Related papers: Dynamics in Systems with Modulated Symmetries
Symmetries rigidly delimit the landscape of quantum matter. Recently uncovered spatially modulated symmetries, whose actions vary with position, enable excitations with restricted mobility, while Lieb-Schultz-Mattis (LSM) type anomalies…
A transition from asymmetric to symmetric patterns in time-dependent extended systems is described. It is found that one dimensional cellular automata, started from fully random initial conditions, can be forced to evolve into complex…
Persistence in spatially extended dynamical systems (like coarsening systems and other nonequilibrium systems) is reviewed. We discuss, in particular, the spatial correlations in the persistent regions and their evolution in time in these…
Microscopic symmetries impose strong constraints on the elasticity of a crystalline solid. In addition to the usual spatial symmetries captured by the tensorial character of the elastic tensor, hidden non-spatial symmetries can occur…
Modulated symmetries are internal symmetries that are not invariant under spacetime symmetry actions. We propose a general way to describe the lattice translation modulated symmetries in 1+1D, including the non-invertible ones, via the…
Synthetic dimensions alter one of the most fundamental properties in nature, the dimension of space. They allow, for example, a real three-dimensional system to act as effectively four-dimensional. Driven by such possibilities, synthetic…
We propose a scaling hypothesis for pattern-forming systems in which modulation of the order parameter results from the competition between a short-ranged interaction and a long-ranged interaction decaying with some power $\alpha$ of the…
Most methods for modelling dynamics posit just two time scales: a fast and a slow scale. But many applications, including many in continuum mechanics, possess a wide variety of space-time scales; often they possess a continuum of space-time…
Flexible mechanical metamaterials possess repeating structural motifs that imbue them with novel, exciting properties including programmability, anomalous elastic moduli and nonlinear and robust response. We address such structures via…
We show that scaling arguments are very useful to analyze the dynamics of periodically modulated noisy systems. Information about the behavior of the relevant quantities, such as the signal-to-noise ratio, upon variations of the noise…
We investigate the macroscopic dynamics of sets of an arbitrary finite number of weakly amplitude-modulated pulses in a multidimensional lattice of particles. The latter are assumed to exhibit scalar displacement under pairwise,…
Spontaneous pattern formation in a variety of spatially extended nonlinear system always occurs through a modulation instability: homogeneous state of the system becomes unstable with respect to growing modulation modes. Therefore, the…
We study discrete Laplacians on two-dimensional lattices under modular iterations, focusing on the emergence of nontrivial large-scale patterns. While purely binary or constant modular sequences quickly collapse into strict periodicity, the…
The chiral Luttinger liquid develops quantum chaos as soon as a -- however slight -- nonlinear dispersion is introduced for the microscopic electronic degrees of freedom. For this nonlinear version of the model, we identify an infinite…
The presence of global conserved quantities in interacting systems generically leads to diffusive transport at late times. Here, we show that systems conserving the dipole moment of an associated global charge, or even higher moment…
We investigate the dynamics of two-dimensional assemblies of rod-shaped magnetic colloids under the influence of an external rotating magnetic field. Using Molecular Dynamics, we simulate the formation of patterns that emerge based on the…
The combination of protrusions and retractions in the movement of polarized cells leads to understand the effect of possible synchronisation between the two ends of the cells. This synchronisation, in turn, could lead to different dynamics…
We explore situations in which certain stochastic and high-dimensional deterministic systems behave effectively as low-dimensional dynamical systems. We define and study moment maps, maps on spaces of low-order moments of evolving…
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…
Imperfections in multimode systems lead to mode-mixing and interferences between propagating modes. Such disorder is typically characterized by a finite correlation time (in quantum evolution) or correlation length (in paraxial evolution).…