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Ying Zhang

Publications and source records attributed to Ying Zhang.

At least 595 records · Page 33Linked to original sources
arXiv2007

On the Correlation of Geographic and Network Proximity at Internet Edges and its Implications for Mobile Unicast and Multicast Routing

Significant effort has been invested recently to accelerate handover operations in a next generation mobile Internet. Corresponding works for developing efficient mobile multicast management are emergent. Both problems simultaneously expose routing complexity between subsequent points of attachment as a characteristic parameter for handover performance in access networks. As continuous mobility handovers necessarily occur between access routers located in geographic vicinity, this paper investigates on the hypothesis that geographically adjacent edge networks attain a reduced network distances as compared to arbitrary Internet nodes. We therefore evaluate and analyze edge distance distributions in various regions for clustered IP ranges on their geographic location such as a city. We use traceroute to collect packet forwarding path and round-trip-time of each intermediate node to scan-wise derive an upper bound of the node distances. Results of different scanning origins are compared to obtain the best estimation of network distance of each pair. Our results are compared with corresponding analysis of CAIDA Skitter data, overall leading to fairly stable, reproducible edge distance distributions. As a first conclusion on expected impact on handover performance measures, our results indicate a general optimum for handover anticipation time in 802.11 networks of 25 ms.

cs.NI↗
arXiv2006

Congruence and Uniqueness of Certain Markoff Numbers

By making use of only simple facts about congruence, we first show that every even Markoff number is congruent to 2 modulo 32, and then, generalizing an earlier result of Baragar, establish the uniqueness for those Markoff numbers c where one of 3c - 2 and 3c + 2 is a prime power, 4 times a prime power, or 8 times a prime power.

math.NT↗
arXiv2006

A survey of length series identities for surfaces, % 3-manifolds and representation varieties

We survey some of our recent results on length series identities for hyperbolic (cone) surfaces, possibly with cusps and/or boundary geodesics; classical Schottky groups; representations/characters of the one-holed torus group to $SL(2, \mathbf C)$; and hyperbolic 3 manifolds obtained by hyperbolic Dehn surgery on punctured torus bundles over the circle. These can be regarded as generalizations and variations of McShane's identity for cusped hyperbolic surfaces, which has found some striking applications in the recent work of Mirzakhani. We discuss some of the methods and techniques used to obtain these identities.

math.GT↗
arXiv2006

Nonlinear 2D Spin Susceptibility in a Finite Magnetic Field: Spin-Polarization Dependence

By theoretically calculating the interacting spin susceptibility of a two-dimensional electron system in the presence of finite spin polarization, we show that the extensively employed technique of measuring the 2D spin susceptibility by linear extrapolation to a zero field from the finite-field experimental data is theoretically unjustified due to the strong nonlinear magnetic field dependence of the interacting susceptibility. Our work compellingly establishes that much of the prevailing interpretation of the 2D susceptibility measurements is incorrect, and, in general, the 2D interacting susceptibility cannot be extracted from the critical magnetic field for full spin polarization, as is routinely done experimentally.

cond-mat.str-el↗
arXiv2005

Spin Polarization Dependence of Carrier Effective Mass in Semiconductor Structures: Spintronic Effective Mass

We introduce the concept of a spintronic effective mass for spin-polarized carriers in semiconductor structures, which arises from the strong spin-polarization dependence of the renormalized effective mass in an interacting spin-polarized electron system. The majority-spin many-body effective mass renormalization differs by more than a factor of 2 at rs=5 between the unpolarized and the fully polarized two-dimensional system, whereas the polarization dependence (~15%) is more modest in three dimensions around metallic densities (rs~5). The spin-polarization dependence of the carrier effective mass is of significance in various spintronic applications.

