arXiv subjects
Publications and source records attributed to Zhuo Li.
We solve the problem of the classification of perfect quantum codes. We prove that the only nontrivial perfect quantum codes are those with the parameters . There exist no other nontrivial perfect quantum codes.
Fermi observations of high-energy gamma-ray emission from GRB 080916C shows that its spectrum is consistent with the Band function from MeV to tens of GeV. Assuming one single emission mechanism dominates in the whole energy range, we show that this spectrum is consistent with synchrotron origin by shock-accelerated electrons. The simple electron inverse-Compton model and the hadronic model are found to be less viable. In the synchrotron scenario, the synchrotron self-Compton scattering is likely to be in the Klein-Nishina regime and therefore the resulting high-energy emission is subdominant, even though the magnetic field energy density is lower than that in relativistic electrons. The Klein-Nishina inverse-Compton cooling may also affect the low-energy electron number distribution and hence results in a low-energy synchrotron photon spectrum $n(ν)\proptoν^{-1}$ below the peak energy. Under the framework of the electron synchrotron interpretation, we constrain the shock microphysical parameters and derive a lower limit of the upstream magnetic fields. The detection of synchrotron emission extending to about 70 GeV in the source frame in GRB 080916C favors the Bohm diffusive shock acceleration if the bulk Lorentz factor of the relativistic outflow is not significantly greater than thousands.
We present a universal framework for quantum error-correcting codes, i.e., the one that applies for the most general quantum error-correcting codes. This framework is established on the group algebra, an algebraic notation for the nice error bases of quantum systems. The nicest thing about this framework is that we can characterize the properties of quantum codes by the properties of the group algebra. We show how it characterizes the properties of quantum codes as well as generates some new results about quantum codes.
We explicitly construct an infinite family of asymptotically good concatenated quantum stabilizer codes where the outer code uses CSS-type quantum Reed-Solomon code and the inner code uses a set of special quantum codes. In the field of quantum error-correcting codes, this is the first time that a family of asymptotically good quantum codes is derived from bad codes. Its occurrence supplies a gap in quantum coding theory.
We construct a new family of quantum MDS codes from classical generalized Reed-Solomon codes and derive the necessary and sufficient condition under which these quantum codes exist. We also give code bounds and show how to construct them analytically. We find that existing quantum MDS codes can be unified under these codes in the sense that when a quantum MDS code exists, then a quantum code of this type with the same parameters also exists. Thus as far as is known at present, they are the most important family of quantum MDS codes.
We show four formulas for calculating the orders of finite reductive monoids with zero. As applications, these formulas are then used to calculate the orders of finite reductive monoids induced from the $F_q$-split $\J$-irreducible monoids $\overline {K^*ρ(G_0)}$ where $G_0$ is a simple algebraic group over the algebraic closure of $F_q$, and $ρ: G_0\to GL(V)$ is the irreducible representation associated with any dominant weight. Finally, we give an explicit formula for the orders of finite symplectic monoids associated with the last fundamental dominant weight of type $C_l$; the connections to $H$-polynomials and Betti numbers are shown.
We describe irreducible representations and character formulas of the Renner monoids for reductive monoids, which generalizes the Munn-Solomon representation theory of rook monoids to any Renner monoids. The type map and polytope associated with reductive monoids play a crucial role in our work. It turns out that the irreducible representations of certain parabolic subgroups of the Weyl groups determine the complete set of irreducible representations of the Renner monoids. An analogue of the Munn-Solomon formula for calculating the character of the Renner monoids, in terms of the characters of the parabolic subgroups, is shown.
We suggest that non-thermal emission can be produced by multiple scatterings of the photons between the supernova ejecta and pre-shock material in supernova shock breakout. Such bulk-Comptonization process may significantly change the original thermal photon spectrum, forming a power-law non-thermal component at higher energies. We then show that the luminous X-ray outburst XRO081009 associated with SN2008D is likely to be such shock breakout emission from an ordinary type Ib/c supernova.
