arXiv subjects

Wei Yan

Publications and source records attributed to Wei Yan.

At least 127 records · Page 7Linked to original sources

arXiv2017

Random data Cauchy problem for a generalized KdV equation in the supercritical case

We consider the Cauchy problem for a generalized KdV equation \begin{eqnarray*} u_{t}+\partial_{x}^{3}u+u^{7}u_{x}=0, \end{eqnarray*} with random data on \R. Kenig, Ponce, Vega(Comm. Pure Appl. Math.46(1993), 527-620)proved that the problem is globally well-posed in H^{s}(\R)$ with s> s_{crit}=\frac{3}{14}, which is the scaling critical regularity indices. Birnir, Kenig, Ponce, Svanstedt, Vega(J. London Math. Soc. 53 (1996), 551-559.) proved that the problem is ill-posed in the sense that the time of existence T and the continuous dependence cannot be expressed in terms of the size of the data in the H^{\frac{3}{14}}-norm. In this present paper, we prove that almost sure local in time well-posedness holds in H^{s}(\R) with s>\frac{17}{112}, whose lower bound is below \frac{3}{14}. The key ingredients are the Wiener randomization of the initial data and probabilistic Strichartz estimates together with some important embedding Theorems.

math.AP↗

arXiv2017

The Cauchy problem for the Ostrovsky equation with positive dispersion

This paper is devoted to studying the Cauchy problem for the Ostrovsky equation \begin{eqnarray*} \partial_{x}\left(u_{t}-β\partial_{x}^{3}u +\frac{1}{2}\partial_{x}(u^{2})\right) -γu=0, \end{eqnarray*} with positive $β$ and $γ$. This equation describes the propagation of surface waves in a rotating oceanic flow. We first prove that the problem is locally well-posed in $H^{-\frac{3}{4}}(\R)$. Then we reestablish the bilinear estimate, by means of the Strichartz estimates instead of calculus inequalities and Cauchy-Schwartz inequalities. As a byproduct, this bilinear estimate leads to the proof of the local well-posedness of the problem in $H^{s}(\R)$ for $ s>-\frac{3}{4}$, with help of a fixed point argument.

math.AP↗

arXiv2017

Evidence of electron-electron interactions around Van Hove singularities of a graphene Moiré superlattice

A variety of new and interesting correlated states have been predicted in graphene monolayer doped to Van Hove singularities (VHSs) of its density-of-state (DOS). However, tuning the Fermi energy to reach a VHS of graphene by either gating or chemical doping is prohibitively difficult, owning to their large energy distance (3 eV). Therefore, these correlated states, which arise from effects of strong electron-electron interactions at the VHSs, have remained experimentally elusive. Here, we report experimental evidences of electron-electron interactions around the VHSs of a twisted bilayer graphene (TBG) through scanning tunneling microscopy measurements. By introducing a small twisted angle between two adjacent graphene sheets, we are able to generate low-energy VHSs arbitrarily approaching the Fermi energy. The split of the VHSs are observed and the symmetry breaking of electronic states around the VHSs are directly visualized. These results experimentally demonstrate the important effects of electron-electron interactions on electronic properties around the VHSs of the TBG, therefore providing motivation for further theoretical and experimental studies in graphene systems with considering many-body interactions.

cond-mat.mes-hall↗

arXiv2017

Flux-Stabilized Majorana Zero Modes in Coupled One-Dimensional Fermi Wires

One promising avenue to study one-dimensional ($1$D) topological phases is to realize them in synthetic materials such as cold atomic gases. Intriguingly, it is possible to realize Majorana boundary modes in a $1$D number-conserving system consisting of two fermionic chains coupled only by pair-hopping processes. It is commonly believed that significant interchain single-particle tunneling necessarily destroys these Majorana modes, as it spoils the $\mathbb{Z}_2$ fermion parity symmetry that protects them. In this Letter, we present a new mechanism to overcome this obstacle, by piercing a (synthetic) magnetic $π$-flux through each plaquette of the Fermi ladder. Using bosonization, we show that in this case there exists an exact leg-interchange symmetry that is robust to interchain hopping, and acts as fermion parity at long wavelengths. We utilize density matrix renormalization group and exact diagonalization to verify that the resulting model exhibits Majorana boundary modes up to large single-particle tunnelings, comparable to the intrachain hopping strength. Our work highlights the unusual impacts of different topologically trivial band structures on these interaction-driven topological phases, and identifies a distinct route to stabilizing Majorana boundary modes in $1$D fermionic ladders.

