Note on R\'{e}nyi entropy of 2D perturbed free fermions

In this paper we study the R\'{e}nyi entropy of 2D massless free fermions perturbed by the $T\bar{T}$ term and the $J\bar{T}$ term at the first order perturbation. Three cases, the vacuum state of infinite size system with $T\bar{T}$ perturbation, the excited states of finite size system with $T\bar{T}$ perturbation, and the vacuum state of infinite size system with $J\bar{T}$ perturbation, are analyzed. We use the bosonization approach to calculate the perturbative expansions of R\'{e}nyi entropy. In the bosonization language the twist operator is known explicitly, with which the computation of correlators in the perturbative expansion can be simply performed. Moreover, we show that the $T\bar{T}$ and $J\bar{T}$ terms have a simple form and are similar with each other. For the first and third cases, we reproduce the known results for R\'{e}nyi entropy using the bosonization method. While for the second case, we obtain new results for the excited states.Comment: 22 page

The Fourth Generation Quark and the 750 GeV Diphoton Excess

Recently, the CMS and ATLAS collaborations have reported a diphoton peak at 750 GeV in the RunII of LHC at 13 TeV. We assume that the heavy fourth generation quark doublet $z,~y$ with $380$GeV mass, and the width of $z,t$ is much less $b$ quark. Then we show that the contributions of the $(z \bar z+y \bar y)/\sqrt{2}$ bound state $\eta_{zy}(1S)$ to the diphoton measurements through $\sigma (pp\to \eta_{zy}(1s)\to \gamma \gamma)$ are $5.6^{+5.6}_{-2.8} {\rm fb}$ at $\sqrt S=13$ TeV. They are constant with the 750 GeV diphoton excess measured by the CMS ant ATLAS collaborations

Note on acoustic black holes from black D3-brane

In this paper, we study the acoustic black hole emerged from the nonextremal black D3-brane, based on the holographic approaches in constructing the acoustic black hole in asymptotically Anti de-Sitter spacetime (AAdS) and the effective hydrodynamic description of the nonextremal black D3-brane. We show that the holographic dual description of the acoustic black hole appeared on the timelike cutoff surface in the nonextremal black D3-brane also exist. The duality includes the dynamical connection between the acoustic black hole and the bulk gravity, a universal equation relating the Hawking-like temperature and the Hawking temperature, and a phonon/scalar channel quasinormal mode correspondence.Comment: 14 pages, no figure

An Intrinsic Advantage of Sexual Reproduction

The prevalence of sexual reproduction ("sex") in eukaryotes is an enigma of evolutionary biology. Sex increases genetic variation only tells its long-term superiority in essence. The accumulation of harmful mutations causes an immediate and ubiquitous pressure for organisms. Contrary to the common sense, our theoretical model suggests that reproductive rate can influence initiatively the accumulation of harmful mutations. The interaction of reproductive rate and the integrated harm of mutations causes a critical reproductive rate R*. A population will become irreversibly extinct once the reproductive rate reduces to lower than R*. A sexual population has a R* lower than 1 and an asexual population has a R* higher than 1. The mean reproductive rate of a population reached to the carrying capacity has to reduce to 1. That explains the widespread sex as well as the persistence of facultative and asexual organisms. Computer simulations support significantly our conclusion.Comment: 32 pages, 6 figure

Production of ΛΛ\Lambda\Lambda and Λnˉ\bar{\Lambda \text{n}} in central Pb+Pb collisions at sNN\sqrt{s_{NN}}=2.76 TeV within a covariant coalescence model

We study the production of $\Lambda\Lambda$ and $\overline{\Lambda \text{n}}$ exotic states in central Pb+Pb collisions at $\sqrt{s_{NN}}=2.76$ TeV at LHC via both hadron and quark coalescence within a covariant coalescence model with a blast-wave-like parametrization for the phase-space configurations of constituent particles at freezeout. In the hadron coalescence, the two states are considered as molecular states while they are considered as six-quark states in the quark coalescence.For $\overline{\Lambda \text{n}}$, we find that the yields of both molecular and six-quark states are much larger than the experimental upper-limits. For $\Lambda\Lambda$, while the molecule-state yield is much larger than the experimental upper-limits, the six-quark-state yield could be lower than the upper-limits. The higher molecule-state yields are mainly due to the large contribution of short-lived strong resonance decays into (anti-)nucleons and (anti-)$\Lambda$ which can significantly enhance the molecule-state yields of $\Lambda\Lambda$ and $\overline{\Lambda \text{n}}$ via hadron coalescence. Our results suggest that the current experimental measurement at LHC cannot exclude the existence of the $\Lambda\Lambda$ as an exotic six-quark state, and if $\Lambda\Lambda$ is a six-quark state, it is then on the brink of being discovered.Comment: 6 pages, 4 figures, 2 tables. Minor modifications. Accepted version to appear in PR