We present a statistical study of the non-thermal X-ray emission of 27 young rotation powered pulsars (RPPs) and 24 pulsar wind nebulae (PWNe) by using the Chandra and the XMM-Newton observations, which with the high spatial resolutions enable us to spatially resolve pulsars from their surrounding PWNe. We obtain the X-ray luminosities and spectra separately for RPPs and PWNe, and then investigate their distribution and relation to each other as well as the relation with the pulsar rotational parameters. In the pair-correlation analysis we find that: (1) the X-ray (2-10 keV) luminosities of both pulsar and PWN (L_{psr} and L_{pwn}) display a strong correlation with pulsar spin down power Edot and characteristic age, and the scalings resulting from a simple linear fit to the data are L_{psr} \propto Edot^{0.92 \pm 0.04} and L_{pwn} \propto Edot^{1.45 \pm 0.08} (68% confidence level), respectively, however, both the fits are not statistically acceptable; (2) L_{psr} also shows a possible weak correlation with pulsar period P and period derivative Pdot, whereas L_{pwn} manifests a similar weak correlation with Pdot only; (3) The PWN photon index Gamma_{pwn} is positively correlated with L_{pwn} and L_{pwn}/Edot. We also found that the PWN X-ray luminosity is typically 1 to 10 times larger than that from the underlying pulsar, and the PWN photon indices span a range of ~1.5 to ~2. The statistic study of PWN spectral properties supports the particle wind model in which the X-ray emitting electrons are accelerated by the termination shock of the wind.
The prompt gamma-ray emission in gamma-ray bursts is believed to be produced by internal shocks within a relativistic unsteady outflow. The recent detection of prompt optical emission accompanying the prompt gamma-ray emission appears to be inconsistent with this model since the out flowing plasma is expected to be highly optically thick to optical photons. We show here that fluctuations in flow properties on short, ~ 1 ms, time scale, which drive the gamma-ray producing collisions at small radii, are expected to lead to "residual" collisions at much larger radii, where the optical depth to optical photons is low. The late residual collisions naturally account for the relatively bright optical emission. The apparent simultaneity of gamma-ray and optical emission is due to the highly relativistic speed with which the plasma expands. Residual collisions may also account for the X-ray emission during the early "steep decline" phase, where the radius is inferred to be larger than the gamma-ray emission radius. Finally, we point out that inverse-Compton emission from residual collisions at large radii is expected to contribute significantly to the emission at high energy, and may therefore "smear" the pair production spectral cut-off.
Electromagnetic energy losses of charged pions and muons suppress the expected high energy, >1E18 eV, neutrino emission from sources of ultrahigh energy, >1E19 eV, cosmic-rays. We show here that >1E19 eV photons produced in such sources by neutral pion decay may escape the sources, thanks to the Klein-Nishina suppression of the pair production cross section, and produce muon pairs in interactions with the cosmic microwave background. The flux of muon decay neutrinos, which are expected to be associated in time and direction with the electromagnetic emission from the sources, may reach a few percent of the Waxman-Bahcall bound. Their detection may allow one to directly identify the sources of >1E19 eV cosmic-rays, and will provide the most stringent constraints on quantum-gravity-induced Lorentz violation.
Buffer insertion is a popular technique to reduce the interconnect delay. The classic buffer insertion algorithm of van Ginneken has time complexity O(n^2), where n is the number of buffer positions. Lillis, Cheng and Lin extended van Ginneken's algorithm to allow b buffer types in time O (b^2 n^2). For modern design libraries that contain hundreds of buffers, it is a serious challenge to balance the speed and performance of the buffer insertion algorithm. In this paper, we present a new algorithm that computes the optimal buffer insertion in O (bn^2) time. The reduction is achieved by the observation that the (Q, C) pairs of the candidates that generate the new candidates must form a convex hull. On industrial test cases, the new algorithm is faster than the previous best buffer insertion algorithms by orders of magnitude.
The predicted thermal flash from SN shock breakout might have been detected for the first time by Swift in GRB 060218/SN 2006aj. The detected thermal X-ray emission in this event implies emergence of a trans-relativistic (TR) SN shock with kinetic energy of E_k>1E49 erg. During TRSN shock breakout, the thermal photons could be "accelerated" by the shock through repeated bulk Compton scattering, forming a nonthermal gamma/X-ray component with dominant energy over thermal one. This mechanism of "photon acceleration" at TRSN shock breakout might also account for gamma-rays in the other similar low-luminosity GRBs, implying that they are atypical GRBs with only TR outflows. TRSNe form a peculiar type of SNe with large kinetic energy, >1E49 erg, in TR ejecta, Γβ~2.
