Parity Violation and the Mean Field Approximation for the Anyon Gas

Caenepeel, Didier; MacKenzie, R.

doi:10.1142/s021773239300163x

Cited by 4 publications

(13 citation statements)

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“…To make these ideas concrete, we can examine the case discussed in [10,12], where the potential was parameterized by a phase shift in the lowest partial wave.…”

Section: Generalitiesmentioning

confidence: 99%

“…In the latter part of the paper, we applied the "asymmetric-scattering" method discussed in [10] on anyons with a hard-disk repulsion in order to extract a criterion for the validity of the MFA. In agreement with previous works, we found that the statistical interaction must be weak both for anyons near bosons and near fermions, the quantitative criteria being given by (17) and (19).…”

Section: Anyons With Hard-disk Repulsionmentioning

confidence: 99%

“…In [10], this interaction was parameterized by introducing a phase shift put into the lowest partial wave. The MFA result was recovered for "generic" phase shift, i.e., for one not near a multiple of π.…”

mentioning

confidence: 99%

“…At a more profound level, it was conjectured [10] that for free anyons, the motion of a single anyon in an anyon gas is not correctly analyzed by regarding it as a sequence of individual scatterings (thus ignoring interference effects between subsequent scatterings).…”

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confidence: 99%

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Mean Field Approximation

Majlis¹

2000

The Quantum Theory of Magnetism

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“…To make these ideas concrete, we can examine the case discussed in [10,12], where the potential was parameterized by a phase shift in the lowest partial wave.…”

Section: Generalitiesmentioning

confidence: 99%

Section: Anyons With Hard-disk Repulsionmentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

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Mean Field Approximation

Majlis¹

2000

The Quantum Theory of Magnetism

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“…In a recent paper [10], another means of justifying the MFA which does not rely on self-consistency was explored. The argument, alluded to in Ref.…”

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confidence: 99%

Parity violation, anyon scattering, and the mean field approximation

Caenepeel

MacKenzie²

1994

Phys. Rev. D

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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 xed. A hard-disk interaction provides a concrete illustration of these general ideas.In the latter part of the paper, scattering with an additional hard-disk interaction is studied in detail, with an eye t o w ards providing a criterion for the validity of the mean-eld approximation for anyons, which is the rst step in virtually any treatment of this system. We nd, consistent with previous work, that the approximation is justied if the statistical interaction is weak, and that it must be more weak for boson-based than for fermion-based anyons.

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Parity violation in Aharonov-Bohm systems: The spontaneous Hall effect

Basagoiti

1994

Phys. Rev. B

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We show how macroscopic manifestations of P (and T ) symmetry breaking can arise in a simple system subject to Aharonov-Bohm interactions. Specifically, we study the conductivity of a gas of charged particles moving through a dilute array of flux tubes. The interaction of the electrons with the flux tubes is taken to be of a purely Aharonov-Bohm type. We find that the system exhibits a non-zero transverse conductivity, i.e., a spontaneous Hall effect. This is in contrast with the fact that the cross sections for both scattering and bremsstrahlung (soft photon emission) of a single electron from a flux tube are invariant under reflections. We argue that the asymmetry in the conductivity coefficients arises from many-body effects. On the other hand, the transverse conductivity has the same dependence on universal constants that appears in the Quantum Hall Effect, a result that we relate to the validity of the Mean Field approximation.

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Parity Violation and the Mean Field Approximation for the Anyon Gas

Cited by 4 publications

References 13 publications

Mean Field Approximation

Mean Field Approximation

Parity violation, anyon scattering, and the mean field approximation

Parity violation in Aharonov-Bohm systems: The spontaneous Hall effect

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