cond-mat.str-el↗

arXiv2016

Quantum corrections in nanoplasmonics: shape, scale, and material

The classical treatment of plasmonics is insufficient at the nanometer-scale due to quantum mechanical surface phenomena. Here, an extension to the classical paradigm is reported which rigorously remedies this deficiency through the incorporation of first-principles surface response functions - the Feibelman d-parameters - in general geometries. Several analytical results for the leading-order plasmonic quantum corrections are obtained in a first-principles setting; particularly, a clear separation of the roles of shape, scale, and material is established. The utility of the formalism is illustrated by the derivation of a modified sum-rule for complementary structures, a rigorous reformulation of Kreibig's phenomenological damping prescription, and an account of the small-scale resonance-shifting of simple and noble metal nanostructures. These insights open the technological design space and deepen our fundamental understanding of nanoplasmonics beyond the classical regime.

cond-mat.mes-hall↗

arXiv2016

The Cauchy problem for higher-order modified Camassa-Holm equations on the circle

In this paper, we investigate the Cauchy problem for the shallow water type equation \begin{eqnarray*} u_{t}+\partial_{x}^{2j+1}u + \frac{1}{2}\partial_{x}(u^{2})+ \partial_{x}(1-\partial_{x}^{2})^{-1}\left[u^{2}+\frac{1}{2}u_{x}^{2}\right]=0 \end{eqnarray*} with low regularity data in the periodic settings. Himonas and Misiolek (Communications in Partial Differential Equations, 23(1998), 123-139.) have proved that the problem is locally well-posed for small initial data in H^{s}(\mathbf{T}) with s\geq-\frac{j}{2}+1,j\in N^{+} with the aid of the standard Fourier restriction norm method. To the best of our knowledge, there is no result of well-posedness about the problem when s<-\frac{j}{2}+1. In this paper, firstly, we prove that the bilinear estimate related to the nonlinear term of the equation in standard Bourgain space is invalid with s<-\frac{j}{2}+1. Then we prove that the Cauchy problem for the periodic shallow water-type equation is locally well-posed in H^{s}(\mathbf{T}) with -j+\frac{3}{2}< s<-\frac{j}{2}+1,j\geq2 for arbitrary initial data. The novelty is that we introduce some new function spaces and give a useful relationship among new spaces.

math.AP↗

arXiv2016

The Cauchy problem for the shallow water typ equations in low regularity spaces on the circle

In this paper, we investigate the Cauchy problem for the shallow water type equation \[ u_{t}+\partial_{x}^{3}u + \frac{1}{2}\partial_{x}(u^{2})+\partial_{x} (1-\partial_{x}^{2})^{-1}\left[u^{2}+\frac{1}{2}u_{x}^{2}\right]=0,x\in {\mathbf T}=\R/2π λ\] with low regularity data in the periodic settings and $λ\geq1$. We prove that the bilinear estimate in $X_{s,b}$ with $s<\frac{1}{2}$ is invalid. We also prove that the problem is locally well-posed in $H^{s}(\mathbf{T})$ with $\frac{1}{6}<s<\frac{1}{2}$ for small initial data. The result of this paper improves the result of case $j=1$ of Himonas and Misiolek (Communications in Partial Differential Equations, 23(1998), 123-139.). The new ingredients are some new function spaces and some new Strichartz estimates.

math.AP↗

arXiv2016

Type-II Topological Meissner States

We study the \emph{orbital effects} of the synthetic magnetic fields in an interacting square lattice two-leg fermionic ladder model with the number-conserving pair hopping that hosting the Majorana bound states. By utilizing density matrix renormalization group and exact diagonalization, we identify a novel type-II topological Meissner $($\emph{topo}-Meissner$)$ phase $($as distinguished from the low-field type-I \emph{topo}-Meissner state$)$ when threading a \emph{high} magnetic flux through the plaquette of the ladder, which not only exhibits a large uniformly circulating chiral current along the legs, the characteristics of the celebrated Meissner state, but also accommodates a topologically protected ground-state manifold due to the \emph{reentrant} emergence of the Majorana end modes. Our work reveals some interesting interference effects resulting from the interplay between the gauge fields and the strong interactions in establishing the intrinsic topological states of matter in low-dimensional quantum systems.

cond-mat.str-el↗

arXiv2016

Surface brightness profiles of blue compact dwarf galaxies in the GOODS-N and GOODS-S field

We investigate the structural properties of the underlying hosts of 34 blue compact dwarf (BCD) galaxies with deep near-infrared (NIR) photometry. The BCD sample is selected from the Cosmic Assembly Near-IR Deep Extragalactic Legacy Survey in the Great observatories origins Deep Survey North and South fields. We extract the surface brightness profile (SBP) in the optical F 435W and NIR F 160W bands. The SBPs of BCDs in the H band reach 26 mag arcsec^-2 at the 3σlevel, which is so far the deepest NIR imaging of BCDs. Then we fit the SBPs with one- and two- component Sersic models. About half of the BCDs favour the two-component model which significantly improves the fit quality. The effective radii of the underlying hosts of BCDs in the B band are smaller than those of early-type dwarfs (dEs) and dwarf irregulars at a fixed luminosity. This discrepancy is similar to findings in many previous works. However, the difference in structural parameters between BCDs and other dwarf galaxies seems to be less significant in the H band. Furthermore, we find a remarkable agreement between the underlying hosts of BCDs and dEs. All dwarf galaxies seem to follow a similar luminosity-radius relationship which suggests a unified structural evolution for dwarf galaxies. We conclude that a possible evolution track from BCDs to dEs cannot be ruled out, with no significant change of structure needed in the evolutionary scenario.

