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

Abdullaev, B.; Ortíz, Gerardo; Rößler, U.; Musakhanov, M.M.; Nakamura, Atsunobu

doi:10.1103/physrevb.68.165105

Cited by 7 publications

(24 citation statements)

References 58 publications

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“…19 This was achieved by using the bosonic representation of anyons and a gauge vector potential to account for the fractional statistics, which allowed us to work with the product ansatz for the N-body wave function. A variational principle has been applied by constructing this wave function from single-particle Gaussians of variable shape.…”

Section: Introductionmentioning

confidence: 99%

“…In the present paper, we make use of previous work for the harmonically confined 2D anyons 19,20 to derive an approximate analytic expression for the ground-state energy of the homogeneous 2D anyon gas. This is done ͑for all values of the statistic parameter ͒ by flattening out the confining potential with a simultaneous increase of the particle number N, but fixed areal density, to obtain the infinite size system, i.e., the thermodynamic limit.…”

Section: Introductionmentioning

confidence: 99%

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Analytic approach to the ground-state energy of charged anyon gases

2007

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We derive an approximate analytic formula for the ground-state energy of the charged anyon gas. Our approach is based on the harmonically confined two-dimensional (2D) Coulomb anyon gas and a regularization procedure for vanishing confinement. To take into account the fractional statistics and Coulomb interaction we introduce a function, which depends on both the statistics and density parameters (nu and r_s, respectively). We determine this function by fitting to the ground state energies of the classical electron crystal at very large r_s (the 2D Wigner crystal), and to the Hartree-Fock (HF) energy of the spin-polarized 2D electron gas, and the dense 2D Coulomb Bose gas at very small r_s. The latter is calculated by use of the Bogoliubov approximation. Applied to the boson system (nu=0) our results are very close to recent results from Monte Carlo (MC) calculations. For spin-polarized electron systems (nu=1) our comparison leads to a critical judgment concerning the density range, to which the HF approximation and MC simulations apply. In dependence on nu, our analytic formula yields ground-state energies, which monotonously increase from the bosonic to the fermionic side if r_s > 1. For r_s leq 1 it shows a nonmonotonous behavior indicating a breakdown of the assumed continuous transformation of bosons into fermions by variation of the parameter nu .Comment: 18 pages, 3 figures. We have added the new reference and Fig. 3 with its description in the text. The result of Fig. 3 is reflected also in the abstrac

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Analytic approach to the ground-state energy of charged anyon gases

2007

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“…Such a periodic variation of the dispersion coefficient leads to a greater stability of the soliton during propagation in (1+1)D [8]. More recently, Abdullaev et al [9] have shown by a variational and numerical solution of the NLS that by employing a rapidly varying dispersion coefficient it is possible to stabilize an optical soliton in (2+1)D over large propagation distances.…”

Section: Introductionmentioning

confidence: 99%

“…The possibility of the stabilization of an optical soliton in (2+1)D by dispersion management [9] and Kerr singularity management [10,11,12] as well as in (3+1)D by Kerr singularity management [13,14] in SF medium has led us to investigate the possibility of the stabilization of an optical soliton in (3+1)D by dispersion management. However, some of these studies were concerned with the stabilization of Bose-Einstein condensates [10,12,13] using the nonlinear Gross-Pitaevskii equation [15] which is very similar to the NLS structurally.…”

Section: Introductionmentioning

confidence: 99%

“…There has already been experimental application of such dispersion management to Bose-Einstein condensates [21]. The effective mass can be varied by changing the parameters of the periodic potential [9]. Once a controlled variation of the effective mass would be possible, it might be possible to stabilize a Bose-Einstein condensate in this fashion.…”

Section: Introductionmentioning

confidence: 99%

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Stabilization of a(3+1)-dimensional soliton in a Kerr medium by a rapidly oscillating dispersion coefficient

Adhikari

2005

Phys. Rev. E

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Using the numerical solution of the nonlinear Schrödinger equation and a variational method it is shown that ͑3+1͒-dimensional spatiotemporal optical solitons can be stabilized by a rapidly oscillating dispersion coefficient in a Kerr medium with cubic nonlinearity. This has immediate consequence in generating dispersionmanaged robust optical soliton in communication as well as possible stabilized Bose-Einstein condensates in periodic optical-lattice potential via an effective-mass formulation. We also critically compare the present stabilization with that obtained by a rapid sinusoidal oscillation of the Kerr nonlinearity parameter.

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Anyon bosonization of 2D fermions and single boson phase diagram implied from experiment on visualizing pair formation in superconductor Bi2Sr2CaCu2O8+δ

Abdullaev¹,

Park²,

Musakhanov³

2011

Physica C: Superconductivity and its Applications

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a b s t r a c tRecently, Gomes et al. [1] have visualized the gap formation in nanoscale regions (NRs) above the critical temperature T c in the high-T c superconductor Bi 2 Sr 2 CaCu 2 O 8+d . It has been found that, as the temperature lowers, the NRs expand in the bulk superconducting state consisted of inhomogeneities. The fact that the size of the inhomogeneity [2] is close to the minimal size of the NR [1] leads to a conclusion that the superconducting phase is a result of these overlapped NRs. In the present paper we perform the charge and percolation regime analysis of NRs and show that at the first critical doping x c1 , when the superconductivity starts on, each NR carries the positive electric charge one in units of electron charge, thus we attribute the NR to a single hole boson, and the percolation lines connecting these bosons emerge. At the second critical doping x c2 , when the superconductivity disappears, our analysis demonstrates that the charge of each NR equals two. The origin of x c2 can be understood by introducing additional normal phase hole fermions in NRs, whose concentration appearing above x c1 increases smoothly with the doping and breaks the percolation lines of bosons at x c2 . The last one results in disappearing the bulk bosonic property of the pseudogap (PG) region, which explains the upper bound for existence of vortices in Nernst effect [3]. Since Gomes et al. [1] has demonstrated the absence of NRs at the PG boundary one can conclude that along this boundary, as well as in x c2 , all bosons disappear. As justification of appearance of single bosons, the bosonization of 2D fermions is rigorously proven using the concept of anyons. The linear density dependence of the energy gap between excited fermionic and bosonic ground states describes the Uemura relation for 2D superconductors.

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

Cited by 7 publications

References 58 publications

Analytic approach to the ground-state energy of charged anyon gases

Analytic approach to the ground-state energy of charged anyon gases

Stabilization of a(3+1)-dimensional soliton in a Kerr medium by a rapidly oscillating dispersion coefficient

Anyon bosonization of 2D fermions and single boson phase diagram implied from experiment on visualizing pair formation in superconductor Bi2Sr2CaCu2O8+δ

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