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

Single-Valued Hamiltonian via Legendre-Fenchel Transformation and Time Translation Symmetry

Under conventional Legendre transformation, systems with a non-convex Lagrangian will result in a multi-valued Hamiltonian as a function of conjugate momentum. This causes problems such as non-unitary time evolution of quantum state and non-determined motion of classical particles, and is physically unacceptable. In this work, we propose a new construction of single-valued Hamiltonian by applying Legendre-Fenchel transformation, which is a mathematically rigorous generalization of conventional Legendre transformation, valid for non-convex Lagrangian systems, but not yet widely known to the physics community. With the new single-valued Hamiltonian, we study spontaneous breaking of time translation symmetry and derive its vacuum state. Applications to theories of cosmology and gravitation are discussed.Comment: Journal Version, 16pp. All results + conclusions un-changed, only minor refinements to clarify the importance of our new LFT method and its physics applications; references adde

Searching for Ξcc+\Xi_{cc}^+ in Relativistic Heavy Ion Collisions

We study the doubly charmed baryon $\Xi_{cc}^+$ in high energy nuclear collisions. We solve the three-body Schroedinger equation with relativistic correction and calculate the $\Xi_{cc}^+$ yield and transverse momentum distribution via coalescence mechanism. For $\Xi_{cc}^+$ production in central Pb+Pb collisions at LHC energy, the yield is extremely enhanced, and the production cross section per binary collision is one order of magnitude larger than that in p+p collisions. This indicates that, it is most probable to discover $\Xi_{cc}^+$ in heavy ion collisions and its discovery can be considered as a probe of the quark-luon plasma formation.Comment: 5 pages and 4 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

Hard-gapped Holographic Superconductors

In this work we discuss the zero temperature limit of a "p-wave" holographic superconductor. The bulk description consists of a non-Abelian SU(2) gauge fields minimally coupled to gravity. We numerically construct the zero temperature solution which is the gravity dual of the superconducting ground state of the "p-wave" holographic superconductors. The solution is a smooth soliton with zero horizon size and shows an emergent conformal symmetry in the IR. We found the expected superconducting behavior. Using the near horizon analysis we show that the system has a "hard gap" for the relevant gauge field fluctuations. At zero temperature the real part of the conductivity is zero for an excitation frequency less than the gap frequency. This is in contrast with what has been observed in similar scalar- gravity-gauge systems (holographic superconductors). We also discuss the low but finite temperature behavior of our solution.Comment: 9 pages, latex, 6 figure