4,141 research outputs found
Complexity and capacity bounds for quantum channels
We generalise some well-known graph parameters to operator systems by
considering their underlying quantum channels. In particular, we introduce the
quantum complexity as the dimension of the smallest co-domain Hilbert space a
quantum channel requires to realise a given operator system as its
non-commutative confusability graph. We describe quantum complexity as a
generalised minimum semidefinite rank and, in the case of a graph operator
system, as a quantum intersection number. The quantum complexity and a closely
related quantum version of orthogonal rank turn out to be upper bounds for the
Shannon zero-error capacity of a quantum channel, and we construct examples for
which these bounds beat the best previously known general upper bound for the
capacity of quantum channels, given by the quantum Lov\'asz theta number
Schur multipliers of Cartan pairs
We define the Schur multipliers of a separable von Neumann algebra M with
Cartan masa A, generalising the classical Schur multipliers of . We
characterise these as the normal A-bimodule maps on M. If M contains a direct
summand isomorphic to the hyperfinite II_1 factor, then we show that the Schur
multipliers arising from the extended Haagerup tensor product are strictly contained in the algebra of all Schur multipliers
Magneto-mechanical interplay in spin-polarized point contacts
We investigate the interplay between magnetic and structural dynamics in
ferromagnetic atomic point contacts. In particular, we look at the effect of
the atomic relaxation on the energy barrier for magnetic domain wall migration
and, reversely, at the effect of the magnetic state on the mechanical forces
and structural relaxation. We observe changes of the barrier height due to the
atomic relaxation up to 200%, suggesting a very strong coupling between the
structural and the magnetic degrees of freedom. The reverse interplay is weak,
i.e. the magnetic state has little effect on the structural relaxation at
equilibrium or under non-equilibrium, current-carrying conditions.Comment: 5 pages, 4 figure
State convertibility in the von Neumann algebra framework
We establish a generalisation of the fundamental state convertibility theorem
in quantum information to the context of bipartite quantum systems modelled by
commuting semi-finite von Neumann algebras. Namely, we establish a
generalisation to this setting of Nielsen's theorem on the convertibility of
quantum states under local operations and classical communication (LOCC)
schemes. Along the way, we introduce an appropriate generalisation of LOCC
operations and connect the resulting notion of approximate convertibility to
the theory of singular numbers and majorisation in von Neumann algebras. As an
application of our result in the setting of -factors, we show that the
entropy of the singular value distribution relative to the unique tracial state
is an entanglement monotone in the sense of Vidal, thus yielding a new way to
quantify entanglement in that context. Building on previous work in the
infinite-dimensional setting, we show that trace vectors play the role of
maximally entangled states for general -factors. Examples are drawn from
infinite spin chains, quasi-free representations of the CAR, and discretised
versions of the CCR.Comment: 36 pages, v2: journal version, 38 page
Hartree-Fock theory of a current-carrying electron gas
State-of-the-art simulation tools for nonequilibrium quantum transport systems typically take the current-carrier occupations to be described in terms of equilibrium distribution functions characterized by two different electrochemical potentials, while for the description of electronic exchange and correlation, the local density approximation (LDA) to density functional theory is generally used. However, this involves an inconsistency because the LDA is based on the homogeneous electron gas in equilibrium, while the system is not in equilibrium and may be far from it. In this paper, we analyze this inconsistency by studying the interplay between nonequilibrium occupancies obtained from a maximum entropy approach and the Hartree-Fock exchange energy, single-particle spectrum and exchange hole, for the case of a two-dimensional homogeneous electron gas. The current dependence of the local exchange potential is also discussed. It is found that the single-particle spectrum and exchange hole have a significant dependence on the current, which has not been taken into account in practical calculations since it is not captured by the commonly used functionals. The exchange energy and the local exchange potential, however, are shown to change very little with respect to their equilibrium counterparts. The weak dependence of these quantities on the current is explained in terms of the symmetries of the exchange hole
On the pulsating strings in Sasaki-Einstein spaces
We study the class of pulsating strings in AdS_5 x Y^{p,q} and AdS_5 x
L^{p,q,r}. Using a generalized ansatz for pulsating string configurations, we
find new solutions for this class in terms of Heun functions, and derive the
particular case of AdS_5 x T^{1,1}, which was analyzed in arXiv:1006.1539
[hep-th]. Unfortunately, Heun functions are still little studied, and we are
not able to quantize the theory quasi-classically and obtain the first
corrections to the energy. The latter, due to AdS/CFT correspondence, is
supposed to give the anomalous dimensions of operators of the gauge theory dual
N=1 superconformal field theory.Comment: 9 pages, talk given at the 2nd Int. Conference AMiTaNS, 21-26 June
2010, Sozopol, Bulgaria, organized by EAC (Euro-American Consortium) for
Promoting AMiTaNS, to appear in the Proceedings of 2nd Int. Conference
AMiTaN
Single-particle and Interaction Effects on the Cohesion and Transport and Magnetic Properties of Metal Nanowires at Finite Voltages
The single-particle and interaction effects on the cohesion, electronic
transport, and some magnetic properties of metallic nanocylinders have been
studied at finite voltages by using a generalized mean-field electron model.
The electron-electron interactions are treated in the self-consistent Hartree
approximation. Our results show the single-particle effect is dominant in the
cohesive force, while the nonzero magnetoconductance and magnetotension
coefficients are attributed to the interaction effect. Both single-particle and
interaction effects are important to the differential conductance and magnetic
susceptibility.Comment: 5 pages, 6 figure
Reconstruction of electrons with the Gaussian-sum filter in the CMS tracker at LHC
The bremsstrahlung energy loss distribution of electrons propagating in
matter is highly non Gaussian. Because the Kalman filter relies solely on
Gaussian probability density functions, it might not be an optimal
reconstruction algorithm for electron tracks. A Gaussian-sum filter (GSF)
algorithm for electron track reconstruction in the CMS tracker has therefore
been developed. The basic idea is to model the bremsstrahlung energy loss
distribution by a Gaussian mixture rather than a single Gaussian. It is shown
that the GSF is able to improve the momentum resolution of electrons compared
to the standard Kalman filter. The momentum resolution and the quality of the
estimated error are studied with various types of mixture models of the energy
loss distribution.Comment: Talk from the 2003 Computing in High Energy and Nuclear Physics
(CHEP03), La Jolla, Ca, USA, March 2003, LaTeX, 14 eps figures. PSN TULT00
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