123,955 research outputs found
Conditions for Nondistortion Interrogation of Quantum System
Under some physical considerations, we present a universal formulation to
study the possibility of localizing a quantum object in a given region without
disturbing its unknown internal state. When the interaction between the object
and probe wave function takes place only once, we prove the necessary and
sufficient condition that the object's presence can be detected in an initial
state preserving way. Meanwhile, a conditioned optimal interrogation
probability is obtained.Comment: 5 pages, Revtex, 1 figures, Presentation improved, corollary 1 added.
To appear in Europhysics Letter
Quantum insulating states of F=2 cold atoms in optical lattices
In this Letter we study various spin correlated insulating states of F=2 cold
atoms in optical lattices. We find that the effective spin exchange interaction
due to virtual hopping contains an {\em octopole} coupling between two
neighboring lattice sites. Depending on scattering lengths and numbers of
particles per site the ground states are either rotationally invariant dimer or
trimer Mott insulators or insulating states with various spin orders. Three
spin ordered insulating phases are ferromagnetic, cyclic and nematic Mott
insulators. We estimate the phase boundaries for states with different numbers
of atoms per lattice site.Comment: 4 pages, 1 figure include
Central limit theorem for signal-to-interference ratio of reduced rank linear receiver
Let with
independent and identically distributed complex random
variables. Write ,
and
. Define
$\beta_{km}=p_k\mathbf{s}_k^*\mathbf{A}_{km}(\mathbf {A}_{km}^*\times\
mathbf{R}_k\mathbf{A}_{km})^{-1}\mathbf{A}_{km}^*\mathbf{s}_kkN/K\to c>0$. Moreover, we provide a
central limit theorem for linear spectral statistics of eigenvalues and
eigenvectors of sample covariance matrices, which is a supplement of Theorem 2
in Bai, Miao and Pan [Ann. Probab. 35 (2007) 1532--1572]. And we also improve
Theorem 1.1 in Bai and Silverstein [Ann. Probab. 32 (2004) 553--605].Comment: Published in at http://dx.doi.org/10.1214/07-AAP477 the Annals of
Applied Probability (http://www.imstat.org/aap/) by the Institute of
Mathematical Statistics (http://www.imstat.org
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