South African-German WE-Heraeus Seminar: Nonlinear dynamics and anomalous transport in low dimension

I discuss a class of dissipative quantum circuits and related Lindblad equations for which some dynamical properties and hydrodynamic behaviours can be determined exactly.

We will discuss a discrete model of an annular array of underdamped superconductor--ferromagnet—superconductor (SFS) phi-zero Josephson junctions. In this model, the anomalous $\varphi_0$ phase shift arises because of the superconducting proximity effect in the magnetic layer with broken inversion symmetry. It produces a bi-directional, direct coupling between the superconducting part of the applied bias current and the magnetic moment within the ferromagnetic material. Here, we include for the first time the effective field, felt by the magnetisation, due to the surface and fluxon-induced currents. We show that this additional coupling can lead to the occurrence of chaos and magnetisation `spin’ waves within the ferromagnetic interlayer. As in other models of Josephson metamaterials, the occurrence of chaos in the present model is not particularly desirable for potential spintronic applications; however, the magnetisation waves, which lead to a reduced critical current in the junction and change the branching structure of the zero-field steps, could potentially improve the efficiency of single-photon detectors for qubit readout.

In this presentation, the methods to construct self-sustained artificial electronic oscillators inspired by biological oscillators are explained. Some applications in the development of complete artificial units or hybrid systems for health care will be presented. The coupling of those bio-inspired electronic oscillators with micromechanical systems or with optoelectronic devices reveals complex dynamical states which be highlighted considering some results from theoretical and experimental investigations.

Many-body chaos is a default property of many-body systems; at the same time, near-integrable behaviour due to weakly interacting quasiparticles is ubiquitous throughout condensed matter at low temperature. There must therefore be a, possibly generic, crossover between these very different regimes. Here, we develop a theory encapsulating the notion of a cascade of lightcones seeded by sequences of scattering of weakly interacting harmonic modes as witnessed by a suitably defined chaos diagnostic (classical decorrelator) that measures the spatiotemporal profile of many-body chaos. Our numerics deals with the concrete case of a classical Heisenberg chain, for either sign of the interaction, at low temperatures where the short-time dynamics are well captured in terms of non-interacting spin waves. To model low-temperature dynamics, we use ensembles of initial states with randomly embedded point defects in an otherwise ordered background, which provides a controlled setting for studying the scattering events. The decorrelator exhibits a short-time integrable regime followed by an intermediate `scarred' regime of the cascade of lightcones in progress; these then overlap, leading to an avalanche of scattering events which finally yields the standard long-time signature of many-body chaos.

We numerically study the spreading of initially localized excitations in a one-dimensional stub lattice (a prototypical flat-band system) in the presence of disorder and nonlinearity. In the periodic limit, the lattice hosts a strictly flat band between two dispersive bands, while weak disorder lifts the flat-band degeneracy and produces a piecewise spectrum with finite gaps that close as disorder increases. By exploring the disorder-nonlinearity parameter space, we identify three dynamical regimes: weak chaos, strong chaos, and self-trapping. When disorder is sufficiently strong to close the frequency gaps, both the weak and strong chaos regimes exhibit subdiffusive spreading, characterized by power-law growth of the second moment and an algebraic decay of the finite-time maximum Lyapunov exponent. This behavior is consistent with the universal phenomenology observed in nonlinear disordered lattices, such as the disordered discrete nonlinear Schroedinger and Klein-Gordon models. For moderate disorder strengths, i.e., near the gap-closing threshold, we find that the presence of small frequency gaps does not significantly affect the spreading dynamics. Overall, our results extend the established phenomenology of chaos-induced subdiffusion in nonlinear disordered lattices to flat-band network geometries.

I will present a study of the spectral and dynamical properties of a collective SU(3) spin-exchange model inspired by cavity QED experiments. Focusing on the interplay between symmetry, chaos, and quantum fluctuations, we show a correspondence between the Hilbert space fragmentation structure of the quantum model and its semiclassical dynamics within the mean-field approximation. Using the two-particle irreducible effective action formalism, we extrapolate between the two regimes and study the beyond-mean-field dynamics via non-Markovian equations of motion that systematically include memory effects to describe the dynamics of single-particle Green's functions. We demonstrate that quantum fluctuations regularize chaotic instabilities and that a self-consistent inclusion of higher-order correlations is necessary to understand the interplay between chaos and quantum fluctuations. This talk comprises material from projects done in collaboration with Federico Balducci, Aleksandr Mikheev, Hossein Hosseinabadi, and Jamir Marino.

