# Zhuo Li - PKU, KIAA

## Contact Details

NameZhuo Li |
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AffiliationPKU, KIAA |
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Location |
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## Pubs By Year |
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## External Links |
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## Pub CategoriesHigh Energy Astrophysical Phenomena (21) Astrophysics (14) Mathematics - Representation Theory (7) Quantum Physics (5) Mathematics - Information Theory (3) Computer Science - Information Theory (3) High Energy Physics - Phenomenology (2) Solar and Stellar Astrophysics (2) Mathematics - Group Theory (2) Cosmology and Nongalactic Astrophysics (2) Computer Science - Architecture (1) Physics - Plasma Physics (1) Mathematics - Combinatorics (1) |

## Publications Authored By Zhuo Li

Muon pairs can be produced in the annihilation of ultra-high energy (UHE, $E \gtrsim 10^{18} \,\mathrm{eV}$) photons with low energy cosmic background radiation in the intergalactic space, giving birth to neutrinos. Although the branching ratio of muon pair production is low, products of other channels, which are mainly electron/positron pairs, will probably transfer most of their energies into the new generated UHE photon in the subsequent interaction with the cosmic background radiation via Compton scattering in deep Klein-Nishina regime. The regeneration of these new UHE photons then provides a second chance to produce the muon pairs, enhancing the neutrino flux. Read More

Fast radio bursts (FRBs) have excessive dispersion measures (DMs) and an all-sky distribution, which point toward an extragalactic or even a cosmological origin. We develop a method to extract the mean host galaxy DM ($\left\langle{\rm DM_{HG,loc}}\right\rangle$) and the characterized luminosity ($L$) of FRBs using the observed DM-Flux data, based on the assumption of a narrow luminosity distribution. Applying Bayesian inference to the data of 21 FRBs, we derive a relatively large mean host DM, i. Read More

IceCube has detected a cumulative flux of PeV neutrinos, which origin is unknown. Blazars, active galactic nuclei with relativistic jets pointing to us, are long and widely expected to be one of the strong candidates of high energy neutrino sources. The neutrino production depends strongly on the cosmic ray power of blazar jets, which is largely unknown. Read More

Starting with a highest weight representation of a Kac-Moody group over the complex numbers, we construct a monoid whose unit group is the image of the Kac-Moody group under the representation, multiplied by the nonzero complex numbers. We show that this monoid has similar properties to those of a J-irreducible reductive linear algebraic monoid. In particular, the monoid is unit regular and has a Bruhat decomposition, and the idempotent lattice of the generalized Renner monoid of the Bruhat decomposition is isomorphic to the face lattice of the convex hull of the Weyl group orbit of the highest weight. Read More

**Affiliations:**

^{1}NAOC,

^{2}PKU

Cassiopeia A (Cas A) as the nearby young remnant of a core-collapse supernova is the best candidate for astrophysical studies in supernova explosion and its environment. We studied hard X-ray emissions from Cas A using the ten-year data of INTEGRAL observations, and first detected non-thermal continuum emission from the source up to 220 keV. The $^{44}$Ti line emissions at 68 and 78 keV are confirmed by our observations with a mean flux of $\sim (2. Read More

We explore full/partial tidal disruption events (TDEs) of stars/planets by stellar compact objects (Black holes; BHs; or neutron stars; NSs), which we term micro-TDEs. Disruption of a star/planet with mass $M_{\star}$ may lead to the formation of a debris disk around the BH/NS. Efficient accretion of a fraction $(f_{acc}=0. Read More

Starting with a highest weight representation of a Kac-Moody group over the complex numbers, we construct a monoid whose unit group is the image of the Kac-Moody group under the representation, multiplied by the nonzero complex numbers. We show that this monoid has similar properties to those of a J-irreducible reductive linear algebraic monoid. In particular, the monoid is unit regular and has a Bruhat decomposition, and the idempotent lattice of the generalized Renner monoid of the Bruhat decomposition is isomorphic to the face lattice of the convex hull of the Weyl group orbit of the highest weight. Read More

