164,383 research outputs found

### van der Waals Heterostructures of Germanene, Stanene and Silicene with Hexagonal Boron Nitride and Their Topological Domain Walls

We investigate van der Waals (vdW) heterostructures made of germanene,
stanene or silicene with hexagonal Boron Nitride (h-BN). The intriguing
topological properties of these buckled honeycomb materials can be maintained
and further engineered in the heterostructures, where the competition between
the substrate effect and external electric fields can be used to control the
tunable topological phase transitions. Using such heterostructures as building
blocks, various vdW topological domain walls (DW) are designed, along which
there exist valley polarized quantum spin Hall edge states or
valley-contrasting edge states which are protected by valley(spin)- resolved
topological charges and can be tailored by the patterning of the
heterojunctions and by external fields.Comment: 8 pages, 6 figures, to appear in pr

### Basic theory of a class of linear functional differential equations with multiplication delay

By introducing a kind of special functions namely exponent-like function,
cosine-like function and sine-like function, we obtain explicitly the basic
structures of solutions of initial value problem at the original point for this
kind of linear pantograph equations. In particular, we get the complete results
on the existence, uniqueness and non-uniqueness of the initial value problems
at a general point for the kind of linear pantograph equations.Comment: 44 pages, no figure. This is a revised version of the third version
of the paper. Some new results and proofs have been adde

### Asymptotic Analysis for Low-Resolution Massive MIMO Systems with MMSE Receiver

The uplink achievable rate of massive multiple- input-multiple-output (MIMO)
systems, where the low-resolution analog-to-digital converters (ADCs) are
assumed to equip at the base station (BS), is investigated in this paper. We
assume that only imperfect channel station information is known at the BS. Then
a new MMSE receiver is designed by taking not only the Gaussian noise, but also
the channel estimation error and quantizer noise into account. By using the
Stieltjes transform of random matrix, we further derive a tight asymptotic
equivalent for the uplink achievable rate with proposed MMSE receiver. We
present a detailed analysis for the number of BS antennas through the
expression of the achievable rates and validate the results using numerical
simulations. It is also shown that we can compensate the performance loss due
to the low-resolution quantization by increasing the number of antennas at the
BS.Comment: 7 pages, 3 figure

### Semi-infinite cohomology and Kazhdan-Lusztig equivalence at positive level

A positive level Kazhdan-Lusztig functor is defined using Arkhipov-Gaitsgory
duality for affine Lie algebras. The functor sends objects in the DG category
of G(O)-equivariant positive level affine Lie algebra modules to objects in the
DG category of modules over Lusztig's quantum group at a root of unity. We
prove that the semi-infinite cohomology functor for positive level modules
factors through the Kazhdan-Lusztig functor at positive level and the quantum
group cohomology functor with respect to the positive part of Lusztig's quantum
group.Comment: 38 page

### Transient behavior of the solutions to the second order difference equations by the renormalization method based on Newton-Maclaurin expansion

The renormalization method based on the Newton-Maclaurin expansion is applied
to study the transient behavior of the solutions to the difference equations as
they tend to the steady-states. The key and also natural step is to make the
renormalization equations to be continuous such that the elementary functions
can be used to describe the transient behavior of the solutions to difference
equations. As the concrete examples, we deal with the important second order
nonlinear difference equations with a small parameter. The result shows that
the method is more natural than the multi-scale method.Comment: 12 page

### The renormalization method from continuous to discrete dynamical systems: asymptotic solutions, reductions and invariant manifolds

The renormalization method based on the Taylor expansion for asymptotic
analysis of differential equations is generalized to difference equations. The
proposed renormalization method is based on the Newton-Maclaurin expansion.
Several basic theorems on the renormalization method are proven. Some
interesting applications are given, including asymptotic solutions of quantum
anharmonic oscillator and discrete boundary layer, the reductions and invariant
manifolds of some discrete dynamics systems. Furthermore, the homotopy
renormalization method based on the Newton-Maclaurin expansion is proposed and
applied to those difference equations including no a small parameter.Comment: 24 pages.arXiv admin note: text overlap with arXiv:1605.0288

### Infinite-dimensional Hamilton-Jacobi theory and $L$-integrability

The classical Liouvile integrability means that there exist $n$ independent
first integrals in involution for $2n$-dimensional phase space. However, in the
infinite-dimensional case, an infinite number of independent first integrals in
involution don't indicate that the system is solvable. How many first integrals
do we need in order to make the system solvable? To answer the question, we
obtain an infinite dimensional Hamilton-Jacobi theory, and prove an infinite
dimensional Liouville theorem. Based on the theorem, we give a modified
definition of the Liouville integrability in infinite dimension. We call it the
$L$-integrability. As examples, we prove that the string vibration equation and
the KdV equation are $L$-integrable. In general, we show that an infinite
number of integrals is complete if all action variables of a Hamilton system
can reconstructed by the set of first integrals.Comment: 13 page

### The geometrical origins of some distributions and the complete concentration of measure phenomenon for mean-values of functionals

We derive out naturally some important distributions such as high order
normal distributions and high order exponent distributions and the Gamma
distribution from a geometrical way. Further, we obtain the exact mean-values
of integral form functionals in the balls of continuous functions space with
$p-$norm, and show the complete concentration of measure phenomenon which means
that a functional takes its average on a ball with probability 1, from which we
have nonlinear exchange formula of expectation.Comment: 8 page

### Average values of functionals and concentration without measure

Although there doesn't exist the Lebesgue measure in the ball $M$ of $C[0,1]$
with $p-$norm, the average values (expectation) $EY$ and variance $DY$ of some
functionals $Y$ on $M$ can still be defined through the procedure of limitation
from finite dimension to infinite dimension. In particular, the probability
densities of coordinates of points in the ball $M$ exist and are derived out
even though the density of points in $M$ doesn't exist. These densities include
high order normal distribution, high order exponent distribution. This also can
be considered as the geometrical origins of these probability distributions.
Further, the exact values (which is represented in terms of finite dimensional
integral) of a kind of infinite-dimensional functional integrals are obtained,
and specially the variance $DY$ is proven to be zero, and then the nonlinear
exchange formulas of average values of functionals are also given. Instead of
measure, the variance is used to measure the deviation of functional from its
average value. $DY=0$ means that a functional takes its average on a ball with
probability 1 by using the language of probability theory, and this is just the
concentration without measure. In addition, we prove that the average value
depends on the discretization.Comment: 32 page

### d+id' Chiral Superconductivity in Bilayer Silicene

We investigate the structure and physical properties of the undoped bilayer
silicene through first-principles calculations and find the system is
intrinsically metallic with sizable pocket Fermi surfaces. When realistic
electron-electron interaction turns on, the system is identified as a chiral
d+id' topological superconductor mediated by the strong spin fluctuation on the
border of the antiferromagnetic spin density wave order. Moreover, the tunable
Fermi pocket area via strain makes it possible to adjust the spin density wave
critical interaction strength near the real one and enables a high
superconducting critical temperature

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