Related papers: Random-walk topological transition revealed via el…
The question of whether the topological insulators can host a stable nontrivial phase in the presence of spatially correlated disorder is a fundamental question of interest. Based on theoretical investigations, we analyze the effect of…
Stochastic processes are commonly used models to describe dynamics of a wide variety of nonequilibrium phenomena ranging from electrical transport to biological motion. The transition matrix describing a stochastic process can be regarded…
We investigate the emergence of charge waves and their temporal dynamics in one-dimensional Su-Schrieffer-Heeger (SSH) topological chains. Contrary to the conventional view that charge oscillations are suppressed in gapped topological…
Topological matter exhibits exotic properties yet phases characterized by large topological invariants are difficult to implement, despite rapid experimental progress. A promising route toward higher topological invariants is via engineered…
We study the typical behavior of random walkers on the microcanonical configuration space of mean-field disordered systems. Passive walks have an ergodicity-breaking transition at precisely the energy density associated with the dynamical…
We study continuous-time (variable speed) random walks in random environments on $\mathbb{Z}^d$, $d\ge2$, where, at time $t$, the walk at $x$ jumps across edge $(x,y)$ at time-dependent rate $a_t(x,y)$. The rates, which we assume stationary…
We study topological properties of phase transition points of one-dimensional topological quantum phase transitions by assigning winding numbers defined on closed circles around the gap closing points in the parameter space of momentum and…
We study a simple run-and-tumble random walk whose switching frequency from run mode to tumble mode and the reverse depend on a stochastic signal. We consider a particularly sharp, step-like dependence, where the run to tumble switching…
In the study of dynamical processes on networks, there has been intense focus on network structure -- i.e., the arrangement of edges and their associated weights -- but the effects of the temporal patterns of edges remains poorly…
Discrete quantum walks are dynamical protocols for controlling a single quantum particle. Despite of its simplicity, quantum walks display rich topological phenomena and provide one of the simplest systems to study and understand…
We present a probabilistic theory of random walks in turbid media with non-scattering regions. It is shown that important characteristics such as diffusion constants, average step lengths, crossing statistics and void spacings can be…
When confined to a topological environment consisting of a cycle coupled with a half-line, quantum walks exhibit long-term statistical tendencies which differ dramatically from the tendencies of classical random walks in the same…
Topological phase transitions track changes in topological properties of a system and occur in real materials as well as quantum engineered systems, all of which differ greatly in terms of dimensionality, symmetries, interactions, and…
Quantum topology categorizes physical systems in integer invariants, which are robust to some deformations and certain types of disorder. A prime example is the Su-Schrieffer-Heeger (SSH) model, which has two distinct topological phases,…
We report the first realization of a fractional topological phase in a fully unitary, noninteracting discrete-time quantum walk implemented on finite cyclic graphs. Using a single-coin split-step cyclic quantum walk (SCSS-CQW), we uncover…
Periodically-driven quantum systems can exhibit topologically non-trivial behaviour, even when their quasi-energy bands have zero Chern numbers. Much work has been conducted on non-interacting quantum-mechanical models where this kind of…
Random flux is commonly believed to be incapable of driving full metal-insulator transitions in non-interacting systems. Here we show that random flux can after all induce a full metal-band insulator transition in the two-dimensional…
The time evolution of a topological Su-Schrieffer-Heeger chain is analyzed through the statistics of speckle patterns. The emergence of topological edge states dramatically affects the dynamical fluctuations of the wavefunction. The…
We numerically investigate the characteristics of the long-time dynamics of a single-site wave-packet excitation in a disordered and nonlinear Su-Schrieffer-Heeger model. In the linear regime, as the parameters controlling the topology of…
In this work, we present a theory for topological phases for quantum systems on tree graphs. Conventionally, topological phases of matter have been studied in regular lattices, but also in quasicrystals and amorphous settings. We consider…