Related papers: Non-local linear response in anomalous transport
Translation-invariant low-dimensional systems are known to exhibit anomalous heat transport. However, there are systems, such as the coupled-rotor chain, where translation invariance is satisfied, yet transport remains diffusive. It has…
It has been observed in many numerical simulations, experiments and from various theoretical treatments that heat transport in one-dimensional systems of interacting particles cannot be described by the phenomenological Fourier's law. The…
We investigate heat transport in various quantum spin chains, using the projector operator technique. We find that anomalous heat transport is linked not to the integrability of the Hamiltonian, but to whether it can be mapped to a model of…
We study anomalous transport in a one-dimensional system with two conserved quantities in presence of thermal baths. In this system we derive exact expressions of the temperature profile and the two point correlations in steady state as…
Using the Zwanzig projection-operator formalism, we derive a causal two-point spatiotemporal kernel for heat conduction, defined microscopically as a space-resolved equilibrium heat-flux time-correlation function, that encodes temporal…
Anomalous behavior is ubiquitous in subsurface solute transport due to the presence of high degrees of heterogeneity at different scales in the media. Although fractional models have been extensively used to describe the anomalous transport…
Transport and diffusion of heat in one dimensional (1D) nonlinear systems which {\it conserve momentum} is typically thought to proceed anomalously. Notable exceptions, however, exist of which the rotator model is a prominent case.…
This paper considers a large class of nonlinear integro-differential scalar equations which involve an anomalous diffusion (e.g. driven by a fractional Laplacian) and a non-local singular convolution kernel. Each of those singular equations…
We provide molecular dynamics simulation of heat transport and thermal energy diffusion in one-dimensional molecular chains with different interparticle pair potentials at zero and non-zero temperature. We model the thermal conductivity…
Anomalous diffusion constitutes a relation between tracer flux and tracer density gradient that is inherently nonlocal in space and/or time. Previous studies emphasize the non-Gaussian character of the tracer distribution that arises from…
We present a data-driven framework for the modeling of nonlocal heat transport in plasmas using a nonlocal theory informed neural network trained on kinetic Particle-in-Cell simulations that span both local and nonlocal regimes. The model…
Anomalous transport processes in which the variance of the distance travelled does not necessarily increase linearly with time are modelled using the formalism of continuous time random walks. We compute particle propagators which have the…
Heating of semiconductor devices limits their performance and lifetime, which must be addressed by thermal management starting at the heat source. It is a common assumption that the heat source and the resulting heat spot locally coincide,…
The kinetic equation of nonlocal and non-instantaneous character unifies the achievements of the transport in dense quantum gases with the Landau theory of quasiclassical transport in Fermi systems. Large cancellations in the off-shell…
We survey the recent progress in the study of heat kernels for a class of non-symmetric non-local operators. We focus on the existence and sharp two-sided estimates of the heat kernels and their connection to jump diffusions.
We propose a class of nonlocal diffusion systems on time-varying domains, and fully characterize their asymptotic dynamics in the asymptotically fixed, time-periodic and unbounded cases. The kernel is not necessarily symmetric or compactly…
Thermal transport is an important energy transfer process in nature. Phonon is the major energy carrier for heat in semiconductor and dielectric materials. In analogy to Ohm's law for electrical conductivity, Fourier's law is a fundamental…
We establish an approach to compute linear-response functions to elucidate heat waves and non-local thermal transport. The theory is able to describe the response of a system to external heat sources that are nonuniform in space and time.…
We apply the hierarchical equations of motion technique to analyzing nonequilibrium heat transport in a spin-boson type model, whereby heat transfer through a central spin is mediated by an intermediate pair of coupled harmonic oscillators.…
Despite the fact that conserved currents have dimensions that are determined solely by dimensional analysis (and hence no anomalous dimensions), Nature abounds in examples of anomalous diffusion in which $L\propto t^\gamma$, with $\gamma\ne…