range interactions represent distinguished ingredients for the formation of complex quantum many-body phases. Their study is hard to realize with conventional quantum simulators. In this regard, Rydberg atoms provide an exception as their excited manifold of states have both density-density and exchange interactions whose strength and range can vary considerably.

Evolution of discrete symmetries.

Symmetries are known to dictate important physical properties and can be used as a design principle in particular in wave physics, including wave structures and the resulting propagation dynamics. Local symmetries, in the sense of a symmetry that holds only in a finite domain of space, can be either the result of a self-organization process or a structural ingredient into a synthetically prepared physical system. Applying local symmetry operations to extend a given finite chain we show that the resulting one-dimensional lattice consists of a transient followed by a subsequent periodic behavior.

Chaos and thermalization in a classical chain of dipoles.

We explore the connection between chaos, thermalization, and ergodicity in a linear chain of N interacting dipoles. Starting from the ground state, and considering chains of different numbers of dipoles, we introduce single site excitations with excess energy ΔK. The time evolution of the chaoticity of the system and the energy localization along the chain is analyzed by computing, up to a very long time, the statistical average of the finite-time Lyapunov exponent λ(t) and the participation ratio Π(t).

Synthetic Dimension-Induced Conical Intersections in Rydberg Molecules.

We observe a series of conical intersections in the potential energy curves governing both the collision between a Rydberg atom and a ground-state atom and the structure of Rydberg molecules. By employing the electronic energy of the Rydberg atom as a synthetic dimension we circumvent the von Neumann-Wigner theorem. These conical intersections can occur when the Rydberg atom's quantum defect is similar in size to the electron-ground-state atom scattering phase shift divided by π, a condition satisfied in several commonly studied atomic species.

External-field-induced dynamics of a charged particle on a closed helix.

We investigate the dynamics of a charged particle confined to move on a toroidal helix while being driven by an external time-dependent electric field. The underlying phase space is analyzed for linearly and circularly polarized fields. For small driving amplitudes and a linearly polarized field, we find a split up of the chaotic part of the phase space, which prevents the particle from inverting its direction of motion.

Entangling Lattice-Trapped Bosons with a Free Impurity: Impact on Stationary and Dynamical Properties.

We address the interplay of few lattice trapped bosons interacting with an impurity atom in a box potential. For the ground state, a classification is performed based on the fidelity allowing to quantify the susceptibility of the composite system to structural changes due to the intercomponent coupling. We analyze the overall response at the many-body level and contrast it to the single-particle level.

Tunable order of helically confined charges.

We investigate a system of equally charged Coulomb-interacting particles confined to a toroidal helix in the presence of an external electric field. Due to the confinement, the particles experience an effective interaction that oscillates with the particle distance and allows for the existence of stable bound states, despite the purely repulsive character of the Coulomb interaction. We design an order parameter to classify these bound states and use it to identify a structural crossover of the particle order, occurring when the electric field strength is varied.

Effective Three-Body Interactions in Cs(6s)-Cs(nd) Rydberg Trimers.

Ultralong-range Rydberg trimer molecules are spectroscopically observed in an ultracold gas of Cs(nd_{3/2}) atoms. The anisotropy of the atomic Rydberg state allows for the formation of angular trimers, whose energies may not be obtained from integer multiples of dimer energies. These nonadditive trimers coexist with Rydberg dimers.

Compact localized states of open scattering media: a graph decomposition approach for an ab initio design.

We study the compact localized scattering resonances of periodic and aperiodic chains of dipolar nanoparticles by combining the powerful equitable partition theorem (EPT) of a graph theory with the spectral dyadic Green's matrix formalism for the engineering of embedded quasi-modes in non-Hermitian open scattering systems in three spatial dimensions. We provide the analytical and numerical design of the spectral properties of compact localized states in electromagnetically coupled chains and establish a connection with the distinctive behavior of bound states in the continuum. Our results extend the concept of compact localization to the scattering resonances of open systems with an arbitrary aperiodic order beyond tight-binding models, and are relevant for the efficient design of novel photonic and plasmonic metamaterial architectures for enhanced light-matter interaction.

Driven power-law oscillator.

We explore the nonlinear dynamics of a driven power-law oscillator whose shape varies periodically in time covering a broad spectrum of anharmonicities. Combining weak and strong confinement of different geometry within a single driving period, the phase space allows not only for regular and chaotic bounded motion but in particular also for an unbounded motion which exhibits an exponential net growth of the corresponding energies. Our computational study shows that phases of motion with energy gain and loss as well as approximate energy conservation alternate within a single period of the oscillator and can be assigned to the change of the underlying confinement geometry.

Energy transfer mechanisms in a dipole chain: From energy equipartition to the formation of breathers.

We study the energy transfer in a classical dipole chain of N interacting rigid rotating dipoles. The underlying high-dimensional potential energy landscape is analyzed in particular by determining the equilibrium points and their stability in the common plane of rotation. Starting from the minimal energy configuration, the response of the chain to excitation of a single dipole is investigated.

Dimensional coupling-induced current reversal in two-dimensional driven lattices.

