42 research outputs found
Classification of 6-dimensional real Drinfeld doubles
Starting from the classification of real Manin triples done in a previous
paper we look for those that are isomorphic as 6-dimensional Lie algebras with
the ad-invariant form used for construction of the Manin triples. We use
several invariants of the Lie algebras to distinguish the non-isomorphic
structures and give explicit form of maps between Manin triples that are
decompositions of isomorphic Drinfeld doubles. The result is a complete list of
6-dimensional real Drinfeld doubles. It consists of 22 classes of
non-isomorphic Drinfeld doubles.Comment: 27 pages, corrected minor mistakes and typos, added reference
A general algorithm for manipulating non-linear and linear entanglement witnesses by using exact convex optimization
A generic algorithm is developed to reduce the problem of obtaining linear
and nonlinear entanglement witnesses of a given quantum system, to convex
optimization problem. This approach is completely general and can be applied
for the entanglement detection of any N-partite quantum system. For this
purpose, a map from convex space of separable density matrices to a convex
region called feasible region is defined, where by using exact convex
optimization method, the linear entanglement witnesses can be obtained from
polygonal shape feasible regions, while for curved shape feasible regions,
envelope of the family of linear entanglement witnesses can be considered as
nonlinear entanglement witnesses. This method proposes a new methodological
framework within which most of previous EWs can be studied. To conclude and in
order to demonstrate the capability of the proposed approach, besides providing
some nonlinear witnesses for entanglement detection of density matrices in
unextendible product bases, W-states, and GHZ with W-states, some further
examples of three qubits systems and their classification and entanglement
detection are included. Also it is explained how one can manipulate most of the
non-decomposable linear and nonlinear three qubits entanglement witnesses
appearing in some of the papers published by us and other authors, by the
method proposed in this paper. Keywords: non-linear and linear entanglement
witnesses, convex optimization. PACS number(s): 03.67.Mn, 03.65.UdComment: 37 page
Perfect transference of a d-level quantum state over pseudo-distance-regular networks
Following the prescription of Ref. \cite{PST} in which perfect state
transference (PST) of a qubit over distance regular spin networks was
discussed, in this paper PST of an arbitrary -level quantum state (qudit)
over antipodes of more general networks called pseudo distance-regular
networks, is investigated. In fact, the spectral analysis techniques used in
the previous work \cite{PST}, and algebraic structures of pseudo
distance-regular graphs are employed to give an explicit formula for suitable
coupling constants in the Hamiltonians so that the state of a particular qudit
initially encoded on one site will evolve freely to the opposite site without
any dynamical control, i.e., we show that how to derive the parameters of the
system so that PST can be achieved.
Keywords:Perfect state transfer, -level quantum state, Stratification,
Pseudo-distance-regular network
PACs Index: 01.55.+b, 02.10.YnComment: 28 pages, 5 figure
Evaluation of effective resistances in pseudo-distance-regular resistor networks
In Refs.[1] and [2], calculation of effective resistances on distance-regular
networks was investigated, where in the first paper, the calculation was based
on the stratification of the network and Stieltjes function associated with the
network, whereas in the latter one a recursive formula for effective
resistances was given based on the Christoffel-Darboux identity. In this paper,
evaluation of effective resistances on more general networks called
pseudo-distance-regular networks [21] or QD type networks \cite{obata} is
investigated, where we use the stratification of these networks and show that
the effective resistances between a given node such as and all of the
nodes belonging to the same stratum with respect to
(, belonging to the -th stratum with respect
to the ) are the same. Then, based on the spectral techniques, an
analytical formula for effective resistances such that
(those nodes , of
the network such that the network is symmetric with respect to them) is given
in terms of the first and second orthogonal polynomials associated with the
network, where is the pseudo-inverse of the Laplacian of the network.
From the fact that in distance-regular networks,
is satisfied for all nodes
of the network, the effective resistances
for ( is diameter of the network which
is the same as the number of strata) are calculated directly, by using the
given formula.Comment: 30 pages, 7 figure
Tunneling in Decaying Cosmologies and the Cosmological Constant Problem
The tunneling rate, with exact prefactor, is calculated to first order in
for an empty closed Friedmann-Robertson-Walker (FRW) universe with
decaying cosmological term ( is the scale factor and
is a parameter ). This model is equivalent to a cosmology
with the equation of state . The calculations are
performed by applying the dilute-instanton approximation on the corresponding
Duru-Kleinert path integral.
