Bosonic Limit Research Articles

Phase-space filling and stimulated scattering of composite bosons

We show that the final-state stimulation of a scattering process involving composite bosons is fundamentally limited by the Pauli exclusion of the constituent fermions. Even though we concentrate on the saturation and Pauli blocking of the statistical enhancement factor for exciton-phonon scattering into a many-body electron-hole pair state, our basic result is valid for a large class of composite bosons and for arbitrary dimensionality. The expression that we obtain explicitly shows that the stimulation is a direct result of the many-body coherence in the final state. For a two-dimensional magnetoexciton gas, we analytically demonstrate the transition from stimulated scattering in the low-density bosonic limit to Pauli blocking of scattering in the high-density limit.

The Hamiltonian structure of the N = 2 supersymmetric GNLS hierarchy

The first two Hamiltonian structures and the recursion operator connecting all evolution systems and Hamiltonian structures of the N=2 supersymmetric (n,m)-GNLS hierarchy are constructed in terms of N=2 superfields in two different superfield bases with local evolution equations. Their bosonic limits are studied in detail. New local and nonlocal bosonic and fermionic integrals both for the N=2 supersymmetric (n,m)-GNLS hierarchy and its bosonic counterparts are derived. As an example, in the n=1, m=1 case, the algebra and the symmetry transformations for some of them are worked out and a rich N=4 supersymmetry structure is uncovered.

Deformed Quantum Statistics

To understand possible physical consequences of quantum deformation, we investigate statistical behaviors of a quon gas. The quon is an object which obeys the minimally deformed commutator (or q-mutator): a\, a^{\dagger} - q a^{\dagger}a=1 with -1\leq q\leq 1. Although q=1 and q=-1 appear to correspond respectively to boson and fermion statistics, it is not easy to create a gas which unifies the boson gas and the fermion gas. We present a model which is able to interpolates between the two limits. The quon gas shows the Bose-Einstein condensation near the Boson limit in two dimensions.

Two-dimensional superintegrable mappings and integrable hierarchies in the (2|2) superspace

The formalism of integrable mappings is applied to the problem of constructing hierarchies of (1 + 2) dimensional integrable systems in the (2|2) superspace. We find new supersymmetric integrable mappings and corresponding to them new hierarchies of integrable systems which, at the reduction to the (1|2) superspace, possess N = 2 supersymmetry. The general formulae obtained for the hierarchies are used to explicitly derive their first nontrivial equations possessing a manifest N = 2 supersymmetry. New bosonic substitutions and hierarchies are obtained from the supersymmetric counterparts in the bosonic limit.

The Maxwell-Boltzmann behavior of a quon gas

A model gas of quons whose operators obey the minimally deformed commutators a ia j † − qa j †a i = δ ij (−1 ≤ q ≤ 1) is studied in two dimensions. While interpolating between the boson limit ( q → 1) and the fermion limit ( q → −1), the gas behaves like a Maxwell-Boltzmann gas when q = 0 at any temperature.

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.

The extended supersymmetrization of the multicomponent Kadomtsev - Petviashvilli hierarchy

We describe three different approaches to the extended (N = 2) supersymmetrization of the multicomponent KP hierarchy. In the first one we utilize only superfermions while in the second only superbosons and in the third superbosons as well as superfermions. It is shown that many soliton equations can be embedded in the supersymmetry theory by using the first approach even if we do not change these equations in the bosonic limit of the supersymmetry. In the second or third approach we obtain a generalization of the soliton equations in the bosonic limit which remains in the class of the usual commuting functions. As a byproduct of our analysis we prove that for the first procedure the bosonic part of the one-component supersymmetric KP hierarchy coincides with the usual classical two-component KP hierarchy.

A NONSTANDARD SUPERSYMMETRIC KP HIERARCHY

We show that the supersymmetric nonlinear Schrödinger equation can be written as a constrained super KP flow in a nonstandard representation of the Lax equation. We construct the conserved charges and show that this system reduces to the super mKdV equation with appropriate identifications. We construct various flows generated by the general nonstandard super Lax equation and show that they contain both the KP and mKP flows in the bosonic limits. This nonstandard supersymmetric KP hierarchy allows us to construct a new super KP equation which is nonlocal.

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.

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.

NONLOCAL MATRIX GENERALIZATIONS OF N=2 SUPER VIRASORO ALGEBRA

We study the generalization of the second Gelfand-Dickey bracket to the superdifferential operators with matrix-valued coefficients. The associated matrix Miura transformation is derived. Using this bracket we work out a nonlocal and nonlinear N=2 superalgebra which contains the N=2 super Virasoro algebra as a subalgebra. The bosonic limit of this superalgebra is considered. We show that when the spin-1 fields in this bosonic algebra are set to zero the resulting Dirac bracket gives precisely the recently derived V2,2 algebra.

Thirring Model as a Gauge Theory

We reformulate the Thirring model in $D$ $(2 \le D < 4)$ dimensions as a gauge theory by introducing $U(1)$ hidden local symmetry (HLS) and study the dynamical mass generation of the fermion through the Schwinger-Dyson (SD) equation. By virtue of such a gauge symmetry we can greatly simplify the analysis of the SD equation by taking the most appropriate gauge (``nonlocal gauge'') for the HLS. In the case of even-number of (2-component) fermions, we find the dynamical fermion mass generation as the second order phase transition at certain fermion number, which breaks the chiral symmetry but preserves the parity in (2+1) dimensions ($D=3$). In the infinite four-fermion coupling (massless gauge boson) limit in (2+1) dimensions, the result coincides with that of the (2+1)-dimensional QED, with the critical number of the 4-component fermion being $N_{\rm cr} = \frac{128}{3\pi^{2}}$. As to the case of odd-number (2-component) fermion in (2+1) dimensions, the regularization ambiguity on the induced Chern-Simons term may be resolved by specifying the regularization so as to preserve the HLS. Our method also applies to the (1+1) dimensions, the result being consistent with the exact solution. The bosonization mechanism in (1+1) dimensional Thirring model is also reproduced in the context of dual-transformed theory for the HLS.

