Related papers: Slow diffusion and Thouless localization criterion…
While the high-temperature spin diffusion in spin chains with random local fields has been the subject of numerous studies concerning the phenomenon of many-body localization (MBL), the energy diffusion in the same models has been much less…
We study the transport and equilibration properties of a classical Heisenberg chain, whose couplings are random variables drawn from a one-parameter family of power-law distributions. The absence of a scale in the couplings makes the system…
We study high temperature spin transport in a disordered Heisenberg chain in the ergodic regime. By employing a density matrix renormalization group technique for the study of the stationary states of the boundary-driven Lindblad equation…
We study transport in spin chains employing the Thouless approach based on the level sensitivity to the boundary conditions, $R$. Although spin transport in the integrable easy-axis XXZ model is diffusive, corresponding $R$ is much closer…
Understanding the physics of the integrable spin-1/2 XXZ chain has witnessed substantial progress, due to the development and application of sophisticated analytical and numerical techniques. In particular, infinite-temperature…
Using an analogy between the conductivity tensor of electronic systems and the spin stiffness tensor of spin systems, we introduce the concept of the Thouless number $g_0$ and the dimensionless frequency dependent conductance $g( \omega )$…
We study the ergodic side of the many-body localization transition in its standard model, the disordered Heisenberg quantum spin chain. We show that the Thouless energy, extracted from long-range spectral statistics and the power-spectrum…
The isotropic Heisenberg chain represents a particular case of an integrable many-body system exhibiting superdiffusive spin transport at finite temperatures. Here, we show that this model has distinct properties also at finite…
We investigate transport in several translationally invariant spin-1/2 chains in the limit of high temperatures. We concretely consider spin transport in the anisotropic Heisenberg chain, the pure Heisenberg chain within an alternating…
As part of condensed-matter physics, the field of Anderson localization concerns the study of conductance of electrons in a random medium. We summarize and explain the results obtained in "A new numerical approach to Anderson…
We address spin transport in the easy-axis Heisenberg spin chain subject to integrability-breaking perturbations. We find that spin transport is subdiffusive with dynamical exponent $z=4$ up to a timescale that is parametrically long in the…
We extend beyond the Euler scales the hydrodynamic theory for quantum and classical integrable models developed in recent years, accounting for diffusive dynamics and local entropy production. We review how the diffusive scale can be…
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…
We consider a nonlinear drift-diffusion system for multiple charged species in a porous medium in 2D and 3D with periodic microstructure. The system consists of a transport equation for the concentration of the species and Poisson's…
A system of drift-diffusion equations with electric field under Dirichlet boundary conditions is analyzed. The system of strongly coupled parabolic equations for particle density and spin density vector describes the spin-polarized…
We study the disordered Heisenberg spin chain, which exhibits many body localization at strong disorder, in the weak to moderate disorder regime. A continued fraction calculation of dynamical correlations is devised, using a variational…
The dynamics of spin at finite temperature in the spin-1/2 Heisenberg chain was found to be superdiffusive in numerous recent numerical and experimental studies. Theoretical approaches to this problem have emphasized the role of nonabelian…
We study high temperature spin transport in a disordered Heisenberg chain in the ergodic regime when bulk dephasing is present. We find that while dephasing always renders the transport diffusive, there is nonetheless a remnant of the…
We study the discrete nonlinear Schr\"oinger equation with weak disorder, focusing on the regime when the nonlinearity is, on the one hand, weak enough for the normal modes of the linear problem to remain well resolved, but on the other,…
We address the nature of spin transport in the integrable XXZ spin chain, focusing on the isotropic Heisenberg limit. We calculate the diffusion constant using a kinetic picture based on generalized hydrodynamics combined with Gaussian…