Thermal X-ray emission which is simultaneous with the prompt gamma-rays has been detected for the first time from a supernova connected with a gamma-ray burst (GRB), namely GRB060218/SN2006aj. It has been interpreted as arising from the breakout of a mildly relativistic, radiation-dominated shock from a dense stellar wind surrounding the progenitor star. There is also evidence for the presence of a mildly relativistic ejecta in GRB980425/SN1998bw, based on its X-ray and radio afterglow. Here we study the process of repeated bulk Compton scatterings of shock breakout thermal photons by the mildly relativistic ejecta. During the shock breakout process, a fraction of the thermal photons would be repeatedly scattered between the pre-shock material and the shocked material as well as the mildly relativistic ejecta and, as a result, the thermal photons get boosted to increasingly higher energies. This bulk motion Comptonization mechanism will produce nonthermal gamma-ray and X-ray flashes, which could account for the prompt gamma-ray burst emission in low-luminosity supernova-connected GRBs, such as GRB060218. A Monte Carlo code has been developed to simulate this repeated scattering process, which confirms that a significant fraction of the thermal photons get "accelerated" to form a nonthermal component, with a dominant luminosity. This interpretation for the prompt nonthermal emission of GRB060218 may imply that either the usual internal shock emission from highly relativistic jets in these low-luminosity GRBs is weak, or alternatively, that there are no highly relativistic jets in this peculiar class of bursts.
The recent detection of X-ray flares during the afterglow phase of gamma-ray bursts (GRBs) suggests an inner-engine origin, at radii inside the forward shock. There must be inverse Compton (IC) emission arising from such flare photons scattered by forward shock afterglow electrons when they are passing through the forward shock. We find that this IC emission produces high energy gamma-ray flares, which may be detected by AGILE, GLAST and ground-based TeV telescopes. The anisotropic IC scattering between flare photons and forward shock electrons does not affect the total IC component intensity, but cause a time delay of the IC component peak relative to the flare peak. The anisotropic scattering effect may also weaken, to some extent, the suppression effect of the afterglow intensity induced by the enhanced electron cooling due to flare photons. We speculate that this IC component may already have been detected by EGRET from a very strong burst--GRB940217. Future observations by GLAST may help to distinguish whether X-ray flares originate from late central engine activity or from external shocks.
Gamma-ray burst (GRB) afterglow emission is believed to be produced by synchrotron emission of electrons accelerated to high energy by a relativistic collisionless shock propagating into a weakly magnetized plasma. Afterglow observations have been used to constrain the post-shock magnetic field and structure, as well as the accelerated electron energy distribution. Here we show that X-ray afterglow observations on day time scale constrain the pre-shock magnetic field to satisfy B>0.2[n/(1/cc)]^{5/8} mG, where n is the pre-shock density. This suggests that either the shock propagates into a highly magnetized fast, v~10^3 km/s, wind, or that the pre-shock magnetic field is strongly amplified, most likely by the streaming of high energy shock accelerated particles. More stringent constraints may be obtained by afterglow observations at high photon energy at late, >1 d, times.
The recent detection of delayed X-ray flares during the afterglow phase of gamma-ray bursts (GRBs) suggests an inner-engine origin, at radii inside the deceleration radius characterizing the beginning of the forward shock afterglow emission. Given the observed temporal overlapping between the flares and afterglows, there must be inverse Compton (IC) emission arising from such flare photons scattered by forward shock afterglow electrons. We find that this IC emission produces GeV-TeV flares, which may be detected by GLAST and ground-based TeV telescopes. We speculate that this kind of emission may already have been detected by EGRET from a very strong burst--GRB940217. The enhanced cooling of the forward shock electrons by the X-ray flare photons may suppress the synchrotron emission of the afterglows during the flare period. The detection of GeV-TeV flares combined with low energy observations may help to constrain the poorly known magnetic field in afterglow shocks. We also consider the self-IC emission in the context of internal-shock and external-shock models for X-ray flares. The emission above GeV from internal shocks is low, while the external shock model can also produce GeV-TeV flares, but with a different temporal behavior from that caused by IC scattering of flare photons by afterglow electrons. This suggests a useful approach for distinguishing whether X-ray flares originate from late central engine activity or from external shocks.
The central engine of gamma-ray bursts (GRBs) is believed to eject double-sided ultra-relativistic jets. For an observed GRB, one of the twin jets should point toward us, and is responsible for the prompt gamma-ray and subsequent afterglow emission. We consider in this Letter the other receding jet, which will give rise to late-time radio re-brightening (RRB) when it becomes non-relativistic (NR) and radiative isotropic. The RRB peaks at a time $5t_{NR}=2(E_{j,51}/n)^{1/3}$ yr after the GRB, where $t_{NR}$ is the observed NR timescale for the preceding jet, $E_j$ is the jet energy and $n$ is the ambient medium density. The peak flux is comparable to the preceding-jet emission at $t_{NR}$. We expect the RRB of GRB 030329 1.7 yr after the burst with a flux $\sim0.6$ mJy at 15 GHz. The cases of GRBs 970508 and 980703 have also been discussed. The detection of RRB, which needs dense monitoring campaign even a few years after a GRB, will be the direct evidence for the existence of double-sided jets in GRBs, and prove the black hole-disk system formation in the cores of progenitors.