Related papers: The chiral random walk: A quantum-inspired framewo…
Using elementary graph theory, we show the existence of interface chiral modes in random oriented scattering networks and discuss their topological nature. For particular regular networks (e.g. L-lattice, Kagome and triangular networks), an…
Chirality, or handedness, is a geometrical property denoting a lack of mirror symmetry. Chirality is ubiquitous in nature and is associated with the non-reciprocal interactions observed in complex systems ranging from biomolecules to…
Topological insulators are fascinating states of matter exhibiting protected edge states and robust quantized features in their bulk. Here, we propose and validate experimentally a method to detect topological properties in the bulk of…
Chiral edge states in quantum Hall effect are the paradigmatic example of the quasi-particle with chirality. In even space-time dimensions, the Nielsen-Ninomiya theorem strictly forbids the chiral states in physical isolation. The…
The random walk of photons in a tight-binding lattice is known to exhibit diffusive motion similar to classical random walks under decoherence, clearly illustrating the quantum-to-classical transition. In this study, we reveal that the…
Mathematical models of motility are often based on random-walk descriptions of discrete individuals that can move according to certain rules. It is usually the case that large masses concentrated in small regions of space have a great…
Over the past few years, topological insulators have taken center stage in solid state physics. The desire to tune the topological invariants of the bulk and thus control the number of edge states has steered theorists and experimentalists…
We consider stochastic dynamics of self-propelled particles with nonlocal normalized alignment interactions subject to phase lag. The role of the lag is to indirectly generate chirality into particle motion. To understand large scale…
Due to the unitary evolution, quantum walks display different dynamical features from that of classical random walks. In contrast to this expectation, in this work, we show that extreme events can arise in unitary dynamics and its…
The motion of self-propelled particles is modeled as a persistent random walk. An analytical framework is developed that allows the derivation of exact expressions for the time evolution of arbitrary moments of the persistent walk's…
Coined discrete-time quantum walks are studied using simple deterministic dynamical systems as coins whose classical limit can range from being integrable to chaotic. It is shown that a Loschmidt echo like fidelity plays a central role and…
We establish the theory of critical transport in amorphous Chern insulators and show that it lies beyond the current paradigm of topological criticality epitomized by the quantum Hall transitions. We consider models of Chern insulators on…
We investigate density fluctuations in three-dimensional chiral active fluids by using a simple model of helical self-propelled particles. Helical motion is generated by a constant angular velocity (or chiral torque) acting on the…
We introduce a continuous-time random walk model on an infinite multilayer structure inspired by transportation networks. Each layer is a copy of $\mathbb{R}^d$, indexed by a non-negative integer. A walker moves within a layer by means of…
We theoretically investigate the flow of the atomic excitations in a driven chiral-coupled atomic chain with nonreciprocal decay channels. This one-dimensional system allows infinite-range dipole-dipole interaction, and enables directional…
Though classical random walks have been studied for many years, research concerning their quantum analogues, quantum random walks, has only come about recently. Numerous simulations of both types of walks have been run and analyzed, and are…
Two-dimensional arrays of periodically driven qubits can host inherently dynamical topological phases with anomalous chiral edge dynamics. These chiral Floquet phases are formally characterized by a dynamical topological invariant, the…
Topological phases, edge states, and flat bands in synthetic quantum systems are a key resource for topological quantum computing and noise-resilient information processing. We introduce a scheme based on step-dependent quantum walks on…
We show through intensive simulations that the paradigmatic features of anomalous diffusion are indeed the features of a (continuous-time) random walk driven by two different Markovian hopping-trap mechanisms. If $p \in (0,1/2)$ and $1-p$…
Although quantum walks exhibit peculiar properties that distinguish them from random walks, classical behavior can be recovered in the asymptotic limit by destroying the coherence of the pure state associated to the quantum system. Here I…