We aim to obtain a variational description of the Klein-Gordon oscillon reproducing its energy-frequency dependence outside the small-amplitude limit. The variational method employing the amplitude and width as collective coordinates leads to a dynamical system with unstable periodic orbits that blow up when perturbed. We propose a multiscale variational approach free from the blowup singularities. An essential feature of the proposed trial function is the inclusion of the third collective variable: a correction for the nonuniform phase growth. In addition to determining the parameters of the oscillon, the new approach detects the onset of its instability. A further refinement of our method uses the full anharmonic oscillation instead of substituting it with a truncated Fourier expansion. Finally, the variational results are compared to standing waves obtained by the numerical solution of a boundary-value problem on a two-dimensional periodic domain.

We consider the dynamics of domain growth in fractonic systems, which are characterized by the presence of excitations with restricted mobility. First, we set the stage by recalling how, in the absence of conserved quantities and following a quench into the ordered phase of the Ising model, the typical size of ordered domains grows in time as $R(t) \sim t^{1/2}$. Then, we review how the domain growth slows to $R(t) \sim t^{1/3}$ when the order parameter is conserved. Finally, we move to the fractonic setting, by requiring the conservation of the center of mass or higher moments of the order parameter. We show, both analytically and numerically, that conservation of the $m$-th multipole moment causes domains to grow anomalously slowly as $R(t) \sim t^{1/(2m+3)}$. This cascade of dynamical critical exponents characterizes a new family of non-equilibrium universality classes. REF: arXiv:2509.04556

We demonstrate the emergence of an intrinsic space-time crystalline order in a long ferromagnetic $\varphi _0$ Josephson junction on a topological insulator without any external periodic modulation. The presence of the exchange and Dzyaloshinskii–Moriya interactions in a ferromagnetic layer with broken inversion symmetry internally modulates the critical current due to the coupling between the magnetic moment and the Josephson phase. This breaks the time translation symmetry, leading to the appearance of the space-time crystalline pattern in the spatiotemporal dependence of the in-plane current, which oscillates with almost twice the ferromagnetic resonance frequency. In the limit where the critical current is not modulated internally, the space-time crystalline order does not occur. In this case, only when an external parametric modulation is applied, the system exhibits a typical classical discrete space-time crystalline order that oscillates at half of the modulation frequency. Considering the still-pending problem of experimental detection, we demonstrate that a recently developed magnetometry device, which visualizes the supercurrent flow at the nanoscale, can be used to detect space-time crystalline patterns in hybrid Josephson junctions experimentally.

Charge ordering induced by strong short-range repulsion in itinerant fermion systems typically follows a two-sites alternation pattern. However, the covariance matrix spectrum of the one dimensional, half-filled, spinless $t-V$ model reveals a post-Hartree-Fock picture at strong repulsion, with emergent four-site disruptions of the underlying staggered mean-field state. These disruptions are captured in a thermodynamically extensive manner by a compact four-fermion Coupled Cluster (doubles) state (CCS). Remarkably, all properties of this state may be computed analytically by combinatorial means, and also derived from an exactly solvable correlated hopping Hamiltonian. Furthermore, this Coupled Cluster state can be re-expressed as a low-rank Matrix Product State (MPS) with bond dimension exactly four. In addition, we unveil a hidden connection between this Coupled Cluster ansatz and a Rokhsar-Kivelson state (RKS), which is the ground state of a solvable parent quantum tetramer model. These results connect several areas in the study of correlated fermions have previously enjoyed limited synergy and make the case for further studies of the covariance matrix for correlated electron systems in which ground states have non-trivial unit-cell structure.

The common intuition is that chaotic quantum many-body systems exhibit diffusive transport and rapid thermalization. In this talk, I will present several recent results in kinetically constrained models, which exhibit various types of anomalous dynamics.