In recent years, as fractional calculus becomes more and more broadly used in research across different academic disciplines, there are increasing demands for the numerical tools for the computation of fractional integration/differentiation, and the simulation of fractional order systems. Time to time, being asked about which tool is suitable for a specific application, the authors decide to carry out this survey to present recapitulative information of the available tools in the literature, in hope of benefiting researchers with different academic backgrounds. With this motivation, the present article collects the scattered tools into a dashboard view, briefly introduces their usage and algorithms, evaluates the accuracy, compares the performance, and provides informative comments for selection. Read More

**Affiliations:**

^{1}Peking University,

^{2}Peking University,

^{3}Peking University

**Category:**High Energy Astrophysical Phenomena

Several types of extra-galactic high-energy transients have been discovered, which include high-luminosity and low-luminosity long-duration gamma-ray bursts (GRBs), short-duration GRBs, supernova shock breakouts (SBOs), and tidal disruption events (TDEs) without or with an associated relativistic jet. In this paper, we apply a unified method to systematically study the redshift-dependent event rate densities and the global luminosity functions (ignoring redshift evolution) of these transients. We introduce some empirical formulae for the redshift-dependent event rate densities for different types of transients, and derive the local specific event rate density, which also represents its global luminosity function. Read More

IceCube has reported the detection of a diffuse TeV-PeV neutrino emission, for which the flat spectrum radio quasars (FSRQs) have been proposed to be the candidate sources. Here we assume that the neutrino flux from FSRQs is proportional to their gamma-ray ones, and obtain the gamma-ray/neutrino flux ratio by the diffuse gamma-ray flux from Fermi-LAT measurement of FSRQs and the diffuse neutrino flux detected by IceCube. We apply this ratio to individual FSRQs and hence predict their neutrino flux. Read More

Let $\lambda$ be a dominant weight of a finite dimensional simple Lie algebra and $W$ the Weyl group. The convex hull of $W\lambda$ is defined as the weight polytope of $\lambda$. We provide a new proof that there is a natural bijection between the set of orbits of the nonempty faces of the weight polytope under the action of the Weyl group and the set of the connected subdiagrams of the extended Dynkin diagram that contain the extended node $\{-\lambda\}$. Read More

**Affiliations:**

^{1}PKU,

^{2}YNO,

^{3}PKU, KIAA

**Category:**High Energy Astrophysical Phenomena

The IceCube (IC) collaboration recently reported the detection of TeV-PeV extraterrestrial neutrinos whose origin is yet unknown. By the photon-neutrino connection in $pp$ and $p\gamma$ interactions, we use the \fermi-LAT observations to constrain the origin of the IC detected neutrinos. We find that Galactic origins, i. Read More

**Affiliations:**

^{1}NAOC,

^{2}KIAA and PKU

A deep hard X-ray survey of the INTEGRAL satellite first detected the non-thermal emission up to 90 keV in the Tycho supernova (SN) remnant. Its 3 -- 100 keV spectrum is fitted with a thermal bremsstrahlung of $kT\sim 0.81\pm 0. Read More

Recently, both theoretical arguments and observational evidence suggested that a small fraction of fast radio bursts (FRBs) could be associated with gamma-ray bursts (GRBs). If such FRB/GRB association systems are commonly detected in the future, the combination of dispersion measure (DM) derived from FRBs and redshifts derived from GRBs makes these systems a plausible tool to conduct cosmography. We quantify uncertainties in deriving the redshift-dependent DM_{IGM} as a function of z, and test how well dark energy models can be constrained with Monte Carlo simulations. Read More

**Affiliations:**

^{1}PKU,

^{2}PKU

**Category:**High Energy Astrophysical Phenomena

The complete high-resolution lightcurves of Swift GRB 080319B present an opportunity for detailed temporal analysis of the prompt optical emission. With a two-component distribution of initial Lorentz factors, we simulate the dynamical process of the ejected shells from the central engine in the framework of the internal shock model. The emitted radiation are decomposed into different frequency ranges for a temporal correlation analysis between the lightcurves in different energy bands. Read More

