25 research outputs found
Topological 2-Dimensional Quantum Mechanics
We define a Chern- Simons Lagrangian for a system of planar particles
topologically interacting at a distance. The anyon model appears as a
particular case where all the particles are identical. We propose exact N-body
eigenstates, set up a perturbative algorithm, discuss the case where some
particles are fixed on a lattice, and also consider curved manifolds. PACS
numbers: 05.30.-d, 11.10.-zComment: 18 pages, Orsay Report IPNO/TH 92-10
Fractional dimensional Fock space and Haldane's exclusion statistics. q/p case
The discussion of Fractional dimensional Hilbert spaces in the context of
Haldane exclusion statistics is extended from the case \cite{IG} of for
the statistical parameter to the case of rational with -coprime
positive integers. The corresponding statistical mechanics for a gas of such
particles is constructed. This procedure is used to define the statistical
mechanics for particles with irrational . Applications to strongly
correlated systems such as the Hubbard and models are discussed.Comment: 11 pages, latex, no figure
Many-body States and Operator Algebra for Exclusion Statistics
We discuss many-body states and the algebra of creation and annihilation
operators for particles obeying exclusion statistics.Comment: 14 pages, plainTex. The first few pages have been modified. Note and
references added. (This version will appear in Nucl. Phys. B.
A remark on interacting anyons in magnetic field
In this remark, we note that the anyons, interacting with each other through
pairwise potential in external magnetic field, exhibit a simple quantum group
symmetry.Comment: IPT-EPFL preprint, typos fixed, minor corrections, references
updated, submitted to Physics Letter A
Nanoscale Phenomenology from Visualizing Pair Formation Experiment
Recently, 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_2Sr_2CaCu_2O_{8+\delta}. 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 [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.Comment: 4 pages, 1 figure. Good quality figure one can find in published
journal paper. Added 4 new references. Section of arXiv: 1010.043
Collective Field Formulation of the Multispecies Calogero Model and its Duality Symmetries
We study the collective field formulation of a restricted form of the
multispecies Calogero model, in which the three-body interactions are set to
zero. We show that the resulting collective field theory is invariant under
certain duality transformations, which interchange, among other things,
particles and antiparticles, and thus generalize the well-known strong-weak
coupling duality symmetry of the ordinary Calogero model. We identify all these
dualities, which form an Abelian group, and study their consequences. We also
study the ground state and small fluctuations around it in detail, starting
with the two-species model, and then generalizing to an arbitrary number of
species.Comment: latex, 53 pages, no figures;v2-minor changes (a paragraph added
following eq. (61)
Exclusion statistics,operator algebras and Fock space representations
We study exclusion statistics within the second quantized approach. We
consider operator algebras with positive definite Fock space and restrict them
in a such a way that certain state vectors in Fock space are forbidden ab
initio.We describe three characteristic examples of such exclusion, namely
exclusion on the base space which is characterized by states with specific
constraint on quantum numbers belonging to base space M (e.g.
Calogero-Sutherland type of exclusion statistics), exclusion in the
single-oscillator Fock space, where some states in single oscillator Fock space
are forbidden (e.g. the Gentile realization of exclusion statistics) and a
combination of these two exclusions (e.g. Green's realization of para-Fermi
statistics). For these types of exclusions we discuss extended Haldane
statistics parameters g, recently introduced by two of us in Mod.Phys.Lett.A
11, 3081 (1996), and associated counting rules. Within these three types of
exclusions in Fock space the original Haldane exclusion statistics cannot be
realized.Comment: Latex,31 pages,no figures,to appear in J.Phys.A : Math.Ge
Approximate formula for the ground state energy of anyons in 2D parabolic well
We determine approximate formula for the ground state energy of anyons in 2D
parabolic well which is valid for the arbitrary anyonic factor \nu and number
of particles N in the system. We assume that centre of mass motion energy is
not excluded from the energy of the system. Formula for ground state energy
calculated by variational principle contains logarithmic divergence at small
distances between two anyons which is regularized by cut-off parameter. By
equating this variational formula to the analogous formula of Wu near bosonic
limit (\nu ~ 0)we determine the value of the cut-off and thus derive the
approximate formula for the ground state energy for the any \nu and N. We
checked this formula at \nu=1, when anyons become fermions, for the systems
containing two to thirty particles. We find that our approximate formula has an
accuracy within 6%. It turns out, at the big number N limit the ground state
energy has square root dependence on factor \nu.Comment: 7 page
Haldane exclusion statistics and second virial coefficient
We show that Haldanes new definition of statistics, when generalised to
infinite dimensional Hilbert spaces, is equal to the high temperature limit of
the second virial coefficient. We thus show that this exclusion statistics
parameter, g , of anyons is non-trivial and is completely determined by its
exchange statistics parameter . We also compute g for quasiparticles in
the Luttinger model and show that it is equal to .Comment: 11 pages, REVTEX 3.