Approximate ground state of a confined Coulomb anyon gas in an external magnetic field

Abstract

We derive an analytic, albeit approximate, expression for the ground state energy of N Coulomb interacting anyons with fractional statistics nu, 0<= |nu| <= 1, confined in a two-dimensional well (with characteristic frequency omega_0 ) and subjected to an external magnetic field (with cyclotron frequency omega_c ). We apply a variational principle combined with a regularization procedure which consists of fitting a cut-off parameter to existing exact analytical results in the non-interacting case, and to numerical calculations for electrons in quantum dots in the interacting case. The resulting expression depends upon parameters of the system |nu|, N, omega_0, r_0, a_B and omega_c, where r_0 represents a characteristic unit length and a_B the Bohr radius. Validity of the result is critically assessed by comparison with exact, approximate, and numerical results from the literature.

20 pages, 5 figures, published in Phys. Rev. B 68, 165105 (2003)

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• Coupled quantum dots as quantum gates
• Addition Spectra of Quantum Dots in Strong Magnetic Fields
• Equation of State of an Anyon Gas in a Strong Magnetic Field
• Diffusion Monte Carlo study of circular quantum dots
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• Nanoscale Phenomenology from Visualizing Pair Formation Experiment
• Complex diffusion Monte-Carlo method: test by the simulation of the 2D fermions