Effects of dark energy on the efficiency of charged AdS black holes as heat engine

In this paper, we study the heat engine where charged AdS black holes surrounded by dark energy is the working substance and the mechanical work is done via $PdV$ term in the first law of black hole thermodynamics in the extended phase space. We first investigate the effects of a kind of dark energy (quintessence field in this paper) on the efficiency of the RN-AdS black holes as heat engine defined as a rectangle closed path in the $P-V$ plane. We get the exact efficiency formula and find that quintessence field can improve the heat engine efficiency which will increase as the field density $\rho_q$ grows. At some fixed parameters, we find that bigger volume difference between the smaller black holes($V_1$) and the bigger black holes($V_2$ ) will lead to a lower efficiency, while the bigger pressure difference $P_1-P_4$ will make the efficiency higher but it is always smaller than 1 and will never be beyond Carnot efficiency which is the maximum value of the efficiency constrained by thermodynamics laws, this is consistent to the heat engine in traditional thermodynamics. After making some special choices for thermodynamical quantities, we find that the increase of electric charge $Q$ and normalization factor $a$ can also promote heat engine efficiency which would infinitely approach the Carnot limit when $Q$ or $a$ goes to infinity.Comment: 28 pages, 16 figures, refernces added, discussion and computation improve

Angular Momentum Independence of the Entropy Sum and Entropy Product for AdS Rotating Black Holes In All Dimensions

In this paper, we investigate the angular momentum independence of the entropy sum and product for AdS rotating black holes based on the first law of thermodynamics and a mathematical lemma related to Vandermonde determinant. The advantage of this method is that the explicit forms of the spacetime metric, black hole mass and charge are not needed but the Hawking temperature and entropy formula on the horizons are necessary for static black holes, while our calculations require the expressions of metric and angular velocity formula. We find that the entropy sum is always independent of angular momentum for all dimensions and the angular momentum-independence of entropy product only holds for the dimensions $d>4$ with at least one rotation parameter $a_i=0$, while the mass-free of entropy sum and entropy product for rotating black holes only stand for higher dimensions ($d>4$) and for all dimensions, respectively. On the other hand, we find that the introduction of a negative cosmological constant does not affect the angular momentum-free of entropy sum and product but the criterion for angular momentum-independence of entropy product will be affected.Comment: 14 pages, 0 figures,accepted for publication in Physics Letters

On K_2 of certain families of curves

We construct families of smooth, proper, algebraic curves in characteristic 0, of arbitrary genus g, together with g elements in the kernel of the tame symbol. We show that those elements are in general independent by a limit calculation of the regulator. Working over a number field, we show that in some of those families the elements are integral. We determine when those curves are hyperelliptic, finding, in particular, that over any number field we have non-hyperelliptic curves of all composite genera g with g independent integral elements in the kernel of the tame symbol.Comment: Revised version: improved exposition. some sections spli

Canonical simulations of supersymmetric SU(N) Yang-Mills quantum mechanics

The fermion loop formulation naturally separates partition functions into their canonical sectors. Here we discuss various strategies to make use of this for supersymmetric SU(N) Yang-Mills quantum mechanics obtained from dimensional reduction in various dimensions and present numerical results for the separate canonical sectors with fixed fermion numbers. We comment on potential problems due to the sign of the contributions from the fermions and due to flat directions.Comment: 7 pages, 3 figure

Ωccc\Omega_{ccc} Production in High Energy Nuclear Collisions

We investigate the production of $\Omega_{ccc}$ baryon in high energy nuclear collisions via quark coalescence mechanism. The wave function of $\Omega_{ccc}$ is solved from the Schr\"odinger equation for the bound state of three charm quarks by using the hyperspherical method. The production cross section of $\Omega_{ccc}$ per binary collision in a central Pb+Pb collision at $\sqrt{s_{NN}}=2.76$ TeV reaches 9 nb, which is at least two orders of magnitude larger than that in a p+p collision at the same energy. Therefore, it is most probable to discover $\Omega_{ccc}$ in heavy ion collisions at LHC, and the observation will be a clear signature of the quark-gluon plasma formation.Comment: 6 pages, 5 figure