76 research outputs found
Extreme points of the set of density matrices with positive partial transpose
We present a necessary and sufficient condition for a finite dimensional
density matrix to be an extreme point of the convex set of density matrices
with positive partial transpose with respect to a subsystem. We also give an
algorithm for finding such extreme points and illustrate this by some examples.Comment: 4 pages, 2 figure
Low rank positive partial transpose states and their relation to product vectors
It is known that entangled mixed states that are positive under partial
transposition (PPT states) must have rank at least four. In a previous paper we
presented a classification of rank four entangled PPT states which we believe
to be complete. In the present paper we continue our investigations of the low
rank entangled PPT states. We use perturbation theory in order to construct
rank five entangled PPT states close to the known rank four states, and in
order to compute dimensions and study the geometry of surfaces of low rank PPT
states. We exploit the close connection between low rank PPT states and product
vectors. In particular, we show how to reconstruct a PPT state from a
sufficient number of product vectors in its kernel. It may seem surprising that
the number of product vectors needed may be smaller than the dimension of the
kernel.Comment: 29 pages, 4 figure
Correlators and fractional statistics in the quantum Hall bulk
We derive single-particle and two-particle correlators of anyons in the
presence of a magnetic field in the lowest Landau level. We show that the
two-particle correlator exhibits signatures of fractional statistics which can
distinguish anyons from their fermionic and bosonic counterparts. These
signatures include the zeroes of the two-particle correlator and its exclusion
behavior. We find that the single-particle correlator in finite geometries
carries valuable information relevant to experiments in which quasiparticles on
the edge of a quantum Hall system tunnel through its bulk.Comment: 4 pages, 3 figures, RevTe
Gravity and Matter in Causal Set Theory
The goal of this paper is to propose an approach to the formulation of
dynamics for causal sets and coupled matter fields. We start from the continuum
version of the action for a Klein-Gordon field coupled to gravity, and rewrite
it first using quantities that have a direct correspondent in the case of a
causal set, namely volumes, causal relations, and timelike lengths, as
variables to describe the geometry. In this step, the local Lagrangian density
for a set of fields is recast into a quasilocal expression
that depends on pairs of causally related points and
is a function of the values of in the Alexandrov set defined by those
points, and whose limit as and approach a common point is .
We then describe how to discretize , and use it to define a
discrete action.Comment: 13 pages, no figures; In version 2, friendlier results than in
version 1 are obtained following much shorter derivation
The Random Discrete Action for 2-Dimensional Spacetime
A one-parameter family of random variables, called the Discrete Action, is
defined for a 2-dimensional Lorentzian spacetime of finite volume. The single
parameter is a discreteness scale. The expectation value of this Discrete
Action is calculated for various regions of 2D Minkowski spacetime. When a
causally convex region of 2D Minkowski spacetime is divided into subregions
using null lines the mean of the Discrete Action is equal to the alternating
sum of the numbers of vertices, edges and faces of the null tiling, up to
corrections that tend to zero as the discreteness scale is taken to zero. This
result is used to predict that the mean of the Discrete Action of the flat
Lorentzian cylinder is zero up to corrections, which is verified. The
``topological'' character of the Discrete Action breaks down for causally
convex regions of the flat trousers spacetime that contain the singularity and
for non-causally convex rectangles.Comment: 20 pages, 10 figures, Typos correcte
A numerical study of the correspondence between paths in a causal set and geodesics in the continuum
This paper presents the results of a computational study related to the
path-geodesic correspondence in causal sets. For intervals in flat spacetimes,
and in selected curved spacetimes, we present evidence that the longest maximal
chains (the longest paths) in the corresponding causal set intervals
statistically approach the geodesic for that interval in the appropriate
continuum limit.Comment: To the celebration of the 60th birthday of Rafael D. Sorki
Bethe Ansatz solution of a new class of Hubbard-type models
We define one-dimensional particles with generalized exchange statistics. The
exact solution of a Hubbard-type Hamiltonian constructed with such particles is
achieved using the Coordinate Bethe Ansatz. The chosen deformation of the
statistics is equivalent to the presence of a magnetic field produced by the
particles themselves, which is present also in a ``free gas'' of these
particles.Comment: 4 pages, revtex. Essentially modified versio
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.
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