Superdiffusion is surprisingly easily observed even in systems without the integrability underpinning this phenomenon. Indeed, the classical Heisenberg chain -- one of the simplest many-body systems, and firmly believed to be non-integrable -- evinces a long-lived regime of anomalous, superdiffusive spin dynamics at finite temperature. Similarly, superdiffusion persists for long timescales, even at high temperature, for small perturbations around a related integrable model. Eventually, however, ordinary diffusion is believed to be asymptotically restored. We examine the timescales governing the lifetime of the superdiffusive regime, and argue that it diverges algebraically fast -- both in deviation from the integrable limit, and at low temperature, where we find $t^* \sim T^{-\zeta}$ with an exponent possibly as large as $\zeta = 8$. This can render the crossover to ordinary diffusion practically inaccessible.

A novel approach is proposed to characterize the dynamics of perturbed many-body integrable systems. Focusing on the paradigmatic case of the Toda chain under non-integrable Hamiltonian perturbations, this study introduces a method based the time evolution of the Lax eigenvalues $\lambda_\alpha$ as a proxy of the quasi-particles velocities and of the perturbed Toda actions. A set of exact equations of motion for the λα is derived that closely resemble those for eigenenergies of a quantum problem (also known as the Pechukas-Yukawa gas). Numerical simulations suggest that the invariant measure of such dynamics is basically the thermal density of states of the Toda lattice, regardless of the form of the perturbation.

In chaotic many-body dynamics the relaxation of local correlation functions to equilibrium is generally understood through the framework of the Eigenstate Thermalization Hypothesis (ETH). An extension of ETH to out-of-time-order correlation functions (OTOCs) has been recently proposed, based on the language of free probability and free cumulants. In this talk I will discuss minimal quantum circuit models for which this emergence of free probability can be understood on a purely dynamical level. In these models the OTOC dynamics can be recast as a Markovian process with eigenmodes corresponding to free cumulants, consistent with predictions from ETH. I will argue that the proposed framework applies to more realistic models of many-body quantum dynamics. (arXiv:2506.11197, arXiv:2509.08060)

This talk covers a few examples of how the dynamics of quantum systems in low dimensions can be unexpectedly different from simple expectations. These dynamical surprises can sometimes be observed in experiment. The easiest way to understand which quantities appear in the standard equations of classical hydrodynamics is to ask which quantities are conserved microscopically. As one-dimensional systems can have infinite lists of conserved quantities, we might expect their hydrodynamics to be modified; it turns out, for the case of spin chains, that different dynamical scaling behaviors in spin transport can exist even within the same integrable model. The most interesting case, the simple Heisenberg spin chain, has superdiffusive dynamics that have been observed in solids, in atomic emulators, and on quantum computers. We study the modifications of this behavior when integrability-breaking perturbations are present, as often happens in real systems. The last part of the talk concerns fully two-dimensional systems, where measurements from neutron scattering on magnetic insulators indicate complex dynamical behaviors that are not yet fully understood with theory or numerics.

I will discuss dynamics of magnetization transfer (or in general, transfer of a conserved charge) between bi-partition of an infinite (or large) spin lattice system, either classical or quantum. We conjecture that for integrable interacting dynamics the scaling of cummulants is anomalous - critical, in the sense that the growth exponents depend on the order of the cumulants. We illustrate the finding by numerical simulations of classical Landau Lifshitz and numerical/quantum simulations of Heisenberg spin chain, as well as a simple exactly solvable model of charged deterministic cellular automaton.

Determining whether a system is in an equilibrium or nonequilibrium state from simulations or experiments is a fundamental problem in statistical physics. In this talk I will discuss how this problem is normally approached by measuring the probability current in space and how it can be made more precise by defining statistical tests involving projections of the current. I will illustrate this point by considering a specific linear projection of the current for diffusion systems, related to the stochastic area, first studied by Paul Lévy in the 1940s for Brownian motion. This area is a good observable for testing the nonequilibrium or nonreversible nature of diffusions as it is a scalar and its statistics can be studied in a precise way using large deviation theory.

Time-periodic driving has become a valuable tool in Floquet engineering of many-body systems in the high frequency limit, but the understanding and utilization of resonances in many-body systems at lower frequencies still remains difficult. After a short discussion of the treatment of resonances with Floquet theory, an alternative mechanism of tuning resonant interactions between cold atoms is proposed, which is based on dynamically creating "Floquet bound states" using time-periodic fields. The resulting predictions explain recent experimental data and provide additional tuning possibilities. By adjusting amplitude, frequency and mean of the applied oscillating field it is possible to accurately choose location and width of clean scattering resonances over a wide range. This paves the road to a versatile toolbox of tailored interactions in setups with multiple species.

