Anyon Gas Research Articles

One-dimensional impenetrable anyons in thermal equilibrium: II. Determinant representation for the dynamic correlation functions

We have obtained a determinant representation for the time- and temperature-dependent field–field correlation function of the impenetrable Lieb–Liniger gas of anyons through direct summation of the form factors. In the static case, the obtained results are shown to be equivalent to those that follow from the anyonic generalization of Lenard's formula.

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

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 ($\ensuremath{\nu}$ 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 $(\ensuremath{\nu}=0)$ our results are very close to recent results from Monte Carlo (MC) calculations. For spin-polarized electron systems $(\ensuremath{\nu}=1)$ our comparison leads to a critical judgment concerning the density range, to which the HF approximation and MC simulations apply. In dependence on $\ensuremath{\nu}$, our analytic formula yields ground-state energies, which monotonously increase from the bosonic to the fermionic side if ${r}_{s}>1$. For ${r}_{s}\ensuremath{\leqslant}1$ it shows a nonmonotonous behavior indicating a breakdown of the assumed continuous transformation of bosons into fermions by variation of the parameter $\ensuremath{\nu}$.

Q-Boson in Quantum Integrable Systems

q-bosonic realization of the underlying Yang-Baxter algebra is identified for a series of quantum integrable systems, including some new models like two-mode q-bosonic model leading to a coupled two-component derivative NLS model, wide range of q-deformed matter-radiation models, q-anyon model etc. Result on a new exactly solvable interacting anyon gas, linked to q-anyons on the lattice is reported.

Anyon-Fermion Mapping and Applications to Ultracold Gases in Tight Waveguides

The Fermi-Bose mapping method for one-dimensional Bose and Fermi gases with zero-range interactions is generalized to an anyon-fermion mapping and applied to exact solution of several models of ultracold gases with anyonic exchange symmetry in tight waveguides: anyonic Calogero-Sutherland model, anyons with point hard-core interaction (anyonic Tonks-Girardeau gas), and spin-aligned anyon gas with infinite zero-range odd-wave attractions (attractive anyonic Tonks-Girardeau, or AATG, gas). It is proved that for even N>or=4 there are states of the AATG gas on a ring, with anyonic phase slips which are odd integral multiples of pi/(N-1), of energy lower than that of the corresponding fermionic ground state. A generalization to a spinor Fermi gas state with anyonic symmetry under purely spatial exchange enables energy lowering by the same mechanism.

One-Dimensional Interacting Anyon Gas: Low-Energy Properties and Haldane Exclusion Statistics

The low-energy properties of the one-dimensional anyon gas with a delta-function interaction are discussed in the context of its Bethe ansatz solution. It is found that the anyonic statistical parameter and the dynamical coupling constant induce Haldane exclusion statistics interpolating between bosons and fermions. Moreover, the anyonic parameter may trigger statistics beyond Fermi statistics for which the exclusion parameter alpha is greater than one. The Tonks-Girardeau and the weak coupling limits are discussed in detail. The results support the universal role of alpha in the dispersion relations.

Dynamical Role of Anyonic Excitation Statistics in Rapidly Rotating Bose Gases

We show that for rotating harmonically trapped Bose gases in a fractional quantum Hall state, the anyonic excitation statistics in the rotating gas can effectively play a dynamical role. For particular values of the two-dimensional coupling constant g=-2pih2(2k-1)/m, where k is a positive integer, the system becomes a noninteracting gas of anyons, with exactly obtainable solutions satisfying Bogomol'nyi self-dual order parameter equations. Attractive Bose gases under rapid rotation thus can be stabilized in the thermodynamic limit due to the anyonic statistics of their quasiparticle excitations.

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

We derive an analytic, albeit approximate, expression for the ground state energy of N Coulomb interacting anyons with fractional statistics nu, 0<= |nu| <= 1, confined in a two-dimensional well (with characteristic frequency omega_0 ) and subjected to an external magnetic field (with cyclotron frequency omega_c ). We apply a variational principle combined with a regularization procedure which consists of fitting a cut-off parameter to existing exact analytical results in the non-interacting case, and to numerical calculations for electrons in quantum dots in the interacting case. The resulting expression depends upon parameters of the system |nu|, N, omega_0, r_0, a_B and omega_c, where r_0 represents a characteristic unit length and a_B the Bohr radius. Validity of the result is critically assessed by comparison with exact, approximate, and numerical results from the literature.

The Bose-Einstein condensation of anyons.

The probability for the Bose-Einstein condensation of anyons is discussed. It is found that the ideal anyon gas near Bose statistics can display BEC behaviour. In addition, the transition point and the specific heat are determined.

Exact Solution of DoubleδFunction Bose Gas through an Interacting Anyon Gas

A 1D Bose gas interacting through $\ensuremath{\delta},{\ensuremath{\delta}}^{\ensuremath{'}}$ and double $\ensuremath{\delta}$ function potentials is shown to be equivalent to a $\ensuremath{\delta}$ anyon gas, allowing an exact Bethe ansatz solution. In the noninteracting limit, it describes an ideal gas with generalized exclusion statistics and solves some recent controversies.

