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arXiv:1807.10904

Hamiltonians for Two-Anyon Systems

Michele Correggi, Luca Oddis

Published Jul 28, 2018• 4 citations
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Abstract

We study the well-posedness of the Hamiltonian of a system of two anyons in the magnetic gauge. We identify all the possible quadratic forms realizing such an operator for non-interacting anyons and prove their closedness and boundedness from below. We then show that the corresponding self-adjoint operators give rise to a one-parameter family of extensions of the naive two-anyon Schrödinger operator. We finally extend the results in presence of a two-body radial interaction.

DOI
10.48550/arxiv.1807.10904

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We study the well-posedness of the Hamiltonian of a system of two anyons in the magnetic gauge. We identify all the possible quadratic forms realizing such an operator for non-interacting anyons and prove their closedness and boundedness from below. We then show that the corresponding self-adjoint operators give rise to a one-parameter family of extensions of the naive two-anyon Schrödinger operator. We finally extend the results in presence of a two-body radial interaction.
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The Hamiltonian of a radial equation is defined on a half-line, and there is a close relation between its hermitian and the boundary condition of the wave functions at the origin. If the wave functions are nonvanishing and convergent at the origin, the Hamiltonian has a one-parameter family of self-adjoint extensions which are related with the vanishness of the radial probability current at the origin. In this paper the problem on the hermitian of the Hamiltonian of a radial equation is studied systematically. Some methods for determining the parameter for the fermion moving in the magnetic monopole field are discussed.