Antimatter Λ4^4_{\Lambda}H Hypernucleus Production and the Λ3^3_{\Lambda}H/3^3He Puzzle in Relativistic Heavy-Ion Collisions

We show that the measured yield ratio $^3_{\Lambda}$H/$^3$He ($^3_{\overline{\Lambda}}\overline{\text{H}}$/$^3\overline{\text{He}}$) in Au+Au collisions at $\sqrt{s_{NN}}=200$ GeV and in Pb+Pb collisions at $\sqrt{s_{NN}}=2.76$ TeV can be understood within a covariant coalescence model if (anti-)$\Lambda$ particles freeze out earlier than (anti-)nucleons but their relative freezeout time is closer at $\sqrt{s_{NN}}=2.76$ TeV than at $\sqrt{s_{NN}}=200$ GeV. The earlier (anti-)$\Lambda$ freezeout can significantly enhance the yield of (anti)hypernucleus $^4_{\Lambda}$H ($^4_{\overline{\Lambda}}\overline{\text{H}}$), leading to that $^4_{\overline{\Lambda}}\overline{\text{H}}$ has a comparable abundance with $^4\overline{\text{He}}$ and thus provides an easily measured antimatter candidate heavier than $^4\overline{\text{He}}$. The future measurement on $^4_{\Lambda}$H ($^4_{\overline{\Lambda}}\overline{\text{H}}$) would be very useful to understand the (anti-)$\Lambda$ freezeout dynamics and the production mechanism of (anti)hypernuclei in relativistic heavy-ion collisions.Comment: 7 pages, 4 figures, 2 tables. Significantly expanded to include some details and discussions. Accepted version to appear in PR

Analysis of stability of community structure across multiple hierarchical levels

The analysis of stability of community structure is an important problem for scientists from many fields. Here, we propose a new framework to reveal hidden properties of community structure by quantitatively analyzing the dynamics of Potts model. Specifically we model the Potts procedure of community structure detection by a Markov process, which has a clear mathematical explanation. Critical topological information regarding to multivariate spin configuration could also be inferred from the spectral significance of the Markov process. We test our framework on some example networks and find it doesn't have resolute limitation problem at all. Results have shown the model we proposed is able to uncover hierarchical structure in different scales effectively and efficiently.Comment: 7 pages, 3 figure

Holographic Dual of the Reissner-Nordstr\"om Black Hole

In this article we give a brief, nevertheless, comprehensive review on recent studies in the quantum gravity description of the Reissner-Nordstr\"om (RN) black hole from the perspective of the AdS/CFT correspondence. We survey the known evidence supporting a two-dimensional conformal field theory (CFT) description holographically dual to the RN black hole.Comment: 10 pages, contribution to the proceedings of IARD 2010 conference, to appear in Journal of Physics: Conference Serie

Inhomogeneous boson realizations of the polynomial angular momentum algebra of arbitrary power

The inhomogeneous single-, two- and three-boson realizations of the more general polynomial angular momentum algebra SU_n(2) are obtained from the Fock representations of SU_n(2) that corresponds to the indecomposable representation on the space of universal enveloping algebra U(SU_n(2)) and to the induced representations on the quotient spaces U(SU_n(2))/I_i, with I_i being some left ideals of U(SU_n(2)).Comment: 8 pages, LaTe

Entanglement Entropy of A Simple Non-minimal Coupling Model

We evaluate the entanglement entropy of a non-minimal coupling Einstein-scalar theory with two approaches in classical Euclidean gravity. By analysing the equation of motion, we find that the entangled surface is restricted to be a minimal surface. The entanglement entropy formula is derived directly from the approach of regularized conical singularity. On the other hand, by expressing Ricci scalar of the conical spacetime, we obtain the same result. In addition, we generalize the reduced geometric approach to Riemann tensor and its derivations.Comment: 6 pages, some parts rewritte