**Affiliations:**

^{1}IAP,

^{2}PKU,

^{3}NJU

The origin of magnetic fields that permeate the blast waves of gamma-ray bursts (GRBs) is a long-standing problem. The present paper argues that in four GRBs revealing extended emission at >100 MeV, with follow-up in the radio, optical and X-ray domains at later times, this magnetization can be described as the partial decay of the micro-turbulence that is generated in the shock precursor. Assuming that the bulk of the extended emission >100 MeV can be interpreted as synchrotron emission of shock accelerated electrons, we model the multi-wavelength light curves of GRB 090902B, GRB 090323, GRB 090328 and GRB 110731A, using a simplified then a full synchrotron calculation with power-law-decaying microturbulence \epsilon_B \propto t^{\alpha_t} (t denotes the time since injection through the shock, in the comoving blast frame). Read More

In this paper we find all conjugacy classes of the first basic Renner monoid of type E_6. They are listed in the tables of the paper. Read More

Observations imply that long \gamma-ray bursts (GRBs) are originated from explosions of massive stars, therefore they may occur in the molecular clouds where their progenitors were born. We show here that the prompt optical-UV emission from GRBs may be delayed due to the dust extinction, which can well explain the observed optical delayed onset and fast rise in GRB 080319B. The density and the size of the molecular cloud around GRB 080319B are roughly constrained to be \sim10^3cm^{-3} and \sim 8pc, respectively. Read More

**Affiliations:**

^{1}PKU

If gamma-ray bursts (GRBs) produce high energy cosmic rays, neutrinos are expected to be generated in GRBs due to photo-pion productions. However we stress that the same process also generates electromagnetic (EM) emission induced by the production of secondary electrons and photons, and that the EM emission is expected to be correlated to the neutrino flux. Using the Fermi/LAT observational results on gamma-ray flux from GRBs, the GRB neutrino emission is limited to be below ~20 GeV/m^2 per GRB event on average, which is independent of the unknown GRB proton luminosity. Read More

In this paper we show that the irreducible representations of a finite inverse semigroup $S$ over an algebraically closed field $F$ are in bijection with the conjugacy classes of $S$ if the characteristic of $F$ is zero or a prime number that does not divide the order of any maximal subgroup of $S$. Read More

In this paper we describe conjugacy classes of a Renner monoid $R$ with unit group $W$, the Weyl group. We show that every element in $R$ is conjugate to an element $ue$ where $u\in W$ and $e$ is an idempotent in a cross section lattice. Denote by $W(e)$ and $W_*(e)$ the centralizer and stabilizer of $e\in \Lambda$ in $W$, respectively. Read More

**Affiliations:**

^{1}PKU

**Category:**High Energy Astrophysical Phenomena

We discuss the implications of Fermi/LAT observations on several aspects of gamma-ray burst (GRB) physics, including the radiation process, the emission sites, the bulk Lorentz factor, and the pre-shock magnetic field: (1) MeV-range emission favors synchrotron process but the highest energy (>10GeV) emission may not be synchrotron origin, more likely inverse Compton origin; (2) GRB should have multi-zone emission region, with MeV emission produced at smaller radii while optical and >100MeV emission at larger radii; (3) the bulk Lorentz factor can be a few 100's, much lower than 10^3, in multi-zone model; (4) the upstream magnetic field of afterglow shock is strongly amplified to be at least in mG scale. Read More

Recently, Fermi-LAT detected GeV emission during the X-ray flaring activity in GRB 100728A. We study various scenarios for its origin. The hard spectrum of the GeV emission favors the external inverse-Compton origin in which X-ray flare photons are up-scattered by relativistic electrons in the external forward shock. Read More

**Affiliations:**

^{1}PKU

**Category:**High Energy Astrophysical Phenomena

We note that the theoretical prediction of neutrinos from gamma-ray bursts (GRBs) by IceCube overestimates the GRB neutrino flux, because they ignore both the energy dependence of the fraction of proton energy transferred to charged pions and the radiative energy loss of secondary pions and muons when calculating the normalization of the neutrino flux. After correction for these facts the GRB neutrino flux is reduced, e.g. Read More

The Lorentz factor (LF) of gamma-ray burst (GRB) ejecta may be constrained by observations of high-energy (HE) spectral attenuation. The recent Fermi-LAT observations of prompt GeV emission from several bright GRBs have leaded to conclusions of unexpectedly large LFs, $\Gamma>10^3$. Here we revisit this problem with two main concerns. Read More

