5,407 research outputs found
Neighbours of Einstein's Equations: Connections and Curvatures
Once the action for Einstein's equations is rewritten as a functional of an
SO(3,C) connection and a conformal factor of the metric, it admits a family of
``neighbours'' having the same number of degrees of freedom and a precisely
defined metric tensor. This paper analyzes the relation between the Riemann
tensor of that metric and the curvature tensor of the SO(3) connection. The
relation is in general very complicated. The Einstein case is distinguished by
the fact that two natural SO(3) metrics on the GL(3) fibers coincide. In the
general case the theory is bimetric on the fibers.Comment: 16 pages, LaTe
A trick for passing degenerate points in Ashtekar formulation
We examine one of the advantages of Ashtekar's formulation of general
relativity: a tractability of degenerate points from the point of view of
following the dynamics of classical spacetime. Assuming that all dynamical
variables are finite, we conclude that an essential trick for such a continuous
evolution is in complexifying variables. In order to restrict the complex
region locally, we propose some `reality recovering' conditions on spacetime.
Using a degenerate solution derived by pull-back technique, and integrating the
dynamical equations numerically, we show that this idea works in an actual
dynamical problem. We also discuss some features of these applications.Comment: 9 pages by RevTeX or 16 pages by LaTeX, 3 eps figures and epsf-style
file are include
Finite-size effects in the dynamics of few bosons in a ring potential
We study the temporal evolution of a small number of ultra-cold bosonic
atoms confined in a ring potential. Assuming that initially the system is in a
solitary-wave solution of the corresponding mean-field problem, we identify
significant differences in the time evolution of the density distribution of
the atoms when it instead is evaluated with the many-body Schr\"odinger
equation. Three characteristic timescales are derived: the first is the period
of rotation of the wave around the ring, the second is associated with a
"decay" of the density variation, and the third is associated with periodic
"collapses" and "revivals" of the density variations, with a factor of separating each of them. The last two timescales tend to infinity in the
appropriate limit of large , in agreement with the mean-field approximation.
These findings are based on the assumption of the initial state being a
mean-field state. We confirm this behavior by comparison to the exact solutions
for a few-body system stirred by an external potential. We find that the exact
solutions of the driven system exhibit similar dynamical features.Comment: To appear in Journal of Physics
Representation of quantum states as points in a probability simplex associated to a SIC-POVM
The quantum state of a -dimensional system can be represented by the
probabilities corresponding to a SIC-POVM, and then this distribution of
probability can be represented by a vector of in a simplex, we
will call this set of vectors . Other way of represent a
-dimensional system is by the corresponding Bloch vector also in
, we will call this set of vectors . In this paper it
is proved that with the adequate scaling . Also we
indicate some features of the shape of .Comment: 12 pages. Added journal referenc
Optimal purification of a generic n-qudit state
We propose a quantum algorithm for the purification of a generic mixed state
of a -qudit system by using an ancillary -qudit system. The
algorithm is optimal in that (i) the number of ancillary qudits cannot be
reduced, (ii) the number of parameters which determine the purification state
exactly equals the number of degrees of freedom of , and (iii)
is easily determined from the density matrix . Moreover, we
introduce a quantum circuit in which the quantum gates are unitary
transformations acting on a -qudit system. These transformations are
determined by parameters that can be tuned to generate, once the ancillary
qudits are disregarded, any given mixed -qudit state.Comment: 8 pages, 9 figures, remarks adde
Causal structure and degenerate phase boundaries
Timelike and null hypersurfaces in the degenerate space-times in the Ashtekar
theory are defined in the light of the degenerate causal structure proposed by
Matschull. Using the new definition of null hypersufaces, the conjecture that
the "phase boundary" separating the degenerate space-time region from the
non-degenerate one in Ashtekar's gravity is always null is proved under certain
circumstances.Comment: 13 pages, Revte
Spectra of phase point operators in odd prime dimensions and the extended Clifford group
We analyse the role of the Extended Clifford group in classifying the spectra
of phase point operators within the framework laid out by Gibbons et al for
setting up Wigner distributions on discrete phase spaces based on finite
fields. To do so we regard the set of all the discrete phase spaces as a
symplectic vector space over the finite field. Auxiliary results include a
derivation of the conjugacy classes of .Comment: Latex, 19page
The reality conditions for the new canonical variables of General Relativity
We examine the constraints and the reality conditions that have to be imposed
in the canonical theory of 4--d gravity formulated in terms of Ashtekar
variables. We find that the polynomial reality conditions are consistent with
the constraints, and make the theory equivalent to Einstein's, as long as the
inverse metric is not degenerate; when it is degenerate, reality conditions
cannot be consistently imposed in general, and the theory describes complex
general relativity.Comment: 11
Unextendible product bases and extremal density matrices with positive partial transpose
In bipartite quantum systems of dimension 3x3 entangled states that are
positive under partial transposition (PPT) can be constructed with the use of
unextendible product bases (UPB). As discussed in a previous publication all
the lowest rank entangled PPT states of this system seem to be equivalent,
under special linear product transformations, to states that are constructed in
this way. Here we consider a possible generalization of the UPB constuction to
low-rank entangled PPT states in higher dimensions. The idea is to give up the
condition of orthogonality of the product vectors, while keeping the relation
between the density matrix and the projection on the subspace defined by the
UPB. We examine first this generalization for the 3x3 system where numerical
studies indicate that one-parameter families of such generalized states can be
found. Similar numerical searches in higher dimensional systems show the
presence of extremal PPT states of similar form. Based on these results we
suggest that the UPB construction of the lowest rank entangled states in the
3x3 system can be generalized to higher dimensions, with the use of
non-orthogonal UPBs.Comment: 23 pages, 2 figures, 1 table. V2: Fixed fig.1 not showin
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