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arXiv · 1405.1549

Self-organization in foliated phase space: Construction of a scale hierarchy by adiabatic invariants of magnetized particles

Z. Yoshida·S. M. Mahajan
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Abstract

Adiabatic invariants foliate phase space, and impart a macro-scale hierarchy by separating microscopic variables. On a macroscopic leaf, long-scale ordered structures are created while maximizing entropy. A plasma confined in a magnetosphere is invoked for unveiling the organizing principle ---in the vicinity of a magnetic dipole, the plasma self-organizes to a state with a steep density gradient. The resulting nontrivial structure has maximum entropy in an appropriate, constrained phase space. One could view such a phase space as a leaf foliated in terms of Casimir invariants ---adiabatic invariants measuring the number of quasi-particles (macroscopic representation of periodic motions) are identified as the relevant Casimir invariants. The density clump is created in response to the inhomogeneity of the energy level (frequency) of quasi-particles.

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Z. Yoshida, S. M. Mahajan. 2014-10-11. Self-organization in foliated phase space: Construction of a scale hierarchy by adiabatic invariants of magnetized particles. https://doi.org/10.1093/ptep%2Fptu104

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