113,396 research outputs found
Decomposition of Triebel-Lizorkin and Besov spaces in the context of Laguerre expansions
A pair of dual frames with almost exponentially localized elements (needlets)
are constructed on \RR_+^d based on Laguerre functions. It is shown that the
Triebel-Lizorkin and Besov spaces induced by Laguerre expansions can be
characterized in terms of respective sequence spaces that involve the needlet
coefficients.Comment: 42 page
Role of Disorder in Mn:GaAs, Cr:GaAs, and Cr:GaN
We present calculations of magnetic exchange interactions and critical
temperature T_c in Mn:GaAs, Cr:GaAs and Cr:GaN. The local spin density
approximation is combined with a linear-response technique to map the magnetic
energy onto a Heisenberg hamiltonion, but no significant further approximations
are made. Special quasi-random structures in large unit cells are used to
accurately model the disorder. T_c is computed using both a spin-dynamics
approach and the cluster variation method developed for the classical
Heisenberg model.
We show the following: (i) configurational disorder results in large
dispersions in the pairwise exchange interactions; (ii) the disorder strongly
reduces T_c; (iii) clustering in the magnetic atoms, whose tendency is
predicted from total-energy considerations, further reduces T_c. Additionally
the exchange interactions J(R) are found to decay exponentially with distance
R^3 on average; and the mean-field approximation is found to be a very poor
predictor of T_c, particularly when J(R) decays rapidly. Finally the effect of
spin-orbit coupling on T_c is considered. With all these factors taken into
account, T_c is reasonably predicted by the local spin-density approximation in
MnGaAs without the need to invoke compensation by donor impurities.Comment: 10 pages, 3 figure
Quantum Phase Transitions beyond the Landau's Paradigm in Sp(4) Spin System
We propose quantum phase transitions beyond the Landau's paradigm of Sp(4)
spin Heisenberg models on the triangular and square lattices, motivated by the
exact Sp(4) SO(5) symmetry of spin-3/2 fermionic cold atomic system
with only wave scattering. On the triangular lattice, we study a phase
transition between the spin ordered phase and a
spin liquid phase, this phase transition is described by an O(8) sigma model in
terms of fractionalized spinon fields, with significant anomalous scaling
dimensions of spin order parameters. On the square lattice, we propose a
deconfined critical point between the Neel order and the VBS order, which is
described by the CP(3) model, and the monopole effect of the compact U(1) gauge
field is expected to be suppressed at the critical point.Comment: 6 pages, 3 figure
The perfect spin injection in silicene FS/NS junction
We theoretically investigate the spin injection from a ferromagnetic silicene
to a normal silicene (FS/NS), where the magnetization in the FS is assumed from
the magnetic proximity effect. Based on a silicene lattice model, we
demonstrated that the pure spin injection could be obtained by tuning the Fermi
energy of two spin species, where one is in the spin orbit coupling gap and the
other one is outside the gap. Moreover, the valley polarity of the spin species
can be controlled by a perpendicular electric field in the FS region. Our
findings may shed light on making silicene-based spin and valley devices in the
spintronics and valleytronics field.Comment: 6 pages, 3 figure
Learning-aided Stochastic Network Optimization with Imperfect State Prediction
We investigate the problem of stochastic network optimization in the presence
of imperfect state prediction and non-stationarity. Based on a novel
distribution-accuracy curve prediction model, we develop the predictive
learning-aided control (PLC) algorithm, which jointly utilizes historic and
predicted network state information for decision making. PLC is an online
algorithm that requires zero a-prior system statistical information, and
consists of three key components, namely sequential distribution estimation and
change detection, dual learning, and online queue-based control.
Specifically, we show that PLC simultaneously achieves good long-term
performance, short-term queue size reduction, accurate change detection, and
fast algorithm convergence. In particular, for stationary networks, PLC
achieves a near-optimal , utility-delay
tradeoff. For non-stationary networks, \plc{} obtains an
utility-backlog tradeoff for distributions that last
time, where
is the prediction accuracy and is a constant (the
Backpressue algorithm \cite{neelynowbook} requires an length
for the same utility performance with a larger backlog). Moreover, PLC detects
distribution change slots faster with high probability ( is the
prediction size) and achieves an convergence time. Our results demonstrate
that state prediction (even imperfect) can help (i) achieve faster detection
and convergence, and (ii) obtain better utility-delay tradeoffs
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