Statistical mechanics of relativistic anyons

We calculated the grand thermodynamical potential and derived the thermodynamic properties of the relativistic anyon gas, using the formalism of the Mellin-transforms. We observed that there is no Bose–Einstein condensation for a relativistic anyon gas, except in the ultra-relativistic limit. We evaluated the virial expansion and obtained a relation between the boson-like anyons and the fermion-like anyons virial coefficients.

The second virial coefficient of spin- interacting anyon system

We evaluate the propagator by the usual time-sliced manner and use it to compute the second virial coefficient of an anyon gas interacting through the repulsive potential of the form . All the cusps for the unpolarized spin- as well as spinless cases disappear in the limit, where is a frequency of the harmonic oscillator which is introduced as a regularization method. As g approaches zero, the result reduces to the noninteracting hard-core limit.

Coulomb Interactions at Quantum Hall Critical Points of Systems in a Periodic Potential

We study the consequences of long-range Coulomb interactions at the critical points between integer/fractional quantum Hall states and an insulator. We use low energy theories for such transitions in anyon gases in the presence of an external periodic potential. We find that Coulomb interactions are marginally irrelevant for the integer quantum Hall case. For the fractional case, depending upon the anyon statistics parameter, we find behavior similar to the integer case, or flow to a novel line of fixed points with exponents $z\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1$, $\ensuremath{\nu}&gt;1$ stable against weak disorder in the position of the critical point, or runaway flow to strong coupling.

Screening in anyon gas

Anyon gas with interparticle (retarded) Coulomb interaction has been studied. The resulting system is shown to be a collection of dressed anyons, with a screening factor introduced in their spin. Close structural similarity with the Chern - Simons construction of anyons has helped considerably in computing the screening effect. Finally, the present model is compared with the conventional Chern - Simons construction.

From random matrix theory to statistical mechanics - anyon gas

Motivated by numerical experiments and studies of quantum systems which are classically chaotic, we take the random matrix description of a hard-sphere gas to the statistical mechanical description. We apply this to the anyon gas and obtain a formal expression for the momentum distribution. Various limiting situations are discussed and are found to be in agreement with the well-known results on hard-sphere gas in the low-density regime.

Statistics of anyon gas and the factorizable property of thermodynamic quantities.

The statistical distribution function of anyon is used to find the eighth viral coefficient in the high-temperature limit and the equation of state in the low-temperature limit. The perturbative results indicate that the thermodynamic quantities, Q(\ensuremath{\alpha}), of the free anyon gas may be factorized in the terms characteristic of the ideal Bose (\ensuremath{\alpha}=0) and fermion (\ensuremath{\alpha}=1) gases, i.e., Q(\ensuremath{\alpha})=\ensuremath{\alpha}Q(1)+(1-\ensuremath{\alpha})Q(0). It is shown that the factorizable property of the thermodynamic quantities, to all orders, can be established from the property of the equivalence between the anyon statistics and statistics in a system with boson-fermion transmutation, which was found by us in a recent paper [W. H. Huang, Phys. Rev. E 51, 3729 (1995)]. \textcopyright{} 1996 The American Physical Society.

Pairing instabilities induced by residual statistical interactions

AbstractAt two space dimensions we consider small changes in quantum statistics around the bosonic and fermionic limits. An anyon gas near the Bose statistics becomes unstable towards pair condensation at arbitrarily small statistical parameter in front of the Aharonov‐Bohm interaction. The self‐consistency problem within the Cooper scattering channel is solved analytically by taking into account the full momentum dependence of the singular two‐particle vertex. The pairing, whose amplitude and critical temperature we calculate in mean‐field approximation, has d‐wave symmetry unlike the p‐wave BCS‐type pairing instability for anyons near the Fermi point. The connection to paired‐boson (holon) superconductivity is pointed out.

Quon gas with the boson, fermion, and near-classical limits.

A simple quon gas model which interpolates between the boson gas and the fermion gas is proposed. The fermion limit is realized without use of the exclusion principle. The second and third virial coefficients are calculated and compared with those of a free anyon gas. If the fugacity is small the system can simulate an anyon gas which has the Maxwell-Boltzmann limit.

Collective Field Theory of Ideal Anyon Gas

Collective Field Theory of Ideal Anyon Gas

Collective Field Theory of Ideal Anyon Gas

Collective Field Theory of Ideal Anyon Gas

Anyonic quon gas

A simple model of a quon gas which exhibits anyonic behavior is proposed. Quons are characterized by the q-mutator, aa † − qa †a = 1 with −1 ≤ q ≤ 1. The gas has the boson and fermion gas limits and can simulate an anyon gas to the second and third virial coefficients.