arXiv subjects

Fei Xu

Publications and source records attributed to Fei Xu.

139 records · Page 8Linked to original sources

arXiv2014

The influence of van der Waals forces on the waveguide deformation and power limit of nanoscale optomechanical systems

The ultra-short range force, van der Waals force (VWF), will rise rapidly when one nanoscale waveguide is close to another one, and be stronger than the external transverse gradient force (TGF). We theoretically investigate the giant influence of the VWF on the device performance in a typical optomechanical system consisting of a suspended silicon waveguide and a silica substrate including waveguide deformation stiction and failure mechanism. The device shows unique optically-activated plastic/elastic behaviors and stiction due to the VWF. When the input optical power is above the critical power, the waveguide is sticking to the substrate and the deformation is plastic and unrecoverable, even though the total force is less than the yield strength of the waveguide material. This is important and helpful for the design and applications of optomechanical devices.

physics.optics↗

arXiv2013

Spectra of tensor triangulated categories over category algebras

Let C be a finite EI category and k be a field. We consider the category algebra kC. Suppose K(C)=D^b(kC-mod) is the bounded derived category of finitely generated left modules. This is a tensor triangulated category and we compute its spectrum in the sense of Balmer. When C=G*P is a finite transporter category, the category algebra becomes Gorenstein so we can define the stable module category \CM k(G*P), of maximal Cohen-Macaulay modules, as a quotient category of K(G*P). Since \CM k(G*P) is also tensor triangulated, we compute its spectrum as well. These spectra are used to classify tensor ideal thick subcategories of the corresponding tensor triangulated categories, despite the fact that the previously mentioned tensor categories are not rigid.

math.RT↗

arXiv2013

Nonlinear Transformation of Orbital Angular Momentum through Quasi-phase Matching

We propose and investigate the quasi-phase matched (QPM) nonlinear optical frequency conversion of optical vortices in periodically poled Lithium Niobate (PPLN). Laguerre-Gaussian (LG) modes are used to represent the orbital angular momentum (OAM) states, characterized with the azimuthal and radial indices. Typical three-wave nonlinear interactions among the involved OAM modes are studied with the help of coupling wave equations. Being different from normal QPM process where the energy and quasi-momentum conservations are satisfied, both of the azimuthal and radial indices of the OAM states keep constant in most of the cases. However, abnormal change of the radial index is observed when there is asynchronous nonlinear conversion in different parts of the beams. The QPM nonlinear evolution of fractional OAM states is also discussed showing some interesting properties. In comparison with the traditional birefringent phase matching (BPM), the QPM technique avoids the undesired walk-off effect to reserve high-quality LG modes. We believe the QPM is an efficient way to convert, amplify and switch OAM states in various optical vortex related applications.

physics.optics↗

arXiv2013

Generation and manipulation of entangled photons in a domain-engineered lithium niobate waveguide

We propose to integrate the electro-optic tuning function into polarization-entangled photon pair generation process in a periodically poled lithium niobate (PPLN). Due to the versatility of PPLN, both the spontaneously parametric down conversion and electro-optic polarization rotation effects could be realized simultaneously. Orthogonally-polarized and parallel-polarized photon pairs thus are instantly switchable by tuning the applied field. The characteristics of the source are investigated showing adjustable bandwidths and high entanglement degrees. Moreover, other kinds of reconfigurable entanglement are also achievable based on suitable domain-design. We believe the domain engineering is a very promising solution for next generation function-integrated quantum circuits.

quant-ph↗

arXiv2012

Efficient surface second-harmonic generation in slot micro/nano-fibers

We propose to use slot micro/nano-fiber (SMNF) to enhance the second-harmonic generation based on surface dipole nonlinearity. The slot structure is simple and promising to manufacture with high accuracy and reliability by mature micromachining techniques. Light field can be enhanced and confined, and the surface area can be increased in the sub-wavelength low-refractive-index air slot. The maximum conversion efficiency of the SMNFs in our calculations is about 24 times higher than that of circular micro/nano-fibers. It is promising to provide a competing platform for a new class of fiber-based ultra-tiny light sources spanning the UV- to the mid-infrared spectrum.

physics.optics↗

arXiv2012

Integral Points for Multi-norm Tori

We construct a finite subgroup of Brauer-Manin obstruction for detecting the existence of integral points on integral models of principle homogeneous spaces of multi-norm tori. Several explicit examples are provided.

math.NT↗

arXiv2012

Counting Integral Points in Certain Homogeneous Spaces

The asymptotic formula of the number of integral points in non-compact symmetric homogeneous spaces of semi-simple simply connected algebraic groups is given by the average of the product of the number of local solutions twisted by the Brauer-Manin obstruction. The similar result is also true for homogeneous spaces of reductive groups with some restriction. As application, we will give the explicit asymptotic formulae of the number of integral points of certain norm equations and explain that the asymptotic formula of the number of integral points in Theorem 1.1 of \cite{EMS} is equal to the product of local integral solutions over all primes and answer a question raised by Borovoi related to the example 6.3 in \cite{BR95}.

