arXiv subjects

Chao Zhang

Publications and source records attributed to Chao Zhang.

At least 1,189 records · Page 66Linked to original sources

arXiv2012

Harnack's inequality for fractional nonlocal equations

We prove interior Harnack's inequalities for solutions of fractional nonlocal equations. Our examples include fractional powers of divergence form elliptic operators with potentials, operators arising in classical orthogonal expansions and the radial Laplacian. To get the results we use an analytic method based on a generalization of the Caffarelli--Silvestre extension problem, the Harnack's inequality for degenerate Schrödinger operators proved by C. E. Gutiérrez, and a transference method. In this manner we apply local PDE techniques to nonlocal operators. On the way a maximum principle and a Liouville theorem for some fractional nonlocal equations are obtained.

math.AP↗

arXiv2012

Pressure-Driven Quantum Criticality in An Iron-Selenide Superconductor

The discovery of superconductivity of about 30 K in iron selenides with very large magnetic moments simulates the examination of completing orders. Here we report a finding of pressure- induced suppression of the superconducting transition temperature Tc and enhancement of the temperature of the resistance hump TH through charge transfer between two iron sites with different occupancies. The activation energy for the electric transport of the high-temperature resistance is observed to go to zero at a critical pressure of 8.7 GPa, at which superconductivity tends to disappear and the semiconductor-to-metal transition takes place. Beyond the critical point, the resistance exhibits a metallic behavior over the whole temperature range studied. All these features indicate the existence of quantum criticality in iron-selenide superconductors.

cond-mat.supr-con↗

arXiv2012

Risk Bounds for Infinitely Divisible Distribution

In this paper, we study the risk bounds for samples independently drawn from an infinitely divisible (ID) distribution. In particular, based on a martingale method, we develop two deviation inequalities for a sequence of random variables of an ID distribution with zero Gaussian component. By applying the deviation inequalities, we obtain the risk bounds based on the covering number for the ID distribution. Finally, we analyze the asymptotic convergence of the risk bound derived from one of the two deviation inequalities and show that the convergence rate of the bound is faster than the result for the generic i.i.d. empirical process (Mendelson, 2003).

stat.ML↗

arXiv2012

Reemerging superconductivity at 48 K across quantum criticality in iron chalcogenides

Pressure plays an essential role in the induction1 and control2,3 of superconductivity in iron-based superconductors. Substitution of a smaller rare-earth ion for the bigger one to simulate the pressure effects has surprisingly raised the superconducting transition temperature Tc to the record high 55 K in these materials4,5. However, Tc always goes down after passing through a maximum at some pressure and the superconductivity eventually tends to disappear at sufficiently high pressures1-3. Here we show that the superconductivity can reemerge with a much higher Tc after its destruction upon compression from the ambient-condition value of around 31 K in newly discovered iron chalcogenide superconductors. We find that in the second superconducting phase the maximum Tc is as high as 48.7 K for K0.8Fe1.70Se2 and 48 K for (Tl0.6Rb0.4)Fe1.67Se2, setting the new Tc record in chalcogenide superconductors. The presence of the second superconducting phase is proposed to be related to pressure-induced quantum criticality. Our findings point to the potential route to the further achievement of high-Tc superconductivity in iron-based and other superconductors.

cond-mat.supr-con↗

arXiv2011

Regularity properties of Schrödinger operators

Let L be a Schrödinger operator of the form L=-Δ+V, where the nonnegative potential V satisfies a reverse Hölder inequality. Using the method of L-harmonic extensions we study regularity estimates at the scale of adapted Hölder spaces. We give a pointwise description of L-Hölder spaces and provide some characterizations in terms of the growth of fractional derivatives of any order and Carleson measures. Applications to fractional powers of L and multipliers of Laplace transform type developed.

math.AP↗

arXiv2011

More counterexamples to Happel's question and Snashall-Solberg's conjecture

In this paper we provide more counterexamples to Happel's question and Snashall-Solberg's conjecture which generalize many counterexamples to these conjectures studied in the literature. In particular, we show that a family of $\mathbb{Z}_n\times \mathbb{Z}_n$-Galois covering algebras of quantized exterior algebra $A_q$ in two variables answer negatively to Happel's question, and meanwhile, the one-point coextensions of $\mathbb{Z}_n$ and $\mathbb{Z}_n\times \mathbb{Z}_m$-Galois covering algebras of $A_q$ negate the Snashall-Solberg's conjecture.

