426 research outputs found
On properties of the space of quantum states and their application to construction of entanglement monotones
We consider two properties of the set of quantum states as a convex
topological space and some their implications concerning the notions of a
convex hull and of a convex roof of a function defined on a subset of quantum
states.
By using these results we analyze two infinite-dimensional versions (discrete
and continuous) of the convex roof construction of entanglement monotones,
which is widely used in finite dimensions. It is shown that the discrete
version may be 'false' in the sense that the resulting functions may not
possess the main property of entanglement monotones while the continuous
version can be considered as a 'true' generalized convex roof construction. We
give several examples of entanglement monotones produced by this construction.
In particular, we consider an infinite-dimensional generalization of the notion
of Entanglement of Formation and study its properties.Comment: 34 pages, the minor corrections have been mad
Generalized compactness in linear spaces and its applications
The class of subsets of locally convex spaces called -compact sets is
considered. This class contains all compact sets as well as several noncompact
sets widely used in applications. It is shown that many results well known for
compact sets can be generalized to -compact sets. Several examples are
considered.
The main result of the paper is a generalization to -compact convex sets
of the Vesterstrom-O'Brien theorem showing equivalence of the particular
properties of a compact convex set (s.t. openness of the mixture map, openness
of the barycenter map and of its restriction to maximal measures, continuity of
a convex hull of any continuous function, continuity of a convex hull of any
concave continuous function). It is shown that the Vesterstrom-O'Brien theorem
does not hold for pointwise -compact convex sets defined by the slight
relaxing of the -compactness condition. Applications of the obtained
results to quantum information theory are considered.Comment: 27 pages, the minor corrections have been mad
NN Interaction JISP16: Current Status and Prospect
We discuss realistic nonlocal NN interactions of a new type - J-matrix
Inverse Scattering Potential (JISP). In an ab exitu approach, these
interactions are fitted to not only two-nucleon data (NN scattering data and
deuteron properties) but also to the properties of light nuclei without
referring to three-nucleon forces. We discuss recent progress with the ab
initio No-core Shell Model (NCSM) approach and respective progress in
developing ab exitu JISP-type NN-interactions together with plans of their
forthcoming improvements.Comment: 9 pages, 3 figures, to be published in Proceedings of Few-body 19
conferenc
Fine-Tuning Renormalization and Two-particle States in Nonrelativistic Four-fermion Model
Various exact solutions of two-particle eigenvalue problems for
nonrelativistic contact four-fermion current-current interaction are obtained.
Specifics of Goldstone mode is investigated. The connection between a
renormalization procedure and construction of self-adjoint extensions is
revealed.Comment: 13 pages, LaTex, no figures, to be published in IJMP
Concentration phase diagram of Ba(x)Sr(1-x)TiO3 solid solutions
Method of derivation of phenomenological thermodynamic potential of solid
solutions is proposed in which the interaction of the order parameters of
constituents is introduced through the account of elastic strain due to misfit
of the lattice parameters of the end-members. The validity of the method is
demonstrated for Ba(x)Sr(1-x)TiO3 system being a typical example of
ferroelectric solid solution. Its phase diagram is determined using
experimental data for the coefficients in the phenomenological potentials of
SrTiO3 and BaTiO3. In the phase diagram of the Ba(x)Sr(1-x)TiO3 system for
small Ba concentration, there are a tricritical point and two multiphase points
one of which is associated with up to 6 possible phases.Comment: 8 pages, 3 figure
Three-loop contribution of the Faddeev-Popov ghosts to the -function of supersymmetric gauge theories and the NSVZ relation
We find the three-loop contribution to the -function of
supersymmetric gauge theories regularized by higher covariant derivatives
produced by the supergraphs containing loops of the Faddeev--Popov ghosts. This
is done using a recently proposed algorithm, which essentially simplifies such
multiloop calculations. The result is presented in the form of an integral of
double total derivatives in the momentum space. The considered contribution to
the -function is compared with the two-loop anomalous dimension of the
Faddeev--Popov ghosts. This allows verifying the validity of the NSVZ equation
written as a relation between the -function and the anomalous dimensions
of the quantum superfields. It is demonstrated that in the considered
approximation the NSVZ equation is satisfied for the renormalization group
functions defined in terms of the bare couplings. The necessity of the
nonlinear renormalization for the quantum gauge superfield is also confirmed.Comment: 20 pages, 4 figures, minor corrections, the final version to appear
in Eur.Phys.J.
Interactions of a boson in the component theory
The amplitudes for boson-boson and fermion-boson interactions are calculated
in the second order of perturbation theory in the Lobachevsky space. An
essential ingredient of the used model is the Weinberg's component
formalism for describing a particle of spin , recently developed
substantially. The boson-boson amplitude is then compared with the two-fermion
amplitude obtained long ago by Skachkov on the ground of the hamiltonian
formulation of quantum field theory on the mass hyperboloid, , proposed by Kadyshevsky. The parametrization of the amplitudes by
means of the momentum transfer in the Lobachevsky space leads to same spin
structures in the expressions of matrices for the fermion and the boson
cases. However, certain differences are found. Possible physical applications
are discussed.Comment: REVTeX 3.0 file. 12pp. Substantially revised version of IFUNAM
preprints FT-93-24, FT-93-3
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