We show that the direction of directed particle transport in a two-dimensional ac-driven lattice can be dynamically reversed by changing the structure of the lattice in the direction perpendicular to the applied driving force. These structural changes introduce dimensional coupling effects, the strength of which governs the timescale of the current reversals. The underlying mechanism is based on the fact that dimensional coupling allows the particles to explore regions of phase space which are inaccessible otherwise.

Simultaneous Control of Multispecies Particle Transport and Segregation in Driven Lattices.

We provide a generic scheme to separate the particles of a mixture by their physical properties like mass, friction, or size. The scheme employs a periodically shaken two-dimensional dissipative lattice and hinges on a simultaneous transport of particles in species-specific directions. This selective transport is achieved by controlling the late-time nonlinear particle dynamics, via the attractors embedded in the phase space and their bifurcations.

Edge modes of scattering chains with aperiodic order.

We study the scattering resonances of one-dimensional deterministic aperiodic chains of electric dipoles using the vectorial Green's matrix method, which accounts for both short- and long-range electromagnetic interactions in open scattering systems. We discover the existence of edge-localized scattering states within fractal energy gaps with characteristic topological band structures. Notably, we report and characterize edge-localized modes in the classical wave analogues of the Su-Schrieffer-Heeger (SSH) dimer model, quasiperiodic Harper and Fibonacci crystals, as well as in more complex Thue-Morse aperiodic systems.

Dynamical ion transfer between coupled Coulomb crystals in a double-well potential.

We investigate the nonequilibrium dynamics of coupled Coulomb crystals of different sizes trapped in a double well potential. The dynamics is induced by an instantaneous quench of the potential barrier separating the two crystals. Due to the intra- and intercrystal Coulomb interactions and the asymmetric population of the potential wells, we observe a complex reordering of ions within the two crystals as well as ion transfer processes from one well to the other.

Highly excited electronic image states of metallic nanorings.

We study electronic image states around a metallic nanoring and show that the interplay between the attractive polarization force and a repulsive centrifugal force gives rise to Rydberg-like image states trapped several nanometers away from the surface. The nanoring is modeled as a perfectly conducting isolated torus whose classical electrostatic image potential is derived analytically. The image states are computed via a two-dimensional finite-difference scheme as solutions of the effective Schrödinger equation describing the outer electron subject to this image potential.

Analysis of the classical phase space and energy transfer for two rotating dipoles with and without external electric field.

We explore the classical dynamics of two interacting rotating dipoles that are fixed in the space and exposed to an external homogeneous electric field. Kinetic energy transfer mechanisms between the dipoles are investigated by varying both the amount of initial excess kinetic energy of one of them and the strength of the electric field. In the field-free case, and depending on the initial excess energy, an abrupt transition between equipartition and nonequipartition regimes is encountered.

Diffusion and transport in locally disordered driven lattices.

We study the effect of disorder on the particle density evolution in a classical Hamiltonian driven lattice setup. If the disorder is localized within a finite sub-domain of the lattice, the emergence of strong tails in the density distribution which even increases towards larger positions is shown, thus yielding a highly non-Gaussian particle density evolution. As the key underlying mechanism, we identify the conversion between different components of the unperturbed systems mixed phase space which is induced by the disorder.

Freezing, accelerating, and slowing directed currents in real time with superimposed driven lattices.

We provide a generic scheme offering real-time control of directed particle transport using superimposed driven lattices. This scheme allows one to accelerate, slow, and freeze the transport on demand by switching one of the lattices subsequently on and off. The underlying physical mechanism hinges on a systematic opening and closing of channels between transporting and nontransporting phase space structures upon switching and exploits cantori structures which generate memory effects in the population of these structures.

Chaotic and ballistic dynamics in time-driven quasiperiodic lattices.

We investigate the nonequilibrium dynamics of classical particles in a driven quasiperiodic lattice based on the Fibonacci sequence. An intricate transient dynamics of extraordinarily long ballistic flights at distinct velocities is found. We argue how these transients are caused and can be understood by a hierarchy of block decompositions of the quasiperiodic lattice.

Nonlinear dynamics of atoms in a crossed optical dipole trap.

We explore the classical dynamics of atoms in an optical dipole trap formed by two identical Gaussian beams propagating in perpendicular directions. The phase space is a mixture of regular and chaotic orbits, the latter becoming dominant as the energy of the atoms increases. The trapping capabilities of these perpendicular Gaussian beams are investigated by considering an atomic ensemble in free motion.

Symmetries and transport in site-dependent driven quantum lattices.

We explore the quantum dynamics of particles in a spatiotemporally driven lattice. A powerful numerical scheme is developed which provides us with the Floquet modes and thus enables a stroboscopic propagation of arbitrary initial states. A detailed symmetry analysis represents the cornerstone for an intricate manipulation of the Floquet spectrum.

Spatiotemporal oscillation patterns in the collective relaxation dynamics of interacting particles in periodic potentials.

We demonstrate the emergence of self-organized structures in the course of the relaxation of an initially excited, dissipative, and finite chain of interacting particles in a periodic potential towards its many particle equilibrium configuration. Specifically, we observe a transition from an in phase correlated motion via phase randomized oscillations towards oscillations with a phase difference π between adjacent particles thereby yielding the growth of long time transient spatiotemporal oscillation patterns. Parameter modifications allow for designing these patterns, including steady states and even states that combine in phase and correlated out of phase oscillations along the chain.