cond-mat.mes-hall↗
arXiv2005

End Invariants for $\SL(2,C)$ characters of the one-holed torus

We define and study the set ${\mathcal E}(ρ)$ of end invariants of a $\SL(2,C)$ character $ρ$ of the one-holed torus $T$. We show that the set ${\mathcal E}(ρ)$ is the entire projective lamination space $\mathscr{PL}$ of $T$ if and only if (i) $ρ$ corresponds to the dihedral representation, or (ii) $ρ$ is real and corresponds to a SU(2) representation; and that otherwise, ${\mathcal E}(ρ)$ is closed and has empty interior in $\mathscr{PL}$. For real characters $ρ$, we give a complete classification of ${\mathcal E}(ρ)$, and show that ${\mathcal E}(ρ)$ has either 0, 1 or infinitely many elements, and in the last case, ${\mathcal E}(ρ)$ is either a Cantor subset of $\mathscr{PL}$ or is $\mathscr{PL}$ itself. We also give a similar classification for "imaginary" characters where the trace of the commutator is less than 2. Finally, we show that for discrete characters (not corresponding to dihedral or SU(2) representations), ${\mathcal E}(ρ)$ is a Cantor subset of $\mathscr{PL}$ if it contains at least three elements.

math.GT↗
arXiv2005

Temperature and magnetization-dependent band-gap renormalization and optical many-body effects in diluted magnetic semiconductors

We calculate the Coulomb interaction induced density, temperature and magnetization dependent many-body band-gap renormalization in a typical diluted magnetic semiconductor GaMnAs in the optimally-doped metallic regime as a function of carrier density and temperature. We find a large (about 0.1 eV) band gap renormalization which is enhanced by the ferromagnetic transition. We also calculate the impurity scattering effect on the gap narrowing. We suggest that the temperature, magnetization, and density dependent band gap renormalization could be used as an experimental probe to determine the valence band or the impurity band nature of carrier ferromagnetism.

cond-mat.mtrl-sci↗
arXiv2005

The SL(2,C) character variety of the one-holed torus

In this note we announce several results concerning the SL(2,C) character variety ${\mathcal X}$ of the one-holed torus. We give a description of the largest open subset ${\mathcal X}_{BQ}$ of ${\mathcal X}$ on which the mapping class group $Γ$ acts properly discontinuously, in terms of two very simple conditions, and show that a series identity generalizing McShane's identity for the punctured torus holds for all characters in this subset. We also give variations of the McShane-Bowditch identities to characters fixed by an Anosov element of $Γ$ with applications to closed hyperbolic three manifolds. Finally we give a definition of end invariants for SL(2,C) characters and give a partial classification of the set of end invariants of a character in ${\mathcal X}$.

math.GT↗
arXiv2005

Density dependent spin susceptibility and effective mass in interacting quasi-two dimensional electron systems

Motivated by recent experimental reports, we carry out a Fermi liquid many-body calculation of the interaction induced renormalization of the spin susceptibility and effective mass in realistic two dimensional (2D) electron systems as a function of carrier density using the leading-order `ladder-bubble' expansion in the dynamically screened Coulomb interaction. Using realistic material parameters for various semiconductor-based 2D systems, we find reasonable quantitative agreement with recent experimental susceptibility and effective mass measurements. We point out a number of open questions regarding quantitative aspects of the comparison between theory and experiment in low-density 2D electron systems.

cond-mat.str-el↗
arXiv2005

Exchange instabilities in electron systems: Bloch versus Stoner Ferromagnetism

We show that 2D and 3D electron systems with the long-range Coulomb electron-electron interaction could develop ferromagnetic instabilities due to strong exchange effects at low densities. The critical densities in both 2D and 3D systems at which the magnetic instability, which could either be of Stoner type (second-order) or of Bloch type (first-order), are higher than the dispersion instability critical density where effective mass at the Fermi surface diverges. We discuss the theoretical as well as experimental implications of the ferromagnetic instability at low electron densities, particularly in low-disorder semiconductor-based two-dimensional systems.

cond-mat.str-el↗
arXiv2005

Generalized Markoff Maps and McShane's Identity

We study general representations of the free group on two generators into $SL(2,C)$, and the connection with generalized Markoff maps, following Bowditch. We show that Bowditch's Q-conditions for generalized Markoff maps are sufficient for the generalized McShane identity to hold for the corresponding representations and that the subset of representations satisfying these conditions is the largest open subset in the relative character variety on which the mapping class group acts properly discontinuously. Moreover we generalize Bowditch's results on variations of McShane's identity for complete, finite volume hyperbolic 3-manifolds which fiber over the circle, with the fiber a punctured-torus, to identities for incomplete hyperbolic structures on such manifolds, hence obtaining identities for closed hyperbolic 3-manifolds which are obtained by doing hyperbolic Dehn surgery on such manifolds.

