Abstract Details
Abstracts
Author: Evdokiya Kostadinova
Requested Type: Poster
Submitted: 2025-03-14 09:02:53
Co-authors: B. Howe, B. Andrew, J. Eskew, D. M. Orlov, E. Howell
Contact Info:
Auburn University
380 Duncan Drive
Auburn, AL 36849
United States
Abstract Text:
Koopman-von-Neumann theory is a framework that reformulates classical mechanics using the mathematics of quantum mechanics (i.e., linear algebra). In this formulation, instead of solving nonlinear dynamics in 6D phase space, one advances an infinite-dimensional linear operator, called the Koopman operator, acting on the Hilbert space, or the space of all possible states that can be measured for a given system. The Koopman operator is linear, advancing measurement functions of the system, and its spectral decomposition completely characterizes the behavior of the nonlinear system. Here we employ the same formulation to the linear Hamiltonian operator, which advances the total energy function in Hilbert space and whose spectrum yields information on the probability for the system to be in any given energy state.
Of specific interest is nonlinear (or anomalous) diffusion driven by non-local interactions and stochasticity. Anomalous diffusion can be studied as a linear problem in Hilbert space using a Hamiltonian with a fractional Laplacian kinetic term and random disorder potential term. We apply this method to the specific problem of electron diffusion in magnetized plasma with magnetic islands (toroidally reconnected magnetic flux tubes) that undergo topological changes due to island growth, island overlap, or structural bifurcation. Assuming that the electrons are highly magnetized, the spectral calculations are used to determine the possibility for sub-diffusive (trapped) or super-diffusive (passing) electron populations for various structural states of the magnetic field.
Work supported by DE-SC0023061, DE-SC0024547, DE-FG02-05ER54809, NSF-PHY-2308742, and NSF-PHY-2440328.
Characterization: 7.0
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