Path Laplacian operators and superdiffusive processes on graphs. II. Two-dimensional lattice

Abstract

In this paper we consider a generalized diffusion equation on a square lattice corresponding to Mellin transforms of the $k$-path Laplacian. In particular, we prove that superdiffusion occurs when the parameter $s$ in the Mellin transform is in the interval $(2,4)$ and that normal diffusion prevails when $s>4$.

References in corpus (15)

• Detecting arbitrary quantum errors via stabilizer measurements on a sublattice of the surface code
• Fermionic transport in a homogeneous Hubbard model: Out-of-equilibrium dynamics with ultracold atoms
• Levy Flight Superdiffusion: An Introduction
• Fractional excitations in the square-lattice quantum antiferromagnet
• Photon localization and Dicke superradiance in atomic gases
• Quantum Anomalous Hall Effect with Cold Atoms Trapped in a Square Lattice
• Experimental observation of controllable kinetic constraints in a cold atomic gas
• Mapping The Ultrafast Flow Of Harvested Solar Energy In Living Photosynthetic Cells
• Strongly Interacting Two-Dimensional Bose Gases
• Superradiance Transition in Photosynthetic Light-Harvesting Complexes
• Two-dimensional Rydberg gases and the quantum hard squares model
• Cooperative Robustness to Static Disorder: Superradiance and localization in a nanoscale ring to model natural light-harvesting systems
• Path Laplacian operators and superdiffusive processes on graphs. I. One-dimensional case
• Magnetic excitations and electronic interactions in Sr${}_2$CuTeO${}_6$: a spin-1/2 square lattice Heisenberg antiferromagnet
• Interaction effects on dynamical localization in driven helium

Cited by in corpus (11)

• Nonlocal network dynamics via fractional graph Laplacians
• Time and space generalized diffusion equation on graphs/networks
• Nonlocal PageRank
• Mathematical modeling for sustainable aphid control in agriculture via intercropping
• Metaplex networks: influence of the exo-endo structure of complex systems on diffusion
• Compatibility, embedding and regularization of non-local random walks on graphs
• Asymptotic spectra of large (grid) graphs with a uniform local structure
• Nonlocal diffusion of variable order on complex networks
• Indirect Influence on Network Diffusion
• Walk based Laplacians for Modeling Diffusion on Complex Networks
• Markov chain approach to anomalous diffusion on Newman-Watts networks