Related papers: Breakdown of superdiffusion in perturbed quantum i…
We investigate diffusion-driven instabilities in a FitzHugh-Nagumo reaction-diffusion system with superdiffusive transport, modeled by fractional Laplacian operators with different diffusion orders for the activator and the inhibitor. A…
Understanding the timescales associated with relaxation to equilibrium in closed quantum many-body systems is one of the central focuses in the study of their non-equilibrium dynamics. At late times, these relaxation processes exhibit…
Non-Hermitian systems exhibit a distinctive type of wave propagation, due to the intricate interplay of non-Hermiticity and disorder. Here, we investigate the spreading dynamics in the archetypal non-Hermitian Aubry-Andr\'e model with…
We study transport in a one-dimensional boundary-driven Anderson insulator (the XX spin chain with onsite disorder) with randomly positioned onsite dephasing, observing a transition from diffusive to subdiffusive spin transport below a…
Isotropic integrable spin chains such as the Heisenberg model feature superdiffusive spin transport belonging to an as-yet-unidentified dynamical universality class closely related to that of Kardar, Parisi, and Zhang (KPZ). To determine…
Anomalous finite-temperature transport has recently been observed in numerical studies of various integrable models in one dimension; these models share the feature of being invariant under a continuous non-abelian global symmetry. This…
We establish rigorously that transport is slower than diffusive for a class of disordered one-dimensional Hamiltonian chains. This is done by deriving quantitative bounds on the variance in equilibrium of the energy or particle current, as…
We study the evolution of two-point correlation functions of one-dimensional Bose-Hubbard model in the semiclassical regime in the framework of Truncated Wigner Approximation (TWA) with quantum jumps as first-order corrections. At early…
This review summarizes recent advances in our understanding of anomalous transport in spin chains, viewed through the lens of integrability. Numerical advances, based on tensor-network methods, have shown that transport in many canonical…
Emergent hydrodynamics (EHD) bridges short-time unitarity with late-time thermodynamics, universal transport phenomena characterize the manner and speed of transport and thermalization. Typical non-integrable systems with few conserved…
We formulate a scaling theory for the long-time diffusive motion in a space occluded by a high density of moving obstacles in dimensions 1, 2 and 3. Our tracers diffuse anomalously over many decades in time, before reaching a diffusive…
Generic short-range interacting quantum systems with a conserved quantity exhibit universal diffusive transport at late times. We employ non-equilibrium quantum field theory and semi-classical phase-space simulations to show how this…
We analyze the stability of spin spiral states in the two-dimensional Heisenberg model. Our analysis reveals that the SU(2) symmetric point hosts a dynamic instability that is enabled by the existence of energetically favorable transverse…
We show that any interacting integrable model possesses a class of initial states for which the leading corrections to ballistic transport are subdiffusive rather than diffusive. These initial states are natural to realize experimentally…
We report a systematic study of finite-temperature spin transport in quantum and classical one-dimensional magnets with isotropic spin interactions, including both integrable and non-integrable models. Employing a phenomenological framework…
We numerically study spin transport and nonequilibrium spin-density profiles in a clean one-dimensional spin-chain with long-range interactions, decaying as a power-law,$r^{-\alpha}$ with distance. We find two distinct regimes of transport:…
A model for anomalous transport of tracer particles diffusing in complex media in two dimensions is proposed. The model takes into account the characteristics of persistent motion that active bath transfer to the tracer, thus the model…
The diffusive transport in two-dimensional incompressible turbulent fields is investigated with the aid of high-quality direct numerical simulations. Three classes of turbulence spectra that are able to capture both short and long-range…
The conventional wisdom suggests that transports of conserved quantities in non-integrable quantum many-body systems at high temperatures are diffusive. However, we discover a counterexample of this paradigm by uncovering anomalous…
Normal and anomalous diffusion are ubiquitous in many complex systems [1] . Here, we define a time and space generalized diffusion equation (GDE), which uses fractional-time derivatives and transformed d-path Laplacian operators on…