20,687 research outputs found
Measurements incompatible in Quantum Theory cannot be measured jointly in any other local theory
It is well known that jointly measurable observables cannot lead to a
violation of any Bell inequality - independent of the state and the
measurements chosen at the other site. In this letter we prove the converse:
every pair of incompatible quantum observables enables the violation of a Bell
inequality and therefore must remain incompatible within any other no-signaling
theory. While in the case of von Neumann measurements it is sufficient to use
the same pair of observables at both sites, general measurements can require
different choices. The main result is obtained by showing that for arbitrary
dimension the CHSH inequality provides the Lagrangian dual of the
characterization of joint measurability. This leads to a simple criterion for
joint measurability beyond the known qubit case.Comment: 4 page
Explicit computations of low lying eigenfunctions for the quantum trigonometric Calogero-Sutherland model related to the exceptional algebra E7
In the previous paper math-ph/0507015 we have studied the characters and
Clebsch-Gordan series for the exceptional Lie algebra E7 by relating them to
the quantum trigonometric Calogero-Sutherland Hamiltonian with coupling
constant K=1. Now we extend that approach to the case of general K
Generating functions and multiplicity formulas: the case of rank two simple Lie algebras
A procedure is described that makes use of the generating function of
characters to obtain a new generating function giving the multiplicities of
each weight in all the representations of a simple Lie algebra. The way to
extract from explicit multiplicity formulas for particular weights is
explained and the results corresponding to rank two simple Lie algebras shown
Coupled equations for Kähler metrics and Yang-Mills connections
We study equations on a principal bundle over a compact complex manifold
coupling a connection on the bundle with a Kahler structure on the base. These
equations generalize the conditions of constant scalar curvature for a Kahler
metric and Hermite-Yang-Mills for a connection. We provide a moment map
interpretation of the equations and study obstructions for the existence of
solutions, generalizing the Futaki invariant, the Mabuchi K-energy and geodesic
stability. We finish by giving some examples of solutions.Comment: 61 pages; v2: introduction partially rewritten; minor corrections and
improvements in presentation, especially in Section 4; added references; v3:
To appear in Geom. Topol. Minor corrections and improvements, following
comments by referee
Excited-state quantum phase transitions in a two-fluid Lipkin model
Background: Composed systems have became of great interest in the framework
of the ground state quantum phase transitions (QPTs) and many of their
properties have been studied in detail. However, in these systems the study of
the so called excited-state quantum phase transitions (ESQPTs) have not
received so much attention.
Purpose: A quantum analysis of the ESQPTs in the two-fluid Lipkin model is
presented in this work. The study is performed through the Hamiltonian
diagonalization for selected values of the control parameters in order to cover
the most interesting regions of the system phase diagram. [Method:] A
Hamiltonian that resembles the consistent-Q Hamiltonian of the interacting
boson model (IBM) is diagonalized for selected values of the parameters and
properties such as the density of states, the Peres lattices, the
nearest-neighbor spacing distribution, and the participation ratio are
analyzed.
Results: An overview of the spectrum of the two-fluid Lipkin model for
selected positions in the phase diagram has been obtained. The location of the
excited-state quantum phase transition can be easily singled out with the Peres
lattice, with the nearest-neighbor spacing distribution, with Poincar\'e
sections or with the participation ratio.
Conclusions: This study completes the analysis of QPTs for the two-fluid
Lipkin model, extending the previous study to excited states. The ESQPT
signatures in composed systems behave in the same way as in single ones,
although the evidences of their presence can be sometimes blurred. The Peres
lattice turns out to be a convenient tool to look into the position of the
ESQPT and to define the concept of phase in the excited states realm
Simultaneous analysis of elastic scattering and transfer/breakup channels for the 6He+208Pb reaction at energies near the Coulomb barrier
The elastic and alpha-production channels for the 6He+208Pb reaction are
investigated at energies around the Coulomb barrier (E_{lab}=14, 16, 18, 22,
and 27 MeV). The effect of the two-neutron transfer channels on the elastic
scattering has been studied within the Coupled-Reaction-Channels (CRC) method.
We find that the explicit inclusion of these channels allows a simultaneous
description of the elastic data and the inclusive alpha cross sections at
backward angles. Three-body Continuum-Discretized Coupled-Channels (CDCC)
calculations are found to reproduce the elastic data, but not the
transfer/breakup data. The trivially-equivalent local polarization potential
(TELP) derived from the CRC and CDCC calculations are found to explain the
features found in previous phenomenological optical model calculations for this
system.Comment: 7 pages, 6 figures (replaced with updated version
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