20,854 research outputs found
The geometric mean is a Bernstein function
In the paper, the authors establish, by using Cauchy integral formula in the
theory of complex functions, an integral representation for the geometric mean
of positive numbers. From this integral representation, the geometric mean
is proved to be a Bernstein function and a new proof of the well known AG
inequality is provided.Comment: 10 page
Complexity growth rates for AdS black holes in massive gravity and gravity
The "complexity = action" duality states that the quantum complexity is equal
to the action of the stationary AdS black holes within the Wheeler-DeWitt patch
at late time approximation. We compute the action growth rates of the neutral
and charged black holes in massive gravity and the neutral, charged and
Kerr-Newman black holes in gravity to test this conjecture. Besides, we
investigate the effects of the massive graviton terms, higher derivative terms
and the topology of the black hole horizon on the complexity growth rate.Comment: 11 pages, no figur
Broadband enhancement of light harvesting in luminescent solar concentrator
Luminescent solar concentrator (LSC) can absorb large-area incident sunlight,
then emit luminescence with high quantum efficiency, which finally be collected
by a small photovoltaic (PV) system. The light-harvesting area of the PV system
is much smaller than that of the LSC system, potentially improving the
efficiency and reducing the cost of solar cells. Here, based on Fermi-golden
rule, we present a theoretical description of the luminescent process in
nanoscale LSCs where the conventional ray-optics model is no longer applicable.
As an example calculated with this new model, we demonstrate that a slot
waveguide consisting of a nanometer-sized low-index slot region sandwiched by
two high-index regions provides a broadband enhancement of light harvesting by
the luminescent centers in the slot region. This is because the slot waveguide
can (1) greatly enhance the spontaneous emission due to the Purcell effect, (2)
dramatically increase the effective absorption cross-section of luminescent
centers, and (3) strongly improve the quantum efficiency of luminescent
centers. It is found that about 80% solar photons can be ultimately converted
to waveguide-coupled luminescent photons even for a low luminescent quantum
efficiency of 0.5. This LSC is potential to construct a tandem structure which
can absorb nearly full-spectrum solar photons, and also may be of special
interest for building integrated nano-PV applications
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