4,749 research outputs found
The Weyl group of the fine grading of associated with tensor product of generalized Pauli matrices
We consider the fine grading of sl(n,\mb C) induced by tensor product of
generalized Pauli matrices in the paper. Based on the classification of maximal
diagonalizable subgroups of PGL(n,\mb C) by Havlicek, Patera and Pelantova,
we prove that any finite maximal diagonalizable subgroup of PGL(n,\mb C)
is a symplectic abelian group and its Weyl group, which describes the symmetry
of the fine grading induced by the action of , is just the isometry group of
the symplectic abelian group . For a finite symplectic abelian group, it is
also proved that its isometry group is always generated by the transvections
contained in it
Fine gradings of complex simple Lie algebras and Finite Root Systems
A -grading on a complex semisimple Lie algebra , where is a finite
abelian group, is called quasi-good if each homogeneous component is
1-dimensional and 0 is not in the support of the grading.
Analogous to classical root systems, we define a finite root system to be
some subset of a finite symplectic abelian group satisfying certain axioms.
There always corresponds to a semisimple Lie algebra together with a
quasi-good grading on it. Thus one can construct nice basis of by means
of finite root systems.
We classify finite maximal abelian subgroups in \Aut(L) for complex
simple Lie algebras such that the grading induced by the action of on
is quasi-good, and show that the set of roots of in is always a
finite root system. There are five series of such finite maximal abelian
subgroups, which occur only if is a classical simple Lie algebra
De-noising of Power Quality Disturbance Detection Based on Ensemble Empirical Mode Decomposition Threshold Algorithm
Actual power quality signal which is often affected by noise pollution impacts the analysis results of the disturbance signal. In this paper, EEMD (Ensemble Empirical Mode Decomposition)-based threshold de-noising method is proposed for power quality signal with different SNR (Signal-to-Noise Ratio). As a comparison, we use other four thresholds, namely, the heuristic threshold, the self-adaptive threshold, the fixed threshold and the minimax threshold to filter the noises from power quality signal. Through the analysis and comparison of three characteristics of the signal pre-and-post de-noised, including waveforms, SNR and MSE (Mean Square Error), furthermore the instantaneous attribute of corresponding time by HHT (Hilbert Huang Transform). Simulation results show that EEMD threshold de-noising method can make the waveform close to the actual value. The SNR is higher and the MSE is smaller compared with other four thresholds. The instantaneous attribute can reflect the actual disturbance signal more exactly. The optimal threshold EEMD-based algorithm is proposed for power quality disturbance signal de-noising. Meanwhile, EEMD threshold de-noising method with adaptivity is suitable for composite disturbance signal de-noising
Superfluid density in the slave-boson theory
Despite of the success of the slave-boson theory in capturing qualitative
physics of high-temperature superconductors like cuprates, it fails to
reproduce the correct temperature-dependent behavior of superfluid density, let
alone the independence of the linear temperature term on doping in the
underdoped regimes of hole-doped cuprate, a common experimental observation in
different cuprates. It remains puzzling up to now in spite of intensive
theoretical efforts. For electron-doped case, even qualitative treatment is not
reported at present time. Here we revisit these problems and provide an
alternative superfluid density formulation by using the London relation instead
of employing the paramagnetic current-current correlation function. The
obtained formula, on the one hand, provides the correct temperature-dependent
behavior of the superfluid density in the whole temperature regime, on the
other hand, makes the doping dependence of the linear temperature term
substantially weaken and a possible interpretation for its independence on
doping is proposed. As an application, electron-doped cuprate is studied, whose
result qualitatively agrees with existing experiments and successfully explains
the origin of - to anisotropic -wave transition across the optimal
doping. Our result remedies some failures of the slave-boson theory as employed
to calculate superfluid density in cuprates and may be useful in the
understanding of the related physics in other strongly correlated systems, e.g.
NaCoOyHO and certain iron-based superconductors with
dominating local magnetic exchange interaction.Comment: 7 pages, 4 figure
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