122 research outputs found
Axial Anomaly in the Presence of the Aharonov-Bohm Gauge Field
We investigate on the plane the axial anomaly for euclidean Dirac fermions in
the presence of a background Aharonov--Bohm gauge potential. The non
perturbative analysis depends on the self--adjoint extensions of the Dirac
operator and the result is shown to be influenced by the actual way of
understanding the local axial current. The role of the quantum mechanical
parameters involved in the expression for the axial anomaly is discussed. A
derivation of the effective action by means of the stereographic projection is
also considered.Comment: 15 pages, Plain.TeX, Preprint DFUB/94 - 1
On the Lieb-Liniger model in the infinite coupling constant limit
We consider the one-dimensional Lieb-Liniger model (bosons interacting via
2-body delta potentials) in the infinite coupling constant limit (the so-called
Tonks-Girardeau model). This model might be relevant as a description of atomic
Bose gases confined in a one-dimensional geometry. It is known to have a
fermionic spectrum since the N-body wavefunctions have to vanish at coinciding
points, and therefore be symmetrizations of fermionic Slater wavefunctions. We
argue that in the infinite coupling constant limit the model is
indistinguishable from free fermions, i.e., all physically accessible
observables are the same as those of free fermions. Therefore, Bose-Einstein
condensate experiments at finite energy that preserve the one-dimensional
geometry cannot test any bosonic characteristic of such a model
Signed area enumeration for lattice walks
We give a summary of recent progress on the signed area enumeration of closed
walks on planar lattices. Several connections are made with quantum mechanics
and statistical mechanics. Explicit combinatorial formulae are proposed which
rely on sums labelled by the multicompositions of the length of the walks.Comment: Version published in S\'eminaire Lotharingien de Combinatoire; 13
pages, 4 figure
Hamiltonian and exclusion statistics approach to discrete forward-moving paths
We use a Hamiltonian (transition matrix) description of height-restricted
Dyck paths on the plane in which generating functions for the paths arise as
matrix elements of the propagator to evaluate the length and area generating
function for paths with arbitrary starting and ending points, expressing it as
a rational combination of determinants. Exploiting a connection between random
walks and quantum exclusion statistics that we previously established, we
express this generating function in terms of grand partition functions for
exclusion particles in a finite harmonic spectrum and present an alternative,
simpler form for its logarithm that makes its polynomial structure explicit.Comment: Updated and expanded version to appear in Phys Rev
Exclusion statistics for particles with a discrete spectrum
We formulate and study the microscopic statistical mechanics of systems of
particles with exclusion statistics in a discrete one-body spectrum. The
statistical mechanics of these systems can be expressed in terms of effective
single-level grand partition functions obeying a generalization of the standard
thermodynamic exclusion statistics equation of state. We derive explicit
expressions for the thermodynamic potential in terms of microscopic cluster
coefficients and show that the mean occupation numbers of levels satisfy a
nesting relation involving a number of adjacent levels determined by the
exclusion parameter. We apply the formalism to the harmonic Calogero model and
point out a relation with the Ramanujan continued fraction identity and
appropriate generalizations.Comment: 20 page
Inclusion statistics and particle condensation in 2 dimensions
We propose a new type of quantum statistics, which we call inclusion
statistics, in which particles tend to coalesce more than ordinary bosons.
Inclusion statistics is defined in analogy with exclusion statistics, in which
statistical exclusion is stronger than in Fermi statistics, but now
extrapolating beyond Bose statistics, resulting in statistical inclusion. A
consequence of inclusion statistics is that the lowest space dimension in which
particles can condense in the absence of potentials is , unlike for
the usual Bose-Einstein condensation. This reduction in the dimension happens
for any inclusion stronger than bosons, and the critical temperature increases
with stronger inclusion. Possible physical realizations of inclusion statistics
involving attractive interactions between bosons may be experimentally
achievable.Comment: 12 pages, 0 figur
Arithmetic area for m planar Brownian paths
We pursue the analysis made in [1] on the arithmetic area enclosed by m
closed Brownian paths. We pay a particular attention to the random variable
S{n1,n2, ...,n} (m) which is the arithmetic area of the set of points, also
called winding sectors, enclosed n1 times by path 1, n2 times by path 2, ...,nm
times by path m. Various results are obtained in the asymptotic limit
m->infinity. A key observation is that, since the paths are independent, one
can use in the m paths case the SLE information, valid in the 1-path case, on
the 0-winding sectors arithmetic area.Comment: 12 pages, 2 figure
Combinatorics of generalized Dyck and Motzkin paths
We relate the combinatorics of periodic generalized Dyck and Motzkin paths to
the cluster coefficients of particles obeying generalized exclusion statistics,
and obtain explicit expressions for the counting of paths with a fixed number
of steps of each kind at each vertical coordinate. A class of generalized
compositions of the integer path length emerges in the analysis.Comment: 27 pages, 11 figure
Integer Partitions and Exclusion Statistics
We provide a combinatorial description of exclusion statistics in terms of
minimal difference partitions. We compute the probability distribution of
the number of parts in a random minimal partition. It is shown that the
bosonic point is a repulsive fixed point for which the limiting
distribution has a Gumbel form. For all positive the distribution is shown
to be Gaussian.Comment: 16 pages, 4 .eps figures include
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