I will discuss simulation of many-body dynamic on Quantinuum's trapped-ion quantum computers, focusing in particular on light-induced superconductivity. While it is possible to induce superconductivity far above their critical temperature in actual material experiments, theoretical modelling of what exactly happens to the electronic structure during these processes is very hard. My main points will be (i) how one can simulate this problem with (trapped-ion) quantum computers, (ii) what is the state of the art and how does it compare to classical simulations and (iii) what needs to happen for quantum computers to capture actual experimental setups.

The dynamics of quantum many-body systems is characterized by quantum observables that are reconstructed from correlation functions at separate points in space and time. In dynamics with fast entanglement generation, however, quantum observables generally become insensitive to the details of the underlying dynamics at long times due to the effects of scrambling. To circumvent this limitation and enable access to relevant dynamics in experimental systems, repeated time-reversal protocols have been successfully implemented4. Here we experimentally measure the second-order out-of-time-order correlators (OTOC^(2)) on a superconducting quantum processor and find that they remain sensitive to the underlying dynamics at long timescales. Furthermore, OTOC^(2) manifests quantum correlations in a highly entangled quantum many-body system that are inaccessible without time-reversal techniques. This is demonstrated through an experimental protocol that randomizes the phases of Pauli strings in the Heisenberg picture by inserting Pauli operators during quantum evolution. The measured values of OTOC^(2) are substantially changed by the protocol, thereby revealing constructive interference between Pauli strings that form large loops in the configuration space. The observed interference mechanism also endows OTOC^(2) with high degrees of classical simulation complexity. These results, combined with the capability of OTOC^(2) in unravelling useful details of quantum dynamics, as shown through an example of Hamiltonian learning, indicate a viable path to practical quantum advantage.

We investigate a nonlinear non-Hermitian optical trimer composed of three lossy waveguides with complex couplings, where Kerr nonlinearity and non-Hermiticity jointly govern a rich variety of dynamical behaviors. The system supports stable stationary and oscillatory regimes over broad coupling–loss parameter ranges, while chaotic dynamics emerge through period-doubling bifurcations confirmed by Lyapunov spectra and semianalytical continuation of solutions. Focusing on the site-resolved dynamics, we uncover transitions between asymmetric and symmetric states mediated by a regime of chaotic hysteresis, in which the edge waveguides display localized chaotic activity. Upon symmetry restoration, chimera-like states arise, marked by frequency differentiation and spatial period doubling within the same minimal configuration. These results reveal how the interplay of dissipation, complex coupling, and nonlinearity orchestrates symmetry breaking and restoration, offering new insight and design principles for controlled symmetry management and dynamical state selection in compact non-Hermitian photonic platforms.

We explore the structure and dynamics of long-range interacting equally charged classical particles confined to a helix. The confinement renders the purely repulsive interaction in free space into an oscillating two-body force and potential which exhibits a variable number of minima and potential wells depending on the pitch and the radius of the helix [1]. We discuss few- and many-body systems and their peculiar behaviour due to this oscillating two-body interaction. For scattering from a helical inhomogeneity we unravel a coupling of the center of mass and relative motion which can lead to bound oppositely charged particles as well as their dissociation in a collision process [2]. We explore the formation of Wigner crystals for charged particles on a toroidal helix. Focusing on certain commensurate cases we show that the ground state undergoes a pitchfork bifurcation from the totally symmetric polygonic to a zig-zag-like configuration with increasing radius of the helix. Remarkably, we find that for a specific value of the helix radius, below the bifurcation point, the vibrational frequency spectrum collapses to a single frequency. This allows for an essentially independent small-amplitude motion of the individual particles and consequently localized excitations can propagate in time without significant spreading. Increasing the radius beyond the degeneracy point, the band structure is inverted, with the out-of-phase oscillation mode becoming lower in frequency than the mode corresponding to the center of mass motion [3]. Nonlinear excitations [4] as well as a pinned-to-sliding transition and structural crossover are explored as well [5]. Finally we discuss the unusual bending behaviour of charged helices [6], the tunable order of charges on a helix [7], formation and crossover of multiple helical chains [8] and the classical scattering and fragmentation of clusters of ions in helical confinement [9]. \\ References: $$$$ [1]P. Schmelcher, Europhysics Letters 95, 50005 (2011).$$$$ [2] A.V. Zampetaki, J. Stockhofe, S. Krönke, and P. Schmelcher, Physical Review E 88, 043202 (2013).$$$$ [3] A.V. Zampetaki, J. Stockhofe and P. Schmelcher, Physical Review A 91, 023409 (2015) $$$$ [4] A.V. Zampetaki, J. Stockhofe and P. Schmelcher, Physical Review E 92, 042905 (2015) $$$$ [5] A.V. Zampetaki, J. Stockhofe and P. Schmelcher, Physical Review E 95, 022205 (2017) $$$$ [6] A.V. Zampetaki, J. Stockhofe and P. Schmelcher, Physical Review E 97, 042503 (2018) $$$$ [7] A. Siemens and P. Schmelcher, Physical Review E 102, 012147 (2020) $$$$ [8] A. Siemens and P. Schmelcher, Journal of Physics A 55, 375205 (2022) $$$$ [9] A. Siemens and P. Schmelcher, Physical Review E 111, 014140 (2025) $$$$

