Non-Abelian Chern-Simons particles in an external magnetic field |
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| Institution: | 1. Department of Anesthesiology (M.H., H.W.), Columbia University, New York, USA;2. Department of Epidemiology (M.H.), Mailman School of Public Health, Columbia University, New York, USA;3. Department of Critical Care Medicine (H.W.), Sunnybrook Health Sciences Centre, Toronto, Ontario, Canada;4. Department of Anesthesiology and Pain Medicine and Interdepartmental Division of Critical Care Medicine (H.W.), University of Toronto, Toronto, Ontario, Canada;5. Department of Anesthesiology, Perioperative & Pain Medicine (R.A.A.), Stanford University, Stanford, California, USA;6. Division of Primary Care and Population Health (R.A.A.), Department of Medicine, Palliative Care Section, Stanford University, Stanford, California, USA |
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| Abstract: | The quantum mechanics and thermodynamics of SU(2) non-Abelian Chern-Simons particles (non-Abelian anyons) in an external magnetic field are addressed. We derive the N-body Hamiltonian in the (anti-) holomorphic gauge when the Hilbert space is projected onto the lowest Landau level of the magnetic field. In the presence of an additional harmonic potential, the N-body spectrum depends linearly on the coupling (statistics) parameter. We calculate the second virial coefficient and find that in the strong magnetic field limit it develops a step-wise behavior as a function of the statistics parameter, in contrast to the linear dependence in the case of Abelian anyons. For small enough values of the statistics parameter we relate the N-body partition functions in the lowest Landau level to these of SU(2) bosons and find that the cluster (and virial) coefficients dependence on the statistics parameter cancels. |
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