**Affiliations:**

^{1}PKU,

^{2}YNO/NAOC

**Category:**High Energy Astrophysical Phenomena

Long-lived >100 MeV emission has been a common feature of most Fermi-LAT detected gamma-ray bursts (GRBs), e.g., detected up to ~10^3s in long GRBs 080916C and 090902B and ~10^2s in short GRB 090510. Read More

**Affiliations:**

^{1}NJU,

^{2}NJU,

^{3}PKU,

^{4}PSU, PMO,

^{5}NJU

**Category:**High Energy Astrophysical Phenomena

Extended high-energy(>100MeV) gamma-ray emission that lasts much longer than the prompt sub-MeV emission has been detected from quite a few gamma-ray bursts (GRBs) by Fermi Large Area Telescope (LAT) recently. A plausible scenario is that this emission is the afterglow synchrotron emission produced by electrons accelerated in the forward shocks. In this scenario, the electrons that produce synchrotron high-energy emission also undergo inverse-Compton (IC) loss and the IC scattering with the synchrotron photons should be in the Klein-Nishina regime. Read More

A famous open problem in the theory of quantum error-correcting codes is whether or not the parameters of an impure quantum code can violate the quantum Hamming bound for pure quantum codes. We partially solve this problem. We demonstrate that there exists a threshold such that an arbitrary quantum code must obey the quantum Hamming bound whenever . Read More

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. Read More

**Affiliations:**

^{1}NJU,

^{2}PKU,

^{3}NJU,

^{4}PSU

**Category:**High Energy Astrophysical Phenomena

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. Read More

We present a universal framework for quantum error-correcting codes, i.e., the one that applies for the most general quantum error-correcting codes. Read More

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. Read More

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. Read More

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 $\overline {K^*\rho(G_0)}$ where $G_0$ is a simple algebraic group over the algebraic closure of $F_q$, and $\rho: G_0\to GL(V)$ 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. Read More

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. Read More

**Affiliations:**

^{1}PKU

**Category:**Astrophysics

The gamma-rays from gamma-ray bursts (GRBs) are believed to be produced by internal shocks driven by small timescale, ~1 ms, variation in the GRB outflows, and a pair-production spectral cutoff is generally expected around the GeV range. However, the observed optical flashes accompanying GRBs suggest that the delayed residual collisions due to large timescale variation continue to accelerate electrons. We show here that the inverse-Compton (IC) scattering of the prompt gamma-rays by these residual internal shock electrons leads to a high energy emission beyond the previously thought spectral cutoff, in agreement with the previous detections of GeV photons by EGRET in several GRBs in conjunction with MeV emission. Read More

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. Read More

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. Read More

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. Read More

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). Read More

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. Read More

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. Read More

**Category:**Astrophysics

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. Read More

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. Read More

**Affiliations:**

^{1}Weizmann Inst.,

^{2}Weizmann Inst.

**Category:**Astrophysics

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. Read More

**Affiliations:**

^{1}PSU, NJU,

^{2}Weizmann Inst,

^{3}PSU

**Category:**Astrophysics

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. Read More

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. Read More

We discuss the prompt emission of GRBs, allowing for $\gamma\gamma$ pair production and synchrotron self-absorption. The observed hard spectra suggest heavy pair-loading in GRBs. The re-emission of the generated pairs results in the energy transmission from high-energy gamma-rays to long-wavelength radiation. Read More

We consider in this paper the effect of synchrotron self-Compton process on X-ray afterglows of gamma-ray bursts. We find that for a wide range of parameter values, especially for the standard values which imply the energy in the electrons behind the afterglow shock is tens times as that in the magnetic field, the electron cooling is dominated by Compton cooling rather than synchrotron one. This leads to a different evolution of cooling frequency in the synchrotron emission component, and hence a different (flatter) light curve slope in the X-ray range. Read More

Gamma-ray bursts (GRBs) are believed to originate from ultra-relativistic winds/fireballs to avoid the "compactness problem". However, the most energetic photons in GRBs may still suffer from $\gamma-\gamma$ absorption leading to electron/positron pair production in the winds/fireballs. We show here that in a wide range of model parameters, the resulting pairs may dominate those electrons associated with baryons. Read More