13 citations · 111 across the 23 of their papers we have counts for
10 papers · 1 filter
Spectral decimation of the magnetic Laplacian on the Sierpinski gasket: Solving the Hofstadter-Sierpinski butterfly
Joe P. Chen, Ruoyu Guo
The magnetic Laplacian (also called the line bundle Laplacian) on a connected weighted graph is a self-adjoint operator wherein the real-valued adjacency weights are replaced by un…
Laplacian growth & sandpiles on the Sierpinski gasket: limit shape universality and exact solutions
Joe P. Chen, Jonah Kudler-Flam
We establish quantitative spherical shape theorems for rotor-router aggregation and abelian sandpile growth on the graphical Sierpinski gasket () when particles are launched fr…
From non-symmetric particle systems to non-linear PDEs on fractals
Joe P. Chen, Michael Hinz, Alexander Teplyaev
We present new results and challenges in obtaining hydrodynamic limits for non-symmetric (weakly asymmetric) particle systems (exclusion processes on pre-fractal graphs) converging…
Power dissipation in fractal AC circuits
Joe P. Chen, Luke G. Rogers, Loren Anderson +8
We extend Feynman's analysis of an infinite ladder circuit to fractal circuits, providing examples in which fractal circuits constructed with purely imaginary impedances can have c…
Singularly continuous spectrum of a self-similar Laplacian on the half-line
Joe P. Chen, Alexander Teplyaev
We investigate the spectrum of the self-similar Laplacian, which generates the so-called " random walk" on the integer half-line . Using the method of spectral de…
Fractal AC circuits and propagating waves on fractals
Eric Akkermans, Joe P. Chen, Gerald Dunne +2
We extend Feynman's analysis of the infinite ladder AC circuit to fractal AC circuits. We show that the characteristic impedances can have positive real part even though all the in…
Wave equation on one-dimensional fractals with spectral decimation and the complex dynamics of polynomials
Ulysses Andrews, Grigory Bonik, Joe P. Chen +2
We study the wave equation on one-dimensional self-similar fractal structures that can be analyzed by the spectral decimation method. We develop efficient numerical approximation t…
Spectral dimension and Bohr's formula for Schrodinger operators on unbounded fractal spaces
Joe P. Chen, Stanislav Molchanov, Alexander Teplyaev
We establish an asymptotic formulas for the eigenvalue counting function of the Schrödinger operator for some unbounded potentials on several types of unbounded fractal…
Heat kernels on 2d Liouville quantum gravity: a numerical study
Grigory Bonik, Joe P. Chen, Alexander Teplyaev
We numerically compute the heat kernel on a square lattice torus equipped with the measure corresponding to Liouville quantum gravity (LQG). From the on-diagonal heat kernel we ver…
Statistical mechanics of Bose gas in Sierpinski carpets
Joe P. Chen
We carry out a mathematically rigorous investigation into the equilibrium thermodynamics of massless and massive bosons confined in generalized Sierpinski carpets (GSCs), a class o…