math.RT↗

arXiv2011

Fractional Vector-Valued Littlewood-Paley-Stein Theory for Semigroups

We consider the fractional derivative of a general Poisson semigroup. With this fractional derivative we define the generalized fractional Littlewood-Paley $g$-function for semigroups acting on $L^p$-spaces of functions with values in Banach spaces. We give a characterization of the classes of Banach spaces for which the fractional Litlewood-Paley $g$-function is bounded on $L^p$-spaces. We show that the class of Banach spaces is independent of the order of derivation and coincides with the classical (Lusin type/cotype) case. It is also shown that the same kind of results exist for the case of the fractional area function and the fractional $g^*_λ$-function on $\mathbb{R}^n$. At last, we consider the relationship of the almost sure finiteness of the fractional Littlewood-Paley $g$-function, area function and $g^*_λ$-function with the Lusin cotype property of the underlying Banach space. As a byproduct of the techniques developed, one can get some results of independent interest for vector-valued Calderón--Zygmund operators. For example, one can get the following characterization, a Banach space $\mathbb{B}$ is UMD if and only if for some (or, equivalently, for every) $p\in [1,\infty)$, $\displaystyle \lim_{ε\rightarrow 0} \int_{|x-y|> ε} \frac{f(y)}{x-y}dy $ exists \textup{a.e.} $x\in \mathbb{R}$ for every $f\in L^p_\mathbb{B}(\mathbb{R}).$

math.FA↗

arXiv2011

Correlation between superconductivity and antiferromagnetism in Rb0.8Fe2Se2-xTex single crystals

We report the first experimental evidence for the intimate connection between superconductivity and antiferromagnetism in Rb0.8Fe2Se2-xTex single crystal under negative chemical pressure by substituting Se with isovalent Te atoms. Electrical resistance measurements in the temperature range from 4 K to 550 K demonstrate that both superconducting transition temperature (Tc) and Neel temperature (TN) were suppressed continuously with the lattice expansion. When the Te concentration x in Rb0.8Fe2Se2-xTex approaches 0.3, the superconducting transition temperature Tc is completely suppressed and the sample behaves like a semiconductor, meanwhile the characteristic peak of antiferromagnetic transition on resistance curve disappears. Our observation suggests that the pressure-induced lattice expansion can be used to tune the correlativity of superconductivity and antiferromagnetism.

cond-mat.supr-con↗

arXiv2011

Universal geometric classification of armchair graphene nanoribbons by their properties in a staggered sublattice potential

We demonstrate the topological properties of the band-gap of armchair graphene nanoribbons in a spatially varying staggered sublattice potential. Several general scaling laws are presented to quantify the band gap variation. It is found that all armchair nanoribbons are described by one of three distinct classes depending on their width, one of which is the well known massless Dirac condition, and the other two we call potentially gapless, and gapless-superlattice. We construct an effective theory which faithfully reproduces these results, and makes explicit the nature of the competing masses and overlap integrals across a particular sample. Finally we propose several systems on which these results should shed considerable light, and which have all already been experimentally realized.

cond-mat.mes-hall↗

arXiv2011

Statistical Delay Control and QoS-Driven Power Allocation Over Two-Hop Wireless Relay Links

The time-varying feature of wireless channels usually makes the hard delay bound for data transmissions unrealistic to guarantee. In contrast, the statistically-bounded delay with a small violation probability has been widely used for delay quality-of-service (QoS) characterization and evaluation. While existing research mainly focused on the statistical-delay control in single-hop links, in this paper we propose the QoS-driven power-allocation scheme over two-hop wireless relay links to statistically upper-bound the end-to-end delay under the decodeand- forward (DF) relay transmissions. Specifically, by applying the effective capacity and effective bandwidth theories, we first analyze the delay-bound violation probability over two tops each with independent service processes. Then, we show that an efficient approach for statistical-delay guarantees is to make the delay distributions of both hops identical, which, however, needs to be obtained through asymmetric resource allocations over the two hops. Motivated by this fact, we formulate and solve an optimization problem aiming at minimizing the average power consumptions to satisfy the specified end-to-end delay-bound violation probability over two-hop relay links. Also conducted is a set of simulations results to show the impact of the QoS requirements, traffic load, and position of the relay node on the power allocation under our proposed optimal scheme.

cs.IT↗

arXiv2011

A Multi-Channel Diversity Based MAC Protocol for Power-Constrained Cognitive Ad Hoc Networks

One of the major challenges in the medium access control (MAC) protocol design over cognitive Ad Hoc networks (CAHNs) is how to efficiently utilize multiple opportunistic channels, which vary dynamically and are subject to limited power resources. To overcome this challenge, in this paper we first propose a novel diversity technology called \emph{Multi-Channel Diversity} (MCD), allowing each secondary node to use multiple channels simultaneously with only one radio per node under the upperbounded power. Using the proposed MCD, we develop a MCD based MAC (MCD-MAC) protocol, which can efficiently utilize available channel resources through joint power-channel allocation. Particularly, we convert the joint power-channel allocation to the Multiple-Choice Knapsack Problem, such that we can obtain the optimal transmission strategy to maximize the network throughput through dynamic programming. Simulation results show that our proposed MCD-MAC protocol can significantly increase the network throughput as compared to the existing protocols.

cs.IT↗

arXiv2011

Optimal Relay Power Allocation for Amplify-and-Forward Relay Networks with Non-linear Power Amplifiers

