The anyon fluid in the Bogoliubov approximation

Trugenberger, Carlo A.

doi:10.1103/physrevd.45.3807

Cited by 20 publications

(27 citation statements)

References 37 publications

(17 reference statements)

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“…However, we are concerned with the dependence when X ′ is near its critical value X ′ c . For ǫ considerably smaller than 1, the appropriate dependence onα can easily be seen from (18) to be quadratic, indicating that the MFA is justified ifα 2 ≪ 1. near fermions (19) In both cases, we recover the results obtained previously [6,7,8,9], but perhaps in a more trustworthy way since self-consistency was not a part of our argument.…”

Section: Anyons With Hard-disk Repulsionsupporting

confidence: 75%

Mean Field Approximation

2007

The Quantum Theory of Magnetism

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Some general features of the scattering of boson-based anyons with an added non-statistical interaction are discussed. Periodicity requirements of the phase shifts are derived, and used to illustrate the danger inherent in separating these phase shifts into the well-known pure Aharanov-Bohm phase shifts, and an additional set which arise due to the interaction. It is proven that the added phase shifts, although due to the non-statistical interaction, necessarily change as the statistical parameter is varied, keeping the interaction fixed. A hard-disk interaction provides a concrete illustration of these general ideas.

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Section: Anyons With Hard-disk Repulsionsupporting

confidence: 75%

Mean Field Approximation

2007

The Quantum Theory of Magnetism

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“…Thus, the particles uniformly fill up the Landau levels determined by this mean magnetic field. The quadratic fluctuations around the mean field can be described [9] by using the Dashen-Sharp current algebra formalism [10]; their diagonalization by a Bogoliubov transformation produces a relativistic longitudinal excitation at low energy, as in the familiar case of the superfluid [11]. This is by far the simplest method for describing anyon superfluidity [6].…”

Section: Introductionmentioning

confidence: 99%

Spontaneous symmetry breaking in the non-abelian anyon fluid

Cappelli

Valtancoli

1995

Nuclear Physics B

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We study the theory of non-relativistic matter coupled to the non-Abelian U(2) Chern-Simons gauge eld in (2+1) dimensions. We adopt the mean eld approximation in the current-algebra formulation already applied to the Abelian anyons. We rst show that this method is able to describe both \boson-based" and \fermion-based" anyons and yields consistent results over the whole range of fractional statistics. In the nonAbelian theory, w e nd a superuid (and superconductive) phase, which is smoothly connected with the Abelian superuid phase originally discovered by Laughlin. The characteristic massless excitation is the Goldstone particle of the specic mechanism of spontaneous symmetry breaking. An additional massive mode is found by diagonalizing the non-local, non-Abelian Hamiltonian in the radial gauge.

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“…In the past 20 years, Aharonov-Bohm (A-B) effect, a topological non-local physical effect at the quantum level, has been of much interest in the studies of cosmic string [1], (2 + 1)-D gravity theories [2] and especially in the context of anyon [3], which has shed light on the understanding of the phenomenon of the fractional quantum Hall effect [4][5][6][7], superconductivity [7,8], repulsive Bose gases [9], and so forth. There are only a few models coupled to different potentials along with an A-B magnetic flux that can be solved exactly.…”

Section: Introductionmentioning

confidence: 99%

Semiclassical quantization for the spherically symmetric systems under an Aharonov-Bohm magnetic flux

2002

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The semiclassical quantization rule is derived for a system with a spherically symmetric potential V (r) ∼ r ν (−2 < ν < ∞) and an Aharonov-Bohm magnetic flux. Numerical results are presented and compared with known results for models with ν = −1, 0, 2, ∞. It is shown that the results provided by our method are in good agreement with previous results. One expects that the semiclassical quantization rule shown in this paper will provide a good approximation for all principle quantum number even the rule is derived in the large principal quantum number limit n ≫ 1. We also discuss the power parameter ν dependence of the energy spectra pattern in this paper.

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The anyon fluid in the Bogoliubov approximation

Cited by 20 publications

References 37 publications

Mean Field Approximation

Mean Field Approximation

Spontaneous symmetry breaking in the non-abelian anyon fluid

Semiclassical quantization for the spherically symmetric systems under an Aharonov-Bohm magnetic flux

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