On an open problem of characterizing the birationality of 4K

We answer an open problem raised by Chen and Zhang in 2008 and prove that, for any minimal projective 3-fold $X$ of general type with the geometric genus $\geq 5$, $X$ is birationally fibred by a pencil of $(1,2)$-surfaces (i.e. $c_1^2=1$, $p_g=2$) if and only if the $4$-canonical map $\varphi_{4,X}$ is non-birational. The statement does not hold for those with the geometric genus $\leq 4$ according to our examples.Comment: 11 page

Coevolution of game and network structure: The temptation increases the cooperator density

Most papers about the evolutionary game on graph assume the statistic network structure. However, social interaction could change the relationship of people. And the changing social structure will affect the people's strategy too. We build a coevolutionary model of prisoner's dilemma game and network structure to study the dynamic interaction in the real world. Based on the asynchronous update rule and Monte Carlo simulation, we find that, when players prefer to rewire their links to the richer, the cooperation density will increase. The reason of it has been analyzed.Comment: 7 pages, 6 figure

Thermodynamic fluctuation in black string flow

It has long been noticed that Laudau-Lifshitz theory can be used to study the fluctuation of a system that contains a black hole. Since the black string can be constructed by extending n-dimensional black hole into one extra dimension. We study the fluctuation of black string flow with a Schwarzschlid-like metric in D=n+1 dimensional spacetime and a charged solution in D=5 dimensional spacetime and get the second moments of the fluctuation of the mass flux and charge flux

Quantum-Inspired Gravitational Wave Detector

A new gravitational-wave detector, which is devised based on quantum weak measurement amplification, is introduced and shown has the potential to significantly improve the strain sensitivity of gravitational-wave detection.Comment: Essay written for the Gravity Research Foundation 2018 Awards for Essays on Gravitation, Comments are welcome

Resonances Driven by a Neutrino Gyroscope and Collective Neutrino Oscillations in Supernovae

We show that flavor evolution of a system of neutrinos with continuous energy spectra as in supernovae can be understood in terms of the response of individual neutrino flavor-isospins (NFIS's) to the mean field. In the case of a system initially consisting of nu_e and anti-nu_e with the same energy spectrum but different number densities, the mean field is very well approximated by the total angular momentum of a neutrino gyroscope. Assuming that NFIS evolution is independent of the initial neutrino emission angle, the so-called single-angle approximation, we find that the evolution is governed by two types of resonances driven by precession and nutation of the gyroscope, respectively. The net flavor transformation crucially depends on the adiabaticity of evolution through these resonances. We show that the results for the system of two initial neutrino species can be extended to a system of four species with the initial number densities of nu_e and anti-nu_e significantly larger than those of nu_x and anti-nu_x. Further, we find that when the dependence on the initial neutrino emission angle is taken into account in the multi-angle approximation, nutation of the mean field is quickly damped out and can be neglected. In contrast, precession-driven resonances still govern the evolution of NFIS's with different energy and emission angles just as in the single-angle approximation. Our pedagogical and analytic study of collective neutrino oscillations in supernovae provides some insights into these seemingly complicated yet fascinating phenomena.Comment: 41 pages, 20 figures, to appear in Physical Review

Intrinsic-Correlation Quantum Key Generation

A new conceptual key generation scheme is presented by using intrinsic quantum correlations of single photons between Alice and Bob. The intrinsic bi-partite correlation functions allow key bit to be generated through high level communication language i.e. a key bit is directly encoded to shared correlation functions not to the state and detection of a photon at Bob does not mean key bit. These make the scheme robust against intercept-resend attack because Alice and Bob can always check the errors in their measurements and reveal the presence of Eve in their channel without leaking any key bit information. The laser source is located in the middle of Alice and Bob, consists of two modes (x,y), relatively random phase-modulated $(\pm \frac{\pi}{2})$ weak coherent states combined in a perfect 50/50 beam splitter. The scheme is strictly relied on the perfect beam splitter and mean photon number less than 1, where more than one photon in a coherent pulse will introduce more errors in Bob even without the presence of Eve. From the percentage of errors in Bob, we can estimate the amount of information will be leaked to Eve in the photon-number splitting attack. This scheme can preserve the randomness of phase-randomized light source for doubling the communication distance as in original Ekert's protocol and providing the raw key generation rate a factor of 2 higher than weak coherent light protocols.Comment: 13 pages, 1 figure, 1 tabl

On projective 3-folds of general type with small positive geometric genus

In this paper we study pluricanonical maps of minimal projective 3-folds of general type with geometric genus $1$, $2$ and $3$. We go in the direction pioneered by Enriques and Bombieri, and other authors, pinning down, for low projective genus, a finite list of exceptions to the birationality of some pluricanonical map. In particular, apart from a finite list of weighted baskets, we prove the birationality of $\varphi_{16}$, $\varphi_{6}$ and $\varphi_{5}$ respectively.Comment: Final version, 36 pages. Electronic Research Archive (to appear

Unified view of quantum amplification based on quantum transformation

A general framework of quantum state amplification using the language of quantum state transformation is given systematically for the first time. The concept of amplification of quantum states is defined specifically and the amplification of a set of quantum states is formulated generally as the transformation of quantum states. Three different kinds of important quantum amplifications, i.e., deterministic noisy quantum amplification, probabilistic noiseless quantum amplification, and deterministic noiseless quantum amplification are identified and discussed. For deterministic quan- tum amplification, the linearity of amplification is proven to be incompatible with the noiseless amplification while it is not true for probabilistic quantum amplification. However, deterministic noiseless quantum amplification is shown physically attainable if the linearity of amplification is given up. The connection between the gain of amplification and the successful probability is discussed for probabilistic quantum amplification. Assuming that successful probability is the same for all quantum states to be amplified, we obtain a generally valid relation between the gain of amplication and the successful probability. Particular interest is given to phase-preserving quantum amplication of Gaussian states which has been shown of theoretical interest and of practical importance in quantum information and quantum communication recently. Our results of quantum state amplification not only enrich the research of quantum amplification but also can be helpful for further practical applications.Comment: 10 pages, 2 figure

Cascaded Weak Measurements Amplification of Ultra-small Phases

The weak measurements based amplification of ultra-small phase was proposed in our previous work. Due to the technical imperfections, the ability of amplification is usually limited in practice. Here we introduce the concept of cascaded weak measurements amplification so that the ability of weak measurements amplification can be further improved. A formula of determining the cascaded number of weak measurements amplification is derived. The method presented here could be found useful in high precision measurement e.g., gravitational waves detection.Comment: Part II of series work. Comments and Suggestions are welcom

Decays of X(3872)X(3872) to χcJπ0\chi_{cJ}\pi^0 and J/ψπ+π−J/\psi\pi^+\pi^-

By describing the $X(3872)$ using the extended Friedrichs scheme, in which $D\bar D^*$ is the dominant component, we calculate the decay rates of the $X(3872)$ to $\pi^0$ and a $P$-wave charmonium $\chi_{cJ}$ state with $J=0,1$, or $2$, and its decays to $J/\psi\pi^+\pi^-$ where $\pi^+\pi^-$ are assumed to be produced via an intermediate $\rho$ state. The decay widths of $X(3872)\to\chi_{cJ}\pi^0$ for $J=0,1,2$ are of the same order. However, this model calculation exhibits that the decay rate of $X(3872)$ to $\chi_{c1}\pi^0$ is one order of magnitude smaller than its decay rate to $J/\psi\pi^+\pi^-$.Comment: 7 pages, 3 figures; v2, some corrections and minor modification of the discussion. Final published versio