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Zero-Energy Flows and Vortex Patterns in Quantum Mechanics

Tsunehiro Kobayashi
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Abstract

We show that zero-energy flows appear in many particle systems as same as in single particle cases in 2-dimensions. Vortex patterns constructed from the zero-energy flows can be investigated in terms of the eigenstates in conjugate spaces of Gel'fand triplets. Stable patterns are written by the superposition of zero-energy eigenstates. On the other hand vortex creations and annihilations are described by the insertions of unstable eigenstates with complex-energy eigenvalues into the stable patterns. Some concrete examples are presented in the 2-dimensional parabolic potential barrier case. %, i.e., $-m γ^2 (x^2+y^2)/2$. We point out three interesting properties of the zero-energy flows; (i) the absolute economy as for the energy consumption, (ii) the infinite variety of the vortex patterns, and (iii) the absolute stability of the vortex patterns .

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Tsunehiro Kobayashi. 2003-02-20. Zero-Energy Flows and Vortex Patterns in Quantum Mechanics. https://doi.org/10.1088/0031-8949%2F70%2F6%2F001

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