145 research outputs found
Hierarchy of random deterministic chaotic maps with an invariant measure
Hierarchy of one and many-parameter families of random trigonometric chaotic
maps and one-parameter random elliptic chaotic maps of type with an
invariant measure have been introduced. Using the invariant measure
(Sinai-Ruelle-Bowen measure), the Kolmogrov-Sinai entropy of the random chaotic
maps have been calculated analytically, where the numerical simulations support
the resultsComment: 11 pages, Late
Generalized Master Function Approach to Quasi-Exactly Solvable Models
By introducing the generalized master function of order up to four together
with corresponding weight function, we have obtained all quasi-exactly solvable
second order differential equations. It is shown that these differntial
equations have solutions of polynomial type with factorziation properties, that
is polynomial solutions Pm(E) can be factorized in terms of polynomial Pn(E)
for m not equal to n. All known quasi-exactly quantum solvable models can be
obtained from these differential equations, where roots of polynomial Pn(E) are
corresponding eigen-values.Comment: 21 Page
Calculating effective resistances on underlying networks of association schemes
Recently, in Refs. \cite{jsj} and \cite{res2}, calculation of effective
resistances on distance-regular networks was investigated, where in the first
paper, the calculation was based on stratification 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 which
are underlying networks of association schemes is considered, where by using
the algebraic combinatoric structures of association schemes such as
stratification and Bose-Mesner algebras, an explicit formula for effective
resistances on these networks is given in terms of the parameters of
corresponding association schemes. Moreover, we show that for particular
underlying networks of association schemes with diameter such that the
adjacency matrix possesses distinct eigenvalues, all of the other
adjacency matrices , can be written as polynomials of ,
i.e., , where is not necessarily of degree . Then, we use
this property for these particular networks and assume that all of the
conductances except for one of them, say , are zero to give a
procedure for evaluating effective resistances on these networks. The
preference of this procedure is that one can evaluate effective resistances by
using the structure of their Bose-Mesner algebra without any need to know the
spectrum of the adjacency matrices.Comment: 41 page
The minimum-error discrimination via Helstrom family of ensembles and Convex Optimization
Using the convex optimization method and Helstrom family of ensembles
introduced in Ref. [1], we have discussed optimal ambiguous discrimination in
qubit systems. We have analyzed the problem of the optimal discrimination of N
known quantum states and have obtained maximum success probability and optimal
measurement for N known quantum states with equiprobable prior probabilities
and equidistant from center of the Bloch ball, not all of which are on the one
half of the Bloch ball and all of the conjugate states are pure. An exact
solution has also been given for arbitrary three known quantum states. The
given examples which use our method include: 1. Diagonal N mixed states; 2. N
equiprobable states and equidistant from center of the Bloch ball which their
corresponding Bloch vectors are inclined at the equal angle from z axis; 3.
Three mirror-symmetric states; 4. States that have been prepared with equal
prior probabilities on vertices of a Platonic solid.
Keywords: minimum-error discrimination, success probability, measurement,
POVM elements, Helstrom family of ensembles, convex optimization, conjugate
states PACS Nos: 03.67.Hk, 03.65.TaComment: 15 page
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