Perturbative anyon gas

Veigy, Alain Dasnières de; Ouvry, Stéphane

doi:10.1016/0550-3213(92)90561-o

Cited by 36 publications

(10 citation statements)

References 19 publications

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“…1), our computed AAs is consistent with the perturbative [14] exPression i'sns for EAs. Since our comPuted K(n) may contain higher powers of a, a direct comparison is…”

supporting

confidence: 81%

“…For n & 0.1, since powers higher than 2 may contribute substantially to AAs, our computed values differ significantly from Ref. [14). According to Sen [8],…”

contrasting

confidence: 65%

“…Although some interesting properties of the third virial coefficient have been derived analytically [5 -10], its actual evaluation is a difficult and challenging problem. Recently, de Veigy and Ouvry [14] have calculated the third virial coefficient perturbatively to order n2. In this paper we report the first fully quantum mechanical calculation of the virial coefficient by diagonalizing the three-body Hamiltonian in a large basis set.…”

mentioning

confidence: 99%

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Quantum third virial coefficient of a fractional-statistics gas

1992

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A quantum calculation of the third virial coefBcient of a two-dimensional gas obeying fractional statistics is performed by diagonalizing the three-body Hamiltonian in a harmonic-oscillator potential with a large fermionic basis. The numerical results for the virial coefficient A3 as a function of the flux strength n (n = 0 for fermions, n = 1 for bosons) are reliable in the range 0 & n & 0.25. A3 increases quadratically with n for very small a, but higher powers contribute substantially for large PACS number (s): 05.30. -d, 03.65.Ge, 05.70.Ce, 74.65.+n In two-space dimensions, particles may obey fractional-statistics [1, 2], being neither bosons nor fermions.The equation of state of such a fractionalstatistics gas is of considerable current interest [3 -14]. The second virial coefficient of such a gas was calculated analytically by Arrovas et aL [3], and showed a cusplike behavior at the bosonic end. Although some interesting properties of the third virial coefficient have been derived analytically [5 -10], its actual evaluation is a difficult and challenging problem. Recently, de Veigy and Ouvry [14] have calculated the third virial coefficient perturbatively to order n2. In this paper we report the first fully quantum mechanical calculation of the virial coefficient by diagonalizing the three-body Hamiltonian in a large basis set. The calculation is successful in determining its behavior over a limited range of the statistical flux parameter.It is convenient, in calculating the properties of a system obeying fractional statistics, to regard it as a collection of either bosons or fermions, and use a statistical gauge interaction to generate the statistical phases [2]. In this paper, we use the fermionic basis, and the strength of the statistical interaction, denoted by n, may vary from n = 0 (fermion) to n = 1 (boson). The following important properties of the third virial coefficient As(ti, ) are already known.(a) The lowest power in As(a) is at least of order n (Refs. [6, 7]). (b) As(n) is symmetric about n = s (the semion), i.e. , As(n) = As(1 -o'. ) (Ref. [8]).(c) The eigenvalues of the three-body system that vary linearly with n do not contribute [9, 10] to As(n).Out of these, particularly useful for our purpose is the result (b) relating to the symmetry about n = s, which implies that it is sufficient to calculate As(n) numerically in the range 0 & a & 2. A direct quantum calculation of As(n) entails an evaluation of the three-body partition function Zs(n) in a box of dimension L or a harmonic oscillator with spacing h~, and evaluate As(n) in the limit A/L or huP~0, where A is the thermal wavelength and P is the inverse temperature (in units of the Boltzmann constant). Such a calculation involves a knowledge of the (nearly) exact eigenvalues of the three-body system to very high excitations (to be quantitatively specified later). Previously, only the very low-lying spectrum of the three-body harmonic-oscillator system had been calculated [15,16]. Following the perturbative method of Ref.[17], Sporre, Verb...

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“…1), our computed AAs is consistent with the perturbative [14] exPression i'sns for EAs. Since our comPuted K(n) may contain higher powers of a, a direct comparison is…”

supporting

confidence: 81%

“…For n & 0.1, since powers higher than 2 may contribute substantially to AAs, our computed values differ significantly from Ref. [14). According to Sen [8],…”

contrasting

confidence: 65%

mentioning

confidence: 99%

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Quantum third virial coefficient of a fractional-statistics gas

1992

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“…Some time ago Dunne, Jackiw and Trugenberger [10] already observed this noncommutativity by noting that in the limit m → 0 the y-coordinate is effectively constrained to the momentum canonical conjugate to the x-coordinate. This result can also be obtained [11,12] by keeping the mass fixed and taking the limit B → ∞. An alternative point of view is to keep the magnetic field and mass finite, but to project the position coordinates onto the lowest (or higher) Landau level.…”

Section: Introductionmentioning

confidence: 71%

“…As the area occupied by the two particles will increase with increasing relative angular momentum, one can deduce from (12) and (2) an absolute lower bound to the average area that a particle in the low energy sector may occupy…”

Section: General Projection On the Low Energy Sectormentioning

confidence: 99%

Interactions and non-commutativity in quantum Hall systems

Scholtz¹,

Chakraborty²,

Gangopadhyay³

et al. 2005

J. Phys. A: Math. Gen.

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We discuss the role that interactions play in the non-commutative structure that arises when the relative coordinates of two interacting particles are projected onto the lowest Landau level. It is shown that the interactions in general renormalize the non-commutative parameter away from the non-interacting value 1 B. The effective non-commutative parameter is in general also angular momentum dependent. An heuristic argument, based on the non-commutative coordinates, is given to find the filling fractions at incompressibilty, which are in general renormalized by the interactions, and the results are consistent with known results in the case of singular magnetic fields.

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Anyons

Myrheim

Aspects Topologiques De La Physique en Basse Dimension. Topological Aspects of Low Dimensional Systems

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Perturbative anyon gas

Cited by 36 publications

References 19 publications

Quantum third virial coefficient of a fractional-statistics gas

Quantum third virial coefficient of a fractional-statistics gas

Interactions and non-commutativity in quantum Hall systems

Anyons

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