We investigate the emergence of multifractality in the steady state of open quantum systems described by Lindbladian dynamics. When the corresponding mean-field classical dynamics are chaotic, the steady-state phase-space distribution exhibits genuine multifractal scaling. Using the Wehrl entropy as a probe, we quantify this multifractality and establish a direct connection to the Lyapunov dimension of the underlying strange attractor. Our results reveal a universal link between classical chaotic structures and quantum steady states, providing a new perspective on the interplay between dissipation, chaos, and multifractality in open quantum systems.

Gutzwiller semi-classical quantization, Boven-Sinai-Ruelle dynamical zeta functions for chaotic dynamical systems, statistical mechanics partition functions, and path integrals of quantum field theory are often presented in ways that make them appear as disjoint, unrelated theories. However, recent advances in describing fluid turbulence by its dynamical, deterministic Navier-Stokes underpinning, without any statistical assumptions, have led to a common field-theoretic description of both (low-dimension) chaotic dynamical systems, and (infinite-dimension) spatiotemporally turbulent flows. In this talk I will use a lattice discretized field theory in 1 and 1+1 dimensions to explain how temporal `chaos', `spatiotemporal chaos' and `quantum chaos' are profitably cast into the same field-theoretic framework.

This study focuses on the modulational dynamics of wave packets propagating in a one-dimensional (1D) hybrid Fermi-Pasta-Ulam-Tsingou / Klein-Gordon (FPUT-KG) type lattice chain, incorporating an arbitrary polynomial (i.e. quadratic and/or cubic) coupling anharmonicity, in the presence of a nonlinear on-site (substrate) potential. Applying Newell’s multiple scales method, we have derived a Nonlinear Schrodinger type equation (NLSE) and thus obtained analytical expressions for the dispersion and nonlinearity coefficients, in terms of the carrier wavenumber k and the intrinsic lattice configuration parameters. We explore the conditions for the focusing versus defocusing regime(s) to occur, which will determine the type of envelope soliton solutions to occur in either case. The analysis is extended to varying types of coupling anharmonicity and onsite potential nonlinearity, offering insight into the interplay between these factors and the system's dynamical behavior. We have focused in particular on extreme amplitude envelope modes (freak waves), e.g. of the Peregrine soliton type, and on their dependence on the various intrinsic system parameter values. Our results are relevant in various contexts where periodic systems (e.g. crystals) may occur. As a novel field of application, and an interesting by-product of our results, this research applies to the modeling of transverse dust-lattice waves in dusty plasma crystals. The substrate potential in this case is provided by electrostatic trapping in laboratory experiments, in combination with gravity, while the inter-site interaction potential is essentially of Debye-Hueckel type. This relation with be briefly discussed, and some preliminary results will be presented.

We construct a new family of exact periodic-wave and soliton solutions of the focusing and defocusing Ablowitz-Ladik equation, \[ i \frac{ \partial \psi_n}{\partial t} + \frac{\psi_{n+1}- 2 \psi_n + \psi_{n-1}}{h^2} + \sigma (\psi_{n+1}+ \psi_{n-1}) |\psi_n|^2 =0. \] Here $\psi_n=\psi_n(t)$ and $\sigma = \pm 1$. Unlike cnoidal waves and solitons that were obtained by earlier authors, our solutions have a phase variable with a nonlinear dependence on time and index. The absolute value of $\psi_n$ describes a sequence of crests and troughs propagating at a constant speed, while its phase velocity sustains periodic swings. Our construction hinges on the availability of a two-point map governing $|\psi_n|^2$; this map gives rise to standing waves centred arbitrarily relative to the lattice sites. The phase variable then forms a configuration allowing the wave to ``slide" down the lattice without experiencing radiation losses.