math.NT↗

arXiv2012

Quantum entanglement based on surface phonon polaritons in condensed matter systems

Condensed matter systems are potential candidates to realize the integration of quantum information circuits. Surface phonon polariton (SPhP) is a special propagation mode in condensed matter systems. We present an investigation on the entanglement of SPhP modes. The entangled pairs are generated from entangled photons injected to the system. Quantum performances of entangled SPhPs are investigated by using the interaction Hamiltonian and the perturbation theory. The wave mechanics approach is taken to describe the coupling process as a comparison. Finally, the correlation of system is examined. A whole set of descriptions of SPhP entanglement thus are presented.

quant-ph↗

arXiv2012

Integral Points for Groups of Multiplicative Type

We construct a finite subgroup of Brauer-Manin obstruction for detecting the existence of integral points on integral models of homogeneous spaces of linear algebraic groups of multiplicative type. As application, the strong approximation theorem for linear algebraic groups of multiplicative type is established. Moreover, the sum of two integral squares over some quadratic fields is discussed.

math.NT↗

arXiv2011

Strong approximation for the total space of certain quadric fibrations

We study equations in four variables (x,y,z,t) of the shape q(x,y,z)=P(t), where q(x,y,z) is an indefinite ternary quadratic form over the integers and P(t) is a polynomial in one variable with integral coefficients. If P(t) is not the product of a constant and the square of a polynomial, strong approximation holds for integral solutions (x,y,z,t). In the general case, we show that the integral Brauer-Manin conditions are the only obstructions to strong approximation. We actually study the analogous situation over an arbitrary number field. --- Nous étudions les équations à quatre variables (x,y,z,t) à coefficients entiers du type q(x,y,z)=P(t), où q(x,y,z) est une forme quadratique entière ternaire indéfinie sur les réels, et P(t) un polynôme à coefficients entiers en une variable. Lorsque le polynôme n'est pas le produit d'une constante et d'un carré de polynôme, nous établissons l'approximation forte pour les solutions de ces équations en entiers (x,y,z,t). Dans le cas général, nous montrons que l'obstruction de Brauer-Manin entière est la seule obstruction à l'approximation forte. Nous étudions la situation sur un corps de nombres quelconque.

math.NT↗

arXiv2011

Support varieties for transporter category algebras

Let G be a finite group. Over any finite G-poset P we may define a transporter category as the corresponding Grothendieck construction. The classifying space of the transporter category is the Borel construction on the G-space BP, while the k-category algebra of the transporter category is the (Gorenstein) skew group algebra on the G-incidence algebra kP. We introduce a support variety theory for the category algebras of transporter categories. It extends Carlson's support variety theory on group cohomology rings to equivariant cohomology rings. In the mean time it provides a class of (usually non selfinjective) algebras to which Snashall-Solberg's (Hochschild) support variety theory applies. Various properties will be developed. Particularly we establish a Quillen stratification for modules.

math.GR↗

arXiv2008

Hochschild and ordinary cohomology rings of small categories

Let C be a small category and k a field. There are two interesting mathematical subjects: the category algebra kC and the classifying space |C|=BC. We study the ring homomorphism HH*(kC) --> H*(|C|,k) and prove it is split surjective. This generalizes the well-known results for groups and posets. Based on this result, we construct a seven-dimensional category algebra whose Hochschild cohomology ring modulo nilpotents is not finitely generated, against a conjecture of Snashall and Solberg.

math.AT↗

arXiv2007

Brauer-Manin obstruction for integral points of homogeneous spaces and representation by integral quadratic forms

An integer may be represented by a quadratic form over each ring of p-adic integers and over the reals without being represented by this quadratic form over the integers. More generally, such failure of a local-global principle may occur for the representation of one integral quadratic form by another integral quadratic form. We show that many such examples may be accounted for by a Brauer-Manin obstruction for the existence of integral points on schemes defined over the integers. For several types of homogeneous spaces of linear algebraic groups, this obstruction is shown to be the only obstruction to the existence of integral points. ----- Une forme quadratique entière peut être représentée par une autre forme quadratique entière sur tous les anneaux d'entiers p-adiques et sur les réels, sans l'être sur les entiers. On en trouve de nombreux exemples dans la littérature. Nous montrons qu'une partie de ces exemples s'explique au moyen d'une obstruction de type Brauer-Manin pour les points entiers. Pour plusieurs types d'espaces homogènes de groupes algébriques linéaires, cette obstruction est la seule obstruction à l'existence d'un point entier.

math.NT↗