Radiative Majorama neutrino masses

We show how Majorana neutrino masses can be radiatively generated, in model where charged lepton masses are radiatively induced, order by order, from heavy sequential lepton seeds. Only the new sequential neutral lepton has a right-handed partner, and its Majorana mass provides the seeds for Majorana neutrino mass generation. Saturating the cosmological bound of 50 eV with m ν τ we find that m ν μ and m ν e could be at most 10 −2, and 10 −3eV, respectively. The electron neutrino mass may vanish in the limit of degenerate charged Higgs bosons. Unfortunately, ν e − ν τ mixing is also radiatively induced, and is too smallk for the sake of solving the solar neutrino problem via the Mikheyev-Smirnov-Wolfenstein effect.

Non perturbative effective potentials of quantum oscillators

Non perturbative analogues of the Gaussian effective potential (GEP) are defined for quantum oscillators obeyingq—or (q,p)—deformed commutation relations. These are called the non perturbativeq-effective potential (NP q EP) and the non perturbativeqp effective potential (NP qp EP), in the respective cases. A system-specific effective potential (SSEP) is also introduced by means of an additional minimization with respect to theq orq andp parameters. The method is applied toq and (q,p) oscillators of the quartic and sextic types. The SSEP in the case of ground states of theq-oscillators corresponds toq=1, which is the ordinary bosonic limit. A potential shape transition that involves the conversion of a double well to a single well or vice versa, is seen to exist in the case of quantum oscillators sitting in a double well potential.

Mott transition in an anyon gas.

We introduce and analyze a lattice model of anyons in a periodic potential and an external magnetic field, which exhibits a transition from a Mott insulator to a quantum Hall fluid. The transition is characterized by the anyon statistics \ensuremath{\alpha}, which can vary between fermions, \ensuremath{\alpha}=0, and bosons, \ensuremath{\alpha}=1. For bosons the transition is in the universality class of the classical three-dimensional XY model. Near the fermion limit, the transition is described by a massless 2+1 Dirac theory coupled to a Chern-Simons gauge field. Analytic calculations perturbative in \ensuremath{\alpha}, and also a large-N expansion, show that due to gauge fluctuations, the critical properties of the transition are dependent on the anyon statistics. Comparison with previous calculations at and near the boson limit, strongly suggest that our lattice model exhibits a fixed line of critical points, with universal critical properties that vary continuously and monotonically as one passes from fermions to bosons. Possible relevance to experiments on the transitions between plateaus in the fractional quantum Hall effect and the magnetic-field-tuned superconductor-insulator transition are briefly discussed.

The Statistical Distribution Function For An Anyon Liquid

Abstract The distribution function for fermions has been derived from collision theory by using the detailed balance hypothesis. Its form goes to the correct boson (n = 1) and fermion (n = 1) limits. Further the equations for the density matrix have been derived from the Hamiltonian. The zero order approximation gives a distribution having the same form as that derived by the detailed balance arguments.

On a class of noninterpolating solutions of the many-anyon problem

In the many-anyon problem in two space dimensions, irregular but square integrable solutions of the Schrodinger equation may exist. A class of such solutions is constructed for anyons confined in a harmonic oscillator. It is shown that these may have lower energies than the usual regular solutions, but they do not exist throughout the range between the bosonic and fermionic limits, and as such do not interpolate continuously.

On the precise formulation of the equivalence theorem.

A systematic analysis of renormalization schemes and a general proof of the precise formulation of the equivalence theorem are given in the ${\mathit{R}}_{\ensuremath{\xi}}$ gauge for both the SU(2${)}_{\mathit{L}}$ and the SU(2)\ifmmode\times\else\texttimes\fi{}U(1) theories. The precise formula for the modification factor ${\mathit{C}}_{\mathrm{mod}}$ is obtained, and a convenient particular scheme in which ${\mathit{C}}_{\mathrm{mod}}$ is exactly unity is proposed. ${\mathit{C}}_{\mathrm{mod}}$ in other schemes are discussed up to one loop in the heavy Higgs boson limit.

Analytic wave functions for understanding the spectrum of the three-anyon problem

We show that the low-lying spectrum of three noninteracting anyons in a harmonic potential can be qualitatively and quantitatively understood on the basis of a simple set of analytic wave functions. These wave functions are exact in both the boson and fermion limits and satisfy the anyon wave-function phase condition at all intermediate values of the statistical parameter 0<α<1. The resulting nonlinear spectrum agrees with those of exact numerical calculations to better than a few parts in a thousand

DERIVATION OF LAUGHLIN'S WAVEFUNCTION IN ANYON SYSTEM

In a semiclassical approximation we derive the ground-state wavefunction of the system of anyons in an external magnetic field, where anyons are interacting via the Coulomb interaction. The statistical interactions are treated in perturbation around the boson limit. The wavefunction coincides with the Laughlin wavefunction except for small corrections due to the Coulomb interaction. We also calculate the ground-state energy and the excitation spectrum.