10,565 research outputs found
States of Local Moment Induced by Nonmagnetic Impurities in Cuprate Superconductors
By using a model Hamiltonian with d-wave superconductivity and competing
antiferromagnetic (AF) orders, the local staggered magnetization distribution
due to nonmagnetic impurities in cuprate superconductors is investigated. From
this, the net magnetic moment induced by a single or double impurities can be
obtained. We show that the net moment induced by a single impurity corresponds
to a local spin with S_z=0, or 1/2 depending on the strength of the AF
interaction and the impurity scattering. When two impurities are placed at the
nearest neighboring sites, the net moment is always zero. For two unitary
impurities at the next nearest neighboring sites, and at sites separated by a
Cu-ion site, the induced net moment has S_z=0, or 1/2, or 1. The consequence of
these results on experiments will be discussed.Comment: 4 pages, 4 figure
Differentially private analysis of networks with covariates via a generalized -model
How to achieve the tradeoff between privacy and utility is one of fundamental
problems in private data analysis.In this paper, we give a rigourous
differential privacy analysis of networks in the appearance of covariates via a
generalized -model, which has an -dimensional degree parameter
and a -dimensional homophily parameter .Under -edge differential privacy, we use the popular Laplace mechanism to
release the network statistics.The method of moments is used to estimate the
unknown model parameters. We establish the conditions guaranteeing consistency
of the differentially private estimators and
as the number of nodes goes to infinity, which reveal an
interesting tradeoff between a privacy parameter and model parameters. The
consistency is shown by applying a two-stage Newton's method to obtain the
upper bound of the error between and its
true value in terms of the distance, which has
a convergence rate of rough order for and
for , respectively. Further, we derive the asymptotic
normalities of and , whose asymptotic
variances are the same as those of the non-private estimators under some
conditions. Our paper sheds light on how to explore asymptotic theory under
differential privacy in a principled manner; these principled methods should be
applicable to a class of network models with covariates beyond the generalized
-model. Numerical studies and a real data analysis demonstrate our
theoretical findings.Comment: 34 pages, 2 figures. arXiv admin note: substantial text overlap with
arXiv:2107.10735 by other author
Compressibility of Interacting Electrons in Bilayer Graphene
Using the renormalized-ring-diagram approximation, we study the
compressibility of the interacting electrons in bilayer graphene. The
compressibility is equivalent to the spin susceptibility apart from a constant
factor. The chemical potential and the compressibility of the electrons can be
significantly altered by an energy gap (tunable by external gate voltages)
between the valence and conduction bands. For zero gap and a typical finite gap
in the experiments, we show both systems are stable.Comment: 5 pages, 6 figure
Correlation evolution and monogamy of two geometric quantum discords in multipartite systems
We explore two different geometric quantum discords defined respectively via
the trace norm (GQD-1) and Hilbert-Schmidt norm (GQD-2) in multipartite
systems. A rigorous hierarchy relation is revealed for the two GQDs in a class
of symmetric two-qubit -shape states. For multiqubit pure states, it is
found that both GQDs are related to the entanglement concurrence, with the
hierarchy relation being saturated. Furthermore, we look into a four-partite
dynamical system consisting of two cavities interacting with independent
reservoirs. It is found that the GQD-2 can exhibit various sudden change
behaviours, while the GQD-1 only evolves asymptotically, with the two GQDs
exhibiting different monogamous properties.Comment: 5 pages, 3 figure
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