A crucial step in computing the spectrum of the maximally supersymmetric N=4 SYM theory arises by mapping its dilatation operator to the Hamiltonian of an integrable 1D spin chain. At one-loop, and in the scalar sector, this is simply the SO(6) XXX Heisenberg model, which can be easily diagonalised by the Bethe ansatz. After reviewing this correspondence, I will move on to the much more exotic, dynamical spin chains that one obtains in the case of N=2 superconformal quiver gauge theories, and the associated algebraic structures, such as twisted algebroids, which are needed to correctly capture their symmetries and understand their potential integrability properties. I will also discuss an alternative formulation of these spin chains as RSOS statistical models.

We investigate the dynamics of energy spreading and thermalisation in a one-dimensional nonlinear Klein-Gordon lattice with long-range interactions and disorder. Pairwise interaction terms in the potential are scaled by $1/r^{\alpha}$, where $r$ is the distance between lattice sites and $\alpha\ge0$ is a parameter which governs the range of interactions. Using measures such as the participation number, second moment and entropy, we study how energy spreading through the lattice depends on the range of interaction by varying the $\alpha$ parameter. In addition, we study the normal modes of the linearised system to understand their influence on the energy spreading dynamics.

(Note: The proceeding topic is under investigation, so the abstract is tentative and serves as a guide of the expected content.)$$$$ The analysis of Parity-Time (PT) symmetric systems has led to significant developments in photonics, Bose-Einstein condensates and quantum optics. A special subset of PT-Symmetric systems are integrable: they retain remarkable analytical properties of solvability and regularity, even though they are nonconservative. Of particular interest are finite discrete systems, known as oligomers – they can be used to model networks of optic fibres, or BECs confined to multiple potential wells. We prove the integrability of a novel PT-symmetric oligomer with gain and loss, obtained via nonlocal reduction of the Ablowitz-Ladik equations. This model exhibits a unique dynamical property known as nonlinear PT-symmetry restoration: In the linear limit, solutions blow up if the gain-loss parameter exceeds a critical value; by contrast, the fully nonlinear system remains bounded.

We investigate the steady state phase diagram of fermionic atoms subjected to an optical lattice and coupled to a high finesse optical cavity with photon losses. The coupling between the atoms and the cavity field is induced by a transverse pump beam. Taking fluctuations around the mean-field solutions into account, we find that a transition to a self-organized phase takes place at a critical value of the pump strength. In the self-organized phase the cavity field takes a finite expectation value and the atoms show a modulation in the density. Surprisingly, at even larger pump strengths two self-organized stable solutions of the cavity field and the atoms occur, signaling the presence of a bistability. We show that the bistable behavior is induced by the atoms-cavity fluctuations and is not captured by the mean-field approach.

Spontaneous symmetry breaking (SSB) refers to the phenomenon where a system transitions from a symmetric to an asymmetric state due to an infinitesimally small change in a parameter. In this talk, SSB will be explored in the context of optical Kerr resonators – nonlinear devices with wide-ranging applications, including frequency comb generation (optical "rulers"), gyroscopes, polarization control, random number generation, and all-optical computing. Designed for a general physics audience, this talk begins by introducing the fundamental concepts behind SSB and Kerr resonators. It then explores symmetry breaking between two – and later four – circulating light fields within these resonators. A central topic will be the formation and behavior of Temporal Cavity Solitons (TCS), localized pulses that persist within the resonator. Their role in SSB and in the creation of optical frequency combs will be discussed in detail. The talk will conclude with highlights from recent research, including the dynamics of coupled resonator systems, systems where TCS structures can interact – effectively “communicating” to create collective system behavior – and an introduction to the newly discovered faticon subset of solitons.