It is shown that the highest tunneling rate occurs for corresponding to
the cosmic string matter universe. The obtained most probable cosmological
term, like one obtained by Strominger, accounts for a possible solution to the
cosmological constant problem.Comment: 21 pages, REVTEX, The section 3 is considerably completed including
some physical mechanisms supporting the time variation of the cosmological
constant, added references for the section 3. Accepted to be published in
Phys. Rev.
Optimal Lewenstein-Sanpera Decomposition for some Biparatite Systems
It is shown that for a given bipartite density matrix and by choosing a
suitable separable set (instead of product set) on the separable-entangled
boundary, optimal Lewenstein-Sanpera (L-S) decomposition can be obtained via
optimization for a generic entangled density matrix. Based on this, We obtain
optimal L-S decomposition for some bipartite systems such as and
Bell decomposable states, generic two qubit state in Wootters
basis, iso-concurrence decomposable states, states obtained from BD states via
one parameter and three parameters local operations and classical
communications (LOCC), Werner and isotropic states, and a one
parameter state. We also obtain the optimal decomposition for
multi partite isotropic state. It is shown that in all systems
considered here the average concurrence of the decomposition is equal to the
concurrence. We also show that for some Bell decomposable states
the average concurrence of the decomposition is equal to the lower bound of the
concurrence of state presented recently in [Buchleitner et al,
quant-ph/0302144], so an exact expression for concurrence of these states is
obtained. It is also shown that for isotropic state where
decomposition leads to a separable and an entangled pure state, the average
I-concurrence of the decomposition is equal to the I-concurrence of the state.
Keywords: Quantum entanglement, Optimal Lewenstein-Sanpera decomposition,
Concurrence, Bell decomposable states, LOCC}
PACS Index: 03.65.UdComment: 31 pages, Late
Finite quantum tomography via semidefinite programming
Using the the convex semidefinite programming method and superoperator
formalism we obtain the finite quantum tomography of some mixed quantum states
such as: qudit tomography, N-qubit tomography, phase tomography and coherent
spin state tomography, where that obtained results are in agreement with those
of References \cite{schack,Pegg,Barnett,Buzek,Weigert}.Comment: 25 page
Spectral fluctuation properties of spherical nuclei
The spectral fluctuation properties of spherical nuclei are considered by use
of NNSD statistic. With employing a generalized Brody distribution included
Poisson, GOE and GUE limits and also MLE technique, the chaoticity parameters
are estimated for sequences prepared by all the available empirical data. The
ML-based estimated values and also KLD measures propose a non regular dynamic.
Also, spherical odd-mass nuclei in the mass region, exhibit a slight deviation
to the GUE spectral statistics rather than the GOE.Comment: 10 pages, 2 figure
Equation of state for Universe from similarity symmetries
In this paper we proposed to use the group of analysis of symmetries of the
dynamical system to describe the evolution of the Universe. This methods is
used in searching for the unknown equation of state. It is shown that group of
symmetries enforce the form of the equation of state for noninteracting scaling
multifluids. We showed that symmetries give rise the equation of state in the
form and energy density
, which
is commonly used in cosmology. The FRW model filled with scaling fluid (called
homological) is confronted with the observations of distant type Ia supernovae.
We found the class of model parameters admissible by the statistical analysis
of SNIa data. We showed that the model with scaling fluid fits well to
supernovae data. We found that and (), which can correspond to (hyper) phantom fluid, and to a
high density universe. However if we assume prior that
then the favoured model is close to concordance
CDM model. Our results predict that in the considered model with
scaling fluids distant type Ia supernovae should be brighter than in
CDM model, while intermediate distant SNIa should be fainter than in
CDM model. We also investigate whether the model with scaling fluid is
actually preferred by data over CDM model. As a result we find from
the Akaike model selection criterion prefers the model with noninteracting
scaling fluid.Comment: accepted for publication versio
Quantum Cosmology and Open Universes
Quantum creation of Universes with compact spacelike sections that have
curvature either closed, flat or open, i.e. are studied. In the
flat and open cases, the superpotential of the Wheeler De Witt equation is
significantly modified, and as a result the qualitative behaviour of a typical
wavefunction differs from the traditional closed case. Using regularity
arguments, it is shown that the only consistent state for the wavefunction is
the Tunneling one. By computing the quantum probabilities for the curvature of
the sections, it is shown that quantum cosmology actually favours that the
Universe be open, . In all cases sufficient inflation
e-foldings is predicted: this is an improvement over classical measures that
generally are ambiguous as to whether inflation is certain to occur.Comment: 11 pages, Revtex, 7 figures. Accepted for publication in PRD. New
material and important corrections added in response to referee's repor