In this paper, we propose an optimal relay power allocation of an Amplify-and-Forward relay networks with non-linear power amplifiers. Based on Bussgang Linearization Theory, we depict the non-linear amplifying process into a linear system, which lets analyzing system performance easier. To obtain spatial diversity, we design a complete practical framework of a non-linear distortion aware receiver. Consider a total relay power constraint, we propose an optimal power allocation scheme to maximum the receiver signal-to-noise ratio. Simulation results show that proposed optimal relay power allocation indeed can improve the system capacity and resist the non-linear distortion. It is also verified that the proposed transmission scheme outperforms other transmission schemes without considering non-linear distortion.

cs.IT↗

arXiv2010

A quantum model for the stock market

Beginning with several basic hypotheses of quantum mechanics, we give a new quantum model in econophysics. In this model, we define wave functions and operators of the stock market to establish the Schrödinger equation for the stock price. Based on this theoretical framework, an example of a driven infinite quantum well is considered, in which we use a cosine distribution to simulate the state of stock price in equilibrium. After adding an external field into the Hamiltonian to analytically calculate the wave function, the distribution and the average value of the rate of return are shown.

q-fin.ST↗

arXiv2010

Phase Diagram of Pressure-induced Superconductivity and its Relation to Hall Coefficient in Bi2Te3 Single Crystal

Pressure-induced superconductivity and its relation to corresponding Hall coefficient (RH) have been reported for Bi2Te3, one of known topological insulators. A full phase diagram is presented which shows a complex dependence of the superconducting transition temperature as a function of pressure over an extensive range. High-pressure RH measurements reveal a close relation of these complex behaviors, particularly, a dramatic change of dRH/dP before structural phase transition and a pressure-induced crossover on RH in the high pressure phase were observed.

cond-mat.supr-con↗

arXiv2010

Evidence for Competition between Superconductivity and Kondo Effect in CeFeAsO0.7F0.3 under High Pressure

We discover a pressure induced quantum phase transition from the superconducting state to the non-superconducting Kondo screened phase associated with a 2% volume collapse in CeFeAsO0.7F0.3 through measurements of high-pressure resistance, synchrotron x-ray diffraction, and x-ray absorption spectroscopy (XAS) in a diamond anvil cell. Our XAS data of Ce-L3 in CeFeAsO0.7F0.3 clearly show a spectral weight transfer from the main line to the satellite line after the transition, demonstrating the formation of the Kondo singlets under pressure in CeFeAsO1-xFx. Our results have revealed a physical picture of a pressure-induce competition between Kondo singlets and BCS singlets in the Ce-pnictide superconductors.

cond-mat.supr-con↗

arXiv2010

Physical origin of superconductivity in EuFe2As1.4P0.6 and EuFe2As2: pressure-induce valence change of europium

Superconductivity can be realized in Eu-containing pnictides by application of chemical (internal) and physical (external) pressure, the intrinsic physical mechanism of which attracts much attention in physics community. Here we present the experimental evidence for the valence change of europium in compounds of EuFe2As1.4P0.6 exposed to ambient pressure and EuFe2As2 to high pressure by x-ray absorption measurements on L3-Eu edge. We find that the absorption spectrum of EuFe2As1.4P0.6 at ambient pressure shows clear spectra weight transfer from a divalent to a trivalent state. Furthermore, application of pressure on EuFe2As2 using a diamond anvil cell shows a similar behavior of valence transition as EuFe2As1.4P0.6. These findings are the first observation of superconductivity mechanized by valence change in pnictides superconductors and elucidate the intrinsic physical origin of superconductivity in EuFe2As1.4P0.6 and compressed EuFe2As2.

cond-mat.supr-con↗

arXiv2009

Pressure-induced lattice collapse in tetragonal phase and structural phase transition in single crystalline Fe1.05Te

We report studies of in-situ x-ray diffraction (XRD) and electronic properties on the single crystalline of Fe1.05Te compound under high pressure. The results demonstrated that the sample undergoes a pressure-induced lattice collapse in tetragonal phase (cT) at 4 GPa at room temperature. The cT phase in turn transfers to monoclinic (M) phase with increasing pressure to 14 GPa. The resistance measurements under pressures show that the onset temperature of structural phase transition (TSTR) decreases upon transformation from the tetragonal (T) to the cT phase and turns up at the 4 GPa where is the boundary pressure of T-cT phase. The onset of antiferromagnetic transition (TAF) shows little change up to 0.8 GPa by magnetization measurements. In the domain of M phase, the sample behaves like semiconductor at low temperature. No superconductivity is observed under the pressure investigated.

cond-mat.supr-con↗

arXiv2009

Transmission resonance in a composite plasmonic structure

The design, fabrication, and optical properties of a composite plasmonic structure, a two-dimentional array of split-ring resonators inserted into periodic square holes of a metal film, have been reported. A new type of transmission resonance, which makes a significant difference from the conventional peaks, has been suggested both theoretically and experimentally. To understand this effect, a mechanism of ring- resonance induced dipole emission is proposed.

physics.optics↗