7,338 research outputs found
Intervalley coupling by quantum dot confinement potentials in monolayer transition metal dichalcogenides
Monolayer transition metal dichalcogenides (TMDs) offer new opportunities for
realizing quantum dots (QDs) in the ultimate two-dimensional (2D) limit. Given
the rich control possibilities of electron valley pseudospin discovered in the
monolayers, this quantum degree of freedom can be a promising carrier of
information for potential quantum spintronics exploiting single electrons in
TMD QDs. An outstanding issue is to identify the degree of valley
hybridization, due to the QD confinement, which may significantly change the
valley physics in QDs from its form in the 2D bulk. Here we perform a
systematic study of the intervalley coupling by QD confinement potentials on
extended TMD monolayers. We find that the intervalley coupling in such geometry
is generically weak due to the vanishing amplitude of the electron wavefunction
at the QD boundary, and hence valley hybridization shall be well quenched by
the much stronger spin-valley coupling in monolayer TMDs and the QDs can well
inherit the valley physics of the 2D bulk. We also discover sensitive
dependence of intervalley coupling strength on the central position and the
lateral length scales of the confinement potentials, which may possibly allow
tuning of intervalley coupling by external controlsComment: 17 pages, 14 figure
Principal component analysis for second-order stationary vector time series
We extend the principal component analysis (PCA) to second-order stationary
vector time series in the sense that we seek for a contemporaneous linear
transformation for a -variate time series such that the transformed series
is segmented into several lower-dimensional subseries, and those subseries are
uncorrelated with each other both contemporaneously and serially. Therefore
those lower-dimensional series can be analysed separately as far as the linear
dynamic structure is concerned. Technically it boils down to an eigenanalysis
for a positive definite matrix. When is large, an additional step is
required to perform a permutation in terms of either maximum cross-correlations
or FDR based on multiple tests. The asymptotic theory is established for both
fixed and diverging when the sample size tends to infinity.
Numerical experiments with both simulated and real data sets indicate that the
proposed method is an effective initial step in analysing multiple time series
data, which leads to substantial dimension reduction in modelling and
forecasting high-dimensional linear dynamical structures. Unlike PCA for
independent data, there is no guarantee that the required linear transformation
exists. When it does not, the proposed method provides an approximate
segmentation which leads to the advantages in, for example, forecasting for
future values. The method can also be adapted to segment multiple volatility
processes.Comment: The original title dated back to October 2014 is "Segmenting Multiple
Time Series by Contemporaneous Linear Transformation: PCA for Time Series
High dimensional stochastic regression with latent factors, endogeneity and nonlinearity
We consider a multivariate time series model which represents a high
dimensional vector process as a sum of three terms: a linear regression of some
observed regressors, a linear combination of some latent and serially
correlated factors, and a vector white noise. We investigate the inference
without imposing stationary conditions on the target multivariate time series,
the regressors and the underlying factors. Furthermore we deal with the
endogeneity that there exist correlations between the observed regressors and
the unobserved factors. We also consider the model with nonlinear regression
term which can be approximated by a linear regression function with a large
number of regressors. The convergence rates for the estimators of regression
coefficients, the number of factors, factor loading space and factors are
established under the settings when the dimension of time series and the number
of regressors may both tend to infinity together with the sample size. The
proposed method is illustrated with both simulated and real data examples
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