astro-ph.GA↗

arXiv2015

Quantum plasmonics: An energy perspective to quantify nonclassical effects

Plasmons are commonly interpreted with classical electrodynamics, while nonclassical effects may influence the dynamics of plasmon resonances as the plasmon confinement is approaching the few--nanometer scale. However, an unambiguous approach to quantify the degree of nonclassical dynamics remains. We propose a nonclassical-impact parameter (NCI) to characterize the degree of nonclassical effects from an energy perspective, i.e. which fraction of the total electromagnetic energy is attributed to classical electrodynamic terms and which fraction is correspondingly to be assigned to nonclassical degrees of freedom? We show that the NCI relates directly to two fundamental parameters of plasmon resonances: the loss function and the quality factor. Guided by the NCI, we discuss the nonclassical effects of plasmon waveguiding modes of metallic slab waveguides, and highlight the general features of the nonclassical effects at different microscopic levels by contrasting the numerical results from the semi-classical hydrodynamic Drude model (HDM) and the microscopic random-phase approximation (RPA). The formal relation between the HDM and the RPA is also established for metals by exploring the limit of an infinite work function.

cond-mat.mes-hall↗

arXiv2015

Sharp well-posedness and ill-posedness of the Cauchy problem for the higher-order KdV

In this paper, we investigate the Cauchy problem for the higher-order KdV-type equation \begin{eqnarray*} u_{t}+(-1)^{j+1}\partial_{x}^{2j+1}u + \frac{1}{2}\partial_{x}(u^{2}) = 0,j\in N^{+},x\in\mathbf{T}= [0,2πλ) \end{eqnarray*} with low regularity data and $λ\geq 1$. Firstly, we show that the Cauchy problem for the periodic higher-order KdV equation is locally well-posed in $H^{s}(\mathbf{T})$ with $s\geq -j+\frac{1}{2},j\geq2.$ By using some new Strichartz estimate and some new function spaces, we also show that the Cauchy problem for the periodic higher-order KdV equation is ill-posed in $H^{s}(\mathbf{T})$ with $s<-j+\frac{1}{2},j\geq2$ in the sense that the solution map is $C^{3}.$ The result of this paper improves the result of \cite{H} with $j\geq2$.

math.AP↗

arXiv2015

Detecting giant electron-hole asymmetry in graphene monolayer generated by strain and charged-defect scattering via Landau level spectroscopy

The electron-hole symmetry in graphene monolayer, which is analogous to the inherent symmetric structure between electrons and positrons of the Universe, plays a crucial role in the chirality and chiral tunnelling of massless Dirac fermions. Here we demonstrate that both strain and charged-defect scattering could break this symmetry dramatically in graphene monolayer. In our experiment, the Fermi velocities of electrons and holes are measured directly through Landau level spectroscopy. In strained graphene with lattice deformation and curvature, the and are measured as 1.2 x 106 m/s and 1.02 x106 m/s, respectively. This giant asymmetry originates from enhanced next-nearest-neighbor hopping in the strained region. Around positively charged-defect, we observe opposite electron-hole asymmetry, and the and are measured to be 0.86x 106 m/s and 1.14 x106 m/s, respectively. Such a large asymmetry is attributed to the fact that the massless Dirac fermions in graphene monolayer are scattered more strongly when they are attracted to the charged-defect than when they are repelled from it.

cond-mat.mtrl-sci↗

arXiv2015

Kerr nonlinearity and plasmonic bistability in graphene nanoribbons

We theoretically examine the role of Kerr nonlinearities for graphene plasmonics in nanostructures, specifically in nanoribbons. The nonlinear Kerr interaction is included semiclassically in the intraband approximation. The resulting electromagnetic problem is solved numerically by self-consistent iteration with linear steps using a real-space discretization. We derive a simple approximation for the resonance shifts in general graphene nanostructures, and obtain excellent agreement with numerics for moderately high field strengths. Near plasmonic resonances the nonlinearities are strongly enhanced due to field enhancement, and the total nonlinearity is significantly affected by the field inhomogeneity of the plasmonic excitation. Finally, we discuss the emergence of a plasmonic bistability which exists for frequencies redshifted relative to the linear resonance. Our results offer new insights into the role of nonlinear interaction in nanostructured graphene and paves the way for experimental investigation.

