Related papers: Mapping the Arnold web with a GPU-supercomputer
We find that Anderson localization ceases to exist when a random medium begins to move, but another type of fundamental quantum effect, Planckian diffusion $D = \alpha\hbar/m$, rises to replace it, with $\alpha $ of order of unity.…
We study the quantum Arnol'd diffusion for a particle moving in a quasi-1D waveguide bounded by a periodically rippled surface, in the presence of the time-periodic electric field. It was found that in a deep semiclassical region the…
We prove a form of Arnold diffusion in the a priori stable case. Let H0(p) + $\epsilon$H1($\theta$, p, t), $\theta$ $\in$ T n , p $\in$ B n , t $\in$ T = R/T be a nearly integrable system of arbitrary degrees of freedom n 2 with a strictly…
The analogy to heat diffusion has enhanced our understanding of information flow in graphs and inspired the development of Graph Neural Networks (GNNs). However, most diffusion-based GNNs emulate passive heat diffusion, which still suffers…
Diffusion has been widely used to describe a random walk of particles or waves, and it requires only one parameter -- the diffusion constant. For waves, however, diffusion is an approximation that disregards the possibility of interference.…
We prove the existence of diffusing solutions in the motion of a charged particle in the presence of an ABC magnetic field. The equations of motion are modeled by a 3DOF Hamiltonian system depending on two parameters. For small values of…
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…
We assume that a symplectic real-analytic map has an invariant normally hyperbolic cylinder and an associated transverse homoclinic cylinder. It is well known that such cylinder is preserved under small perturbations. We prove that for a…
We provide an illustration of a mechanism for Arnold's diffusion following a nonvariational approach and find explicit estimates for the diffusion time.
Diffusion models have achieved great success in synthesizing high-quality images. However, generating high-resolution images with diffusion models is still challenging due to the enormous computational costs, resulting in a prohibitive…
Inspired by random walk on graphs, diffusion map (DM) is a class of unsupervised machine learning that offers automatic identification of low-dimensional data structure hidden in a high-dimensional dataset. In recent years, among its many…
Efficient methods for generating samples of wave packet trajectories are needed to build machine learning models for quantum dynamics. However, simulating such data by direct integration of the time-dependent Schrodinger equation can be…
We propose a quantum algorithm for simulation of the Anderson transition in disordered lattices and study numerically its sensitivity to static imperfections in a quantum computer. In the vicinity of the critical point the algorithm gives a…
We created an efficient algorithm suitable for graphics processing units (GPUs) to perform Monte Carlo simulations of a subset of reaction-diffusion models. The algorithm uses techniques that are specific to GPU programming, and combines…
We introduce a variant of the Gatenby-Gawlinski model for acid-mediated tumor invasion, accounting for anisotropic and heterogeneous diffusion of the lactic acid across the surrounding healthy tissues. Numerical simulations are performed…
We discuss and demonstrate an unsupervised machine-learning procedure to detect topological order in quantum many-body systems. Using a restricted Boltzmann machine to define a variational ansatz for the low-energy spectrum, we sample wave…
Graph diffusion models achieve state-of-the-art performance in graph generation but suffer from quadratic complexity in the number of nodes -- and much of their capacity is wasted modeling the absence of edges in sparse graphs. Inspired by…
Modern graphics processing units (GPUs) provide impressive computing resources, which can be accessed conveniently through the CUDA programming interface. We describe how GPUs can be used to considerably speed up molecular dynamics (MD)…
Arnold's diffusion in quasi integrable hamiltonian systems occurs in exponentially large time. We study an initially hyperbolic system which admits diffusion in polynomial time.
Experimental quantum simulators have become large and complex enough that discovering new physics from the huge amount of measurement data can be quite challenging, especially when little theoretical understanding of the simulated model is…