6,687 research outputs found
General correlation functions of the Clauser-Horne-Shimony-Holt inequality for arbitrarily high-dimensional systems
We generalize the correlation functions of the Clauser-Horne-Shimony-Holt
(CHSH) inequality to arbitrarily high-dimensional systems. Based on this
generalization, we construct the general CHSH inequality for bipartite quantum
systems of arbitrarily high dimensionality, which takes the same simple form as
CHSH inequality for two-dimension. This inequality is optimal in the same sense
as the CHSH inequality for two dimensional systems, namely, the maximal amount
by which the inequality is violated consists with the maximal resistance to
noise. We also discuss the physical meaning and general definition of the
correlation functions. Furthermore, by giving another specific set of the
correlation functions with the same physical meaning, we realize the inequality
presented in [Phys. Rev. Lett. {\bf 88,}040404 (2002)].Comment: 4 pages, accepted by Phys. Rev. Let
The Complexity of Testing Monomials in Multivariate Polynomials
The work in this paper is to initiate a theory of testing monomials in
multivariate polynomials. The central question is to ask whether a polynomial
represented by certain economically compact structure has a multilinear
monomial in its sum-product expansion. The complexity aspects of this problem
and its variants are investigated with two folds of objectives. One is to
understand how this problem relates to critical problems in complexity, and if
so to what extent. The other is to exploit possibilities of applying algebraic
properties of polynomials to the study of those problems. A series of results
about and polynomials are obtained in this paper,
laying a basis for further study along this line
Dependence of Temporal Properties on Energy in Long-Lag, Wide-Pulse Gamma-Ray Bursts
We employed a sample compiled by Norris et al. (2005, ApJ, 625, 324) to study
the dependence of the pulse temporal properties on energy in long-lag,
wide-pulse gamma-ray bursts. Our analysis shows that the pulse peak time, rise
time scale and decay time scale are power law functions of energy, which is a
preliminary report on the relationships between the three quantities and
energy. The power law indexes associated with the pulse width, rise time scale
and decay time scale are correlated and the correlation between the indexes
associated with the pulse width and the decay time scale is more obvious. In
addition, we have found that the pulse peak lag is strongly correlated with the
CCF lag, but the centroid lag is less correlated with the peak lag and CCF lag.
Based on these results and some previous investigations, we tend to believe
that all energy-dependent pulse temporal properties may come from the joint
contribution of both the hydrodynamic processes of the outflows and the
curvature effect, where the energy-dependent spectral lag may be mainly
dominated by the dynamic process and the energy-dependent pulse width may be
mainly determined by the curvature effect.Comment: 20 pages, 7 figures, added references, matched to published version,
accepted for publication in PAS
Josephson Oscillation and Transition to Self-Trapping for Bose-Einstein-Condensates in a Triple-Well Trap
We investigate the tunnelling dynamics of Bose-Einstein-Condensates(BECs) in
a symmetric as well as in a tilted triple-well trap within the framework of
mean-field treatment. The eigenenergies as the functions of the zero-point
energy difference between the tilted wells show a striking entangled star
structure when the atomic interaction is large. We then achieve insight into
the oscillation solutions around the corresponding eigenstates and observe
several new types of Josephson oscillations. With increasing the atomic
interaction, the Josephson-type oscillation is blocked and the self-trapping
solution emerges. The condensates are self-trapped either in one well or in two
wells but no scaling-law is observed near transition points. In particular, we
find that the transition from the Josephson-type oscillation to the
self-trapping is accompanied with some irregular regime where tunnelling
dynamics is dominated by chaos. The above analysis is facilitated with the help
of the Poicar\'{e} section method that visualizes the motions of BECs in a
reduced phase plane.Comment: 10 pages, 11 figure
Exotic phase separation in one-dimensional hard-core boson system with two- and three-body interactions
We investigate the ground state phase diagram of hard-core boson system with
repulsive two-body and attractive three-body interactions in one-dimensional
optic lattice. When these two interactions are comparable and increasing the
hopping rate, physically intuitive analysis indicates that there exists an
exotic phase separation regime between the solid phase with charge density wave
order and superfluid phase. We identify these phases and phase transitions by
numerically analyzing the density distribution, structure factor of
density-density correlation function, three-body correlation function and von
Neumann entropy estimator obtained by density matrix renormalization group
method. These exotic phases and phase transitions are expected to be observed
in the ultra-cold polar molecule experiments by properly tuning interaction
parameters, which is constructive to understand the physics of ubiquitous
insulating-superconducting phase transitions in condensed matter systems
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