56,524 research outputs found
Field Induced Positional Shift of Bloch Electrons and its Dynamical Implications
We derive the field correction to the Berry curvature of Bloch electrons,
which can be traced back to a positional shift due to the interband mixing
induced by external electromagnetic fields. The resulting semiclassical
dynamics is accurate to second order in the fields, in the same form as before,
provided that the wave packet energy is derived up to the same order. As
applications, we discuss the orbital magnetoelectric polarizability and predict
nonlinear anomalous Hall effects
The Sampling-and-Learning Framework: A Statistical View of Evolutionary Algorithms
Evolutionary algorithms (EAs), a large class of general purpose optimization
algorithms inspired from the natural phenomena, are widely used in various
industrial optimizations and often show excellent performance. This paper
presents an attempt towards revealing their general power from a statistical
view of EAs. By summarizing a large range of EAs into the sampling-and-learning
framework, we show that the framework directly admits a general analysis on the
probable-absolute-approximate (PAA) query complexity. We particularly focus on
the framework with the learning subroutine being restricted as a binary
classification, which results in the sampling-and-classification (SAC)
algorithms. With the help of the learning theory, we obtain a general upper
bound on the PAA query complexity of SAC algorithms. We further compare SAC
algorithms with the uniform search in different situations. Under the
error-target independence condition, we show that SAC algorithms can achieve
polynomial speedup to the uniform search, but not super-polynomial speedup.
Under the one-side-error condition, we show that super-polynomial speedup can
be achieved. This work only touches the surface of the framework. Its power
under other conditions is still open
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