math.GT↗
arXiv2005

Necessary and sufficient conditions for McShane's identity and variations

Greg McShane introduced a remarkable identity for lengths of simple closed geodesics on the once punctured torus with a complete, finite volume hyperbolic structure. Bowditch later generalized this and gave sufficient conditions for the identity to hold for general type-preserving representations of a free group on two generators Γto SL(2,C). In this note we extend Bowditch's result by giving necessary and sufficient conditions for the identity to hold, and also for the generalized McShane identity to hold for arbitrary (not necessarily type preserving) representations. We also give a version of Bowditch's variation of McShane's identity to once-punctured torus bundles, to the case where the monodromy is generated by a reducible element, and provide necessary and sufficient conditions for the variation to hold.

math.GT↗
arXiv2005

Dispersion Instability in Strongly Interacting Electron Liquids

We show that the low-density strongly interacting electron liquid, interacting via the long-range Coulomb interaction, could develop a dispersion instability at a critical density associated with the approximate flattening of the quasiparticle energy dispersion. At the critical density the quasiparticle effective mass diverges at the Fermi surface, but the signature of this Fermi surface instability manifests itself away from the Fermi momentum at higher densities. For densities below the critical density the system is unstable since the quasiparticle velocity becomes negative. We show that one physical mechanism underlying the dispersion instability is the emission of soft plasmons by the quasiparticles. The dispersion instability occurs both in two and three dimensional electron liquids. We discuss the implications of the dispersion instability for experiments at low electron densities.

cond-mat.str-el↗
arXiv2004

Quasiparticle effective mass divergence in two dimensional electron systems

Within the infinite series of ring (or bubble) diagram approximation for the electronic self-energy as appropriate for the long-range Coulomb interaction, we calculate the density-dependent T=0 Fermi liquid quasiparticle effective mass renormalization in two dimensional (2D) electron systems in the random-phase-approximation (RPA). We find that the quasiparticle effective mass increases very strongly with increasing $r_s$, exhibiting an unexpected divergence at a critical $r_s$ value ($\sim 16$ in the ideal 2D system). We discuss the possibility for and the consequences of such an interaction induced effective mass divergence as the electron density decreases, and critically comment on the likely theoretical scenarios which could lead to such a low density effective mass divergence in electron liquids.

cond-mat.str-el↗
arXiv2004

McShane's identity for classical Schottky Groups

Greg McShane introduced a remarkable identity for the lengths of simple closed geodesics on cusped hyperbolic surfaces. This was subsequently generalized by the authors to hyperbolic cone-surfaces, possibly with cusps and/or geodesic boundary. In this paper, we generalize the identity further to the case of classical Schottky groups. As a consequence, we obtain some surprising new identities in the case of fuchsian Schottky groups. For classical Schottky groups of rank 2, we also give generalizations of the Weierstrass identities, first given by McShane.

math.GT↗
arXiv2004

Generalizations of McShane's identity to hyperbolic cone-surfaces

We generalize McShane's identity for the length series of simple closed geodesics on a cusped hyperbolic surface to hyperbolic cone-surfaces (with all cone angles $\le π$), possibly with cusps and/or geodesic boundary. In particular, by applying the generalized identity to the orbifolds obtained from taking the quotient of the one-holed torus by its elliptic involution, and the closed genus two surface by its hyper-elliptic involution, we obtain generalizations of the Weierstrass identities for the one-holed torus, and identities for the genus two surface, also obtained by McShane using different methods. We also give an interpretation of the identity in terms of complex lengths, gaps, and the direct visual measure of the boundary.

math.GT↗
arXiv2004

Temperature dependent effective mass renormalization in 2D electron systems

We calculate, as a function of temperature and density, the electron-electron interaction induced quasiparticle effective mass renormalization in 2D electron systems within the leading-order dynamically screened Coulomb interaction expansion. We find an unexpected nonanalyticity and nonmonotonicity in the temperature dependent effective mass with the renormalized mass linearly increasing with temperature at low temperatures for all densities.

cond-mat.mes-hall↗