Helium star evolutionary channel to super-Chandrasekhar mass type Ia supernovae

Recent discovery of several overluminous type Ia supernovae (SNe Ia) indicates that the explosive masses of white dwarfs may significantly exceed the canonical Chandrasekhar mass limit. Rapid differential rotation may support these massive white dwarfs. Based on the single-degenerate scenario, and assuming that the white dwarfs would differentially rotate when the accretion rate $\dot{M}>3\times 10^{-7}M_{\odot}\rm yr^{-1}$, employing Eggleton's stellar evolution code we have performed the numerical calculations for $\sim$ 1000 binary systems consisting of a He star and a CO white dwarf (WD). We present the initial parameters in the orbital period - helium star mass plane (for WD masses of $1.0 M_{\odot}$ and $1.2 M_{\odot}$, respectively), which lead to super-Chandrasekhar mass SNe Ia. Our results indicate that, for an initial massive WD of $1.2 M_{\odot}$, a large number of SNe Ia may result from super-Chandrasekhar mass WDs, and the highest mass of the WD at the moment of SNe Ia explosion is 1.81 $M_\odot$, but very massive ($>1.85M_{\odot}$) WDs cannot be formed. However, when the initial mass of WDs is $1.0 M_{\odot}$, the explosive masses of SNe Ia are nearly uniform, which is consistent with the rareness of super-Chandrasekhar mass SNe Ia in observations.Comment: 6 pages, 7 figures, accepted for publication in Astronomy and Astrophysic

A bijection between unicellular and bicellular maps

In this paper we present a combinatorial proof of a relation between the generating functions of unicellular and bicellular maps. This relation is a consequence of the Schwinger-Dyson equation of matrix theory. Alternatively it can be proved using representation theory of the symmetric group. Here we give a bijective proof by rewiring unicellular maps of topological genus $(g+1)$ into bicellular maps of genus $g$ and pairs of unicellular maps of lower topological genera. Our result has immediate consequences for the folding of RNA interaction structures, since the time complexity of folding the transformed structure is $O((n+m)^5)$, where $n,m$ are the lengths of the respective backbones, while the folding of the original structure has $O(n^6)$ time complexity, where $n$ is the length of the longer sequence.Comment: 18 pages, 13 figure

A n-qubit controlled phase gate with superconducting quantum interference devices coupled to a resonator

We present a way to realize a $n$-qubit controlled phase gate with superconducting quantum interference devices (SQUIDs) by coupling them to a superconducting resonator. In this proposal, the two logical states of a qubit are represented by the two lowest levels of a SQUID. An intermediate level of each SQUID is utilized to facilitate coherent control and manipulation of quantum states of the qubits. It is interesting to note that a $n$-qubit controlled phase gate can be achieved with $n$ SQUIDs by successively applying a $\pi /2$ Jaynes-Cummings pulse to each of the $n-1$ control SQUIDs before and after a $\pi$ Jaynes-Cummings pulse on the target SQUID.Comment: 9 pages, 4 figures, 1 table, RevTeX, Resubmitted to Phys. Rev.

Commuting Simplicity and Closure Constraints for 4D Spin Foam Models

Spin Foam Models are supposed to be discretised path integrals for quantum gravity constructed from the Plebanski-Holst action. The reason for there being several models currently under consideration is that no consensus has been reached for how to implement the simplicity constraints. Indeed, none of these models strictly follows from the original path integral with commuting B fields, rather, by some non standard manipulations one always ends up with non commuting B fields and the simplicity constraints become in fact anomalous which is the source for there being several inequivalent strategies to circumvent the associated problems. In this article, we construct a new Euclidian Spin Foam Model which is constructed by standard methods from the Plebanski-Holst path integral with commuting B fields discretised on a 4D simplicial complex. The resulting model differs from the current ones in several aspects, one of them being that the closure constraint needs special care. Only when dropping the closure constraint by hand and only in the large spin limit can the vertex amplitudes of this model be related to those of the FK Model but even then the face and edge amplitude differ. Curiously, an ad hoc non-commutative deformation of the $B^{IJ}$ variables leads from our new model to the Barrett-Crane Model in the case of Barbero-Immirzi parameter goes to infinity.Comment: 41 pages, 4 figure

Asymptotics of Spinfoam Amplitude on Simplicial Manifold: Lorentzian Theory

The present paper studies the large-j asymptotics of the Lorentzian EPRL spinfoam amplitude on a 4d simplicial complex with an arbitrary number of simplices. The asymptotics of the spinfoam amplitude is determined by the critical configurations. Here we show that, given a critical configuration in general, there exists a partition of the simplicial complex into three type of regions R_{Nondeg}, R_{Deg-A}, R_{Deg-B}, where the three regions are simplicial sub-complexes with boundaries. The critical configuration implies different types of geometries in different types of regions, i.e. (1) the critical configuration restricted into R_{Nondeg}$implies a nondegenerate discrete Lorentzian geometry, (2) the critical configuration restricted into R_{Deg-A}$ is degenerate of type-A in our definition of degeneracy, but implies a nondegenerate discrete Euclidean geometry on R_{Deg-A}, (3) the critical configuration restricted into R_{Deg-B} is degenerate of type-B, and implies a vector geometry on R_{Deg-B}. With the critical configuration, we further make a subdivision of the regions R_{Nondeg} and R_{Deg-A} into sub-complexes (with boundary) according to their Lorentzian/Euclidean oriented 4-simplex volume V_4(v), such that sgn(V_4(v)) is a constant sign on each sub-complex. Then in the each sub-complex, the spinfoam amplitude at the critical configuration gives the Regge action in Lorentzian or Euclidean signature respectively on R_{Nondeg} or R_{Deg-A}. The Regge action reproduced here contains a sign factor sgn(V_4(v)) of the oriented 4-simplex volume. Therefore the Regge action reproduced here can be viewed a discretized Palatini action with on-shell connection. Finally the asymptotic formula of the spinfoam amplitude is given by a sum of the amplitudes evaluated at all possible critical configurations, which are the products of the amplitudes associated to different type of geometries.Comment: 54 pages, 2 figures, reference adde

Post-Newtonian gravitational radiation and equations of motion via direct integration of the relaxed Einstein equations. IV. Radiation reaction for binary systems with spin-spin coupling

Using post-Newtonian equations of motion for fluid bodies that include radiation-reaction terms at 2.5 and 3.5 post-Newtonian (PN) order O[(v/c)^5] and O[(v/c)^7] beyond Newtonian order), we derive the equations of motion for binary systems with spinning bodies, including spin-spin effects. In particular we determine the effects of radiation-reaction coupled to spin-spin effects on the two-body equations of motion, and on the evolution of the spins. We find that radiation damping causes a 3.5PN order, spin-spin induced precession of the individual spins. This contrasts with the case of spin-orbit coupling, where there is no effect on the spins at 3.5PN order. Employing the equations of motion and of spin precession, we verify that the loss of total energy and total angular momentum induced by spin-spin effects precisely balances the radiative flux of those quantities calculated by Kidder et al.Comment: 10 pages, coincides with published versio