In this talk I will address nonlinear waves in non-reciprocal nonlinear lattices — systems with active couplings that break the symmetry between forward and backward propagation. In the linear regime, such lattices display both real and complex spectra, together with out-of-equilibrium effects such as unidirectional wave amplification, known as the non-Hermitian skin effect. We extend this effect into the nonlinear regime, demonstrating the emergence of nonlinear skin states that evolve from their linear counterparts. We then explore the interplay between non-reciprocity, topology, and nonlinearity, showing how this interaction generates nonlinear edge states with features distinct from those of the skin modes. Both families of modes correspond to spatially localized, standing nonlinear excitations that form at the system’s boundaries. Finally, we discuss their formation mechanisms, stability, and dynamics, emphasizing how these nonlinear localized states exhibit behaviours beyond those typically achievable in reciprocal or Hermitian lattices.

Flexible mechanical metamaterials (flexMMs) are architected structures capable of supporting large elastic deformations and exhibiting rich nonlinear behavior. A particularly intriguing feature arises from the existence of zero-energy kinks—localized transitions between distinct ground states that can form and propagate without energy cost. Enabled by careful topological design, these kinks bypass the Peierls–Nabarro barrier and exhibit unique long-lived dynamics. In this talk, I will discuss how zero-energy kinks emerge in flexMMs, their exceptional mobility, and their role in enabling robust and controllable reconfiguration. These properties open new avenues for phonon-mediated manipulation of nonlinear excitations and the design of adaptive, shape-morphing, and signal-transmitting metamaterials.

We extend the recently introduced [1] strong disorder renormalization group method in real space, well suited to study bond disordered antiferromagnetic power law coupled quantum spin chains, to study excited states, and finite temperature properties. First, we apply it to a short range coupled spin chain, which is defined by the model with power law interaction, keeping only interactions between adjacent spins. We show that the distribution of the absolute value of the couplings is the infinite randomness fixed point distribution. However, the sign of the couplings becomes distributed, and the number of negative couplings increases with temperature $T$. Next, we derive the Master equation for the power law long range interaction between all spins with power exponent $\alpha$. While the sign of the couplings is found to be distributed, the distribution of the coupling amplitude is given by the strong disorder distribution with finite width $2 \alpha$, with small corrections for $\alpha > 2$ [2]. Resulting finite temperature properties of both short and power law long ranged spin systems are derived, including the magnetic susceptibility, concurrence and entanglement entropy dynamics after a quantum quench[2]. We discuss the application of the strong disorder RG to quantum spin systems in higher dimensions.$$$$ [1] S. Kettemann, Strong Disorder Renormalization Group Method for Bond Disor- dered Antiferromagnetic Quantum Spin Chains with Long Range Interactions: Ground State Properties, https://arxiv.org/abs/2501.07298, submitted to PRB (2025).$$$$ [2] S. Kettemann, Strong Disorder Renormalization Group Method for Bond Disordered Antiferromagnetic Quantum Spin Chains with Long Ran- ge Interactions: Excited States and Finite Temperature Properties, https://arxiv.org/abs/2509.17828v1 (2025).

Transition metal dichalcogenides constitute a broad family of two-dimensional materials and they have attracted intense research interest due to their exceptional optoelectronic properties. The most known members of this family are MoS$_2$, MoSe$_2$, WS$_2$, and WSe$_2$. Lateral heterostructures consisting of one member of these materials in the interior which is surrounded by another member outside have been engineered, demonstrating tunable properties. The in-plane heat dissipation of such lateral heterostructures is investigated using molecular dynamics simulations. In our simulations, the central region of the material is thermally excited and then the excitation is allowed to dissipate and reach thermal equilibrium. Anomalous, non-exponential relaxation processes are observed, which are quantified in terms of characteristic relaxation times.

The Caputo fractional standard map (C-fSM) is a two-dimensional nonlinear map with memory given in action-angle variables $(I,\theta)$. It is parameterized by $K$ and $\alpha\in(1,2]$ which control the strength of nonlinearity and the fractional order of the Caputo derivative, respectively. In this work we perform a scaling study of the average squared action $\left< I^2 \right>$ along strongly chaotic orbits, i.e.~when~$K\gg1$. We numerically prove that $\left< I^2 \right>\propto n^\mu$ with $0\le\mu(\alpha)\le1$, for large enough discrete times $n$. That is, we demonstrate that the C-fSM displays subdiffusion for $1<\alpha<2$. Specifically, we show that diffusion is suppressed for $\alpha\to1$ since $\mu(1)=0$, while standard diffusion is recovered for $\alpha=2$ where $\mu(2)=1$. We describe our numerical results with a phenomenological analytical estimation.