cond-mat.mes-hall↗

arXiv2015

Projected-Dipole Model for Quantum Plasmonics

Quantum effects of plasmonic phenomena have been explored through ab-initio studies, but only for exceedingly small metallic nanostructures, leaving most experimentally relevant structures too large to handle. We propose instead an effective description with the computationally appealing features of classical electrodynamics, while quantum properties are described accurately through an infinitely thin layer of dipoles oriented normally to the metal surface. The nonlocal polarizability of the dipole layer is mapped from the free-electron distribution near the metal surface as obtained with 1D quantum calculations, such as time-dependent density-functional theory (TDDFT), and is determined once and for all. The model can be applied to any system size that is tractable within classical electrodynamics, while capturing quantum plasmonic aspects of nonlocal response and a finite work function with TDDFT-level accuracy. Applying the theory to dimers we find quantum-corrections to the hybridization even in mesoscopic dimers as long as the gap is sub-nanometric itself.

cond-mat.mes-hall↗

arXiv2015

Landau Quantization and Fermi Velocity Renormalization in Twisted Graphene Bilayers

Currently there is a lively discussion concerning Fermi velocity renormalization in twisted bilayers and several contradicted experimental results are reported. Here we study electronic structures of the twisted bilayers by scanning tunneling microscopy (STM) and spectroscopy (STS). The interlayer coupling strengths between the adjacent bilayers are measured according to energy separations of two pronounced low-energy van Hove singularities (VHSs) in the STS spectra. We demonstrate that there is a large range of values for the interlayer interaction in different twisted bilayers. Below the VHSs, the observed Landau quantization in the twisted bilayers is identical to that of massless Dirac fermions in graphene monolayer, which allows us to measure the Fermi velocity directly. Our result indicates that the Fermi velocity of the twisted bilayers depends remarkably on both the twisted angles and the interlayer coupling strengths. This removes the discrepancy about the Fermi velocity renormalization in the twisted bilayers and provides a consistent interpretation of all current data.

cond-mat.mtrl-sci↗

arXiv2015

The Cauchy problem for a higher order shallow water type equation on the circle

In this paper, we investigate the Cauchy problem for a higher order shallow water type equation \begin{eqnarray*} u_{t}-u_{txx}+\partial_{x}^{2j+1}u-\partial_{x}^{2j+3}u+3uu_{x}-2u_{x}u_{xx}-uu_{xxx}=0, \end{eqnarray*} where $x\in \mathbf{T}=\mathbf{R}/2π$ and $j\in N^{+}.$ Firstly, we prove that the Cauchy problem for the shallow water type equation is locally well-posed in $H^{s}(\mathbf{T})$ with $s\geq -\frac{j-2}{2}$ for arbitrary initial data. By using the $I$-method, we prove that the Cauchy problem for the shallow water type equation is globally well-posed in $H^{s}(\mathbf{T})$ with $\frac{2j+1-j^{2}}{2j+1}<s\leq 1.$ Our results improve the result of A. A. Himonas, G. Misiolek (Communications in partial Differential Equations, 23(1998), 123-139;Journal of Differential Equations, 161(2000), 479-495.)

math.AP↗

arXiv2015

Global well-posedness for the 3-D density-dependent liquid crystal flows in the critical Besov spaces

In this paper, we prove the local well-posedness of 3-D density-dependent liquid crystal flows with initial data in the critical Besov spaces, without assumptions of small density variation. Furthermore, if the initial density is close enough to a positive constant and the critical Besov norm of the liquid crystal orientation field and the horizontal components of the initial velocity field polynomially small compared with the critical Besov norm to the veritcal component of the initial velocity field, then the system has a unique global solution.

math.AP↗

arXiv2015

Spatially resolving unconventional interface Landau quantization in a graphene monolayer-bilayer planar junction

Graphene hybrid planar structures consisting of two regions with different quantum Hall (QH) states exhibit unusual transport properties1-5, originating from chiral edge states equilibration at the interface of the two different regions6. Here we present a sub-nanometre-resolved scanning tunnelling microscopy (STM) and spectroscopy (STS) study of a monolayer-bilayer graphene planar junction in the QH regime. The atomically well-defined interface of such a junction allows us to spatially resolve the interface electronic properties. Around the interface, we detect Landau quantization of massless Dirac fermions, as expected in graphene monolayer, below the charge neutrality point Nc of the junction, whereas unexpectedly, only Landau quantization of massive Dirac fermions, as expected in graphene bilayer, is observed above the Nc. The observed unconventional interface Landau quantization arises from the fact that the quantum conductance across the interface is solely determined by the minimum filling factors (number of edge modes) in the graphene monolayer and bilayer regions of the junction6,7.

cond-mat.mes-hall↗