A lattice field theory of spatiotemporal chaos
Author(s)
Liang, Han
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Abstract
Traditional periodic orbit theory enables the evaluation of statistical properties of finite-dimensional chaotic dynamical systems through the hierarchy of their periodic orbits. However, this approach becomes impractical for spatiotemporally chaotic systems over large or infinite spatial domains. As the spatial extents of these systems increase, the physical dimensions grow linearly, requiring exponentially more distinct periodic orbits to describe the dynamics to the same accuracy. To address this challenge, we propose a novel approach, describing spatiotemporally chaotic or turbulent systems using the chaotic field theories discretized over multi-dimensional spatiotemporal lattices. The 'chaos theory' is here recast in the language of statistical mechanics, field theory, and solid state physics, with traditional periodic orbit theory of low-dimensional, temporally chaotic dynamics a special, one-dimensional case. Using the lattice field theory formulation, we extend the temporal periodic orbit theory to spatiotemporal systems. The statistical properties of the systems are then evaluated via the spatiotemporal zeta function formulation in terms of their prime orbits.
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Date
2025-05-14
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Dissertation