Conditions for Phase Equilibrium in Supernovae, Proto-Neutron and Neutron Stars

We investigate the qualitative properties of phase transitions in a general way, if not the single particle numbers of the system but only some particular charges like e.g. baryon number are conserved. In addition to globally conserved charges we analyze the implications of locally conserved charge fractions, like e.g. local electric charge neutrality or locally fixed proton or lepton fractions. The conditions for phase equilibrium are derived and it is shown, that the properties of the phase transition do not depend on the locally conserved fractions. Finally, the general formalism is applied to the liquid-gas phase transition and the hadron-quark phase transition for typical astrophysical environments like in supernovae, proto-neutron or a neutron stars. We demonstrate that the Maxwell construction known from cold-deleptonized neutron star matter with two locally charge neutral phases requires modifications and further assumptions concerning the applicability for hot lepton-rich matter. All possible combinations of local and global conservation laws are analyzed, and the physical meaningful cases are identified. Several new kinds of mixed phases are presented, as e.g. a locally charge neutral mixed phase in proto-neutron stars which will disappear during the cooling and deleptonization of the proto-neutron star.Comment: 18 page

A new possible quark-hadron mixed phase in protoneutron stars

The phase transition from hadronic matter to quark matter at high density might be a strong first order phase transition in presence of a large surface tension between the two phases. While this implies a constant-pressure mixed phase for cold and catalyzed matter this is not the case for the hot and lepton rich matter formed in a protoneutron star. We show that it is possible to obtain a mixed phase with non-constant pressure by considering the global conservation of lepton number during the stage of neutrino trapping. In turn, it allows for the appearance of a new kind of mixed phase as long as neutrinos are trapped and its gradual disappearance during deleptonization. This new mixed phase, being composed by two electric neutral phases, does not develop a Coulomb lattice and it is formed only by spherical structures, drops and bubbles, which can have macroscopic sizes. The disappearance of the mixed phase at the end of deleptonization might lead to a delayed collapse of the star into a more compact configuration containing a core of pure quark phase. In this scenario, a significant emission of neutrinos and, possibly, gravitational waves are expected.Comment: 4 pages, 4 figure

Mass, radius, and composition of the outer crust of nonaccreting cold neutron stars

The properties and composition of the outer crust of nonaccreting cold neutron stars are studied by applying the model of Baym, Pethick, and Sutherland, which was extended by including higher order corrections of the atomic binding, screening, exchange and zero-point energy. The most recent experimental nuclear data from the atomic mass table of Audi, Wapstra, and Thibault from 2003 is used. Extrapolation to the drip line is utilized by various state-of-the-art theoretical nuclear models (finite range droplet, relativistic nuclear field and non-relativistic Skyrme Hartree-Fock parameterizations). The different nuclear models are compared with respect to the mass and radius of the outer crust for different neutron star configurations and the nuclear compositions of the outer crust.Comment: 5 pages, 2 figures, submitted to J. Phys. G, part of the proceedings of the Nuclear Physics in Astrophysics III conference in Dresde

Dynamical Systems On Three Manifolds Part II: 3-Manifolds,Heegaard Splittings and Three-Dimensional Systems

The global behaviour of nonlinear systems is extremely important in control and systems theory since the usual local theories will only give information about a system in some neighbourhood of an operating point. Away from that point, the system may have totally different behaviour and so the theory developed for the local system will be useless for the global one. In this paper we shall consider the analytical and topological structure of systems on 2- and 3- manifolds and show that it is possible to obtain systems with 'arbitrarily strange' behaviour, i.e., arbitrary numbers of chaotic regimes which are knotted and linked in arbitrary ways. We shall do this by considering Heegaard Splittings of these manifolds and the resulting systems defined on the boundaries.Comment: 15 pages with 9 pictures. Accepted by Int. J. of Bifurcation and Chao

Pushing 1D CCSNe to explosions: model and SN 1987A

We report on a method, PUSH, for triggering core-collapse supernova explosions of massive stars in spherical symmetry. We explore basic explosion properties and calibrate PUSH such that the observables of SN1987A are reproduced. Our simulations are based on the general relativistic hydrodynamics code AGILE combined with the detailed neutrino transport scheme IDSA for electron neutrinos and ALS for the muon and tau neutrinos. To trigger explosions in the otherwise non-exploding simulations, we rely on the neutrino-driven mechanism. The PUSH method locally increases the energy deposition in the gain region through energy deposition by the heavy neutrino flavors. Our setup allows us to model the explosion for several seconds after core bounce. We explore the progenitor range 18-21M$_{\odot}$. Our studies reveal a distinction between high compactness (HC) and low compactness (LC) progenitor models, where LC models tend to explore earlier, with a lower explosion energy, and with a lower remnant mass. HC models are needed to obtain explosion energies around 1 Bethe, as observed for SN1987A. However, all the models with sufficiently high explosion energy overproduce $^{56}$Ni. We conclude that fallback is needed to reproduce the observed nucleosynthesis yields. The nucleosynthesis yields of $^{57-58}$Ni depend sensitively on the electron fraction and on the location of the mass cut with respect to the initial shell structure of the progenitor star. We identify a progenitor and a suitable set of PUSH parameters that fit the explosion properties of SN1987A when assuming 0.1M$_{\odot}$ of fallback. We predict a neutron star with a gravitational mass of 1.50M$_{\odot}$. We find correlations between explosion properties and the compactness of the progenitor model in the explored progenitors. However, a more complete analysis will require the exploration of a larger set of progenitors with PUSH.Comment: revised version as accepted by ApJ (results unchanged, text modified for clarification, a few references added); 26 pages, 20 figure

Strange matter in core-collapse supernovae

We discuss the possible impact of strange quark matter on the evolution of core-collapse supernovae with emphasis on low critical densities for the quark-hadron phase transition. For such cases the hot proto-neutron star can collapse to a more compact hybrid star configuration hundreds of milliseconds after core-bounce. The collapse triggers the formation of a second shock wave. The latter leads to a successful supernova explosion and leaves an imprint on the neutrino signal. These dynamical features are discussed with respect to their compatibility with recent neutron star mass measurements which indicate a stiff high density nuclear matter equation of state.Comment: 8 pages, 3 figures, Invited talk at the "Strangeness in Quark Matter" conference, 18-24 September 2011, Polish Academy of Arts and Sciences, Cracow, Polan

Finite-size effects in dynamics of zero-range processes

The finite-size effects prominent in zero-range processes exhibiting a condensation transition are studied by using continuous-time Monte Carlo simulations. We observe that, well above the thermodynamic critical point, both static and dynamic properties display fluid-like behavior up to a density {\rho}c (L), which is the finite-size counterpart of the critical density {\rho}c = {\rho}c (L \rightarrow \infty). We determine this density from the cross-over behavior of the average size of the largest cluster. We then show that several dynamical characteristics undergo a qualitative change at this density. In particular, the size distribution of the largest cluster at the moment of relocation, the persistence properties of the largest cluster and correlations in its motion are studied.Comment: http://pre.aps.org/abstract/PRE/v82/i3/e03111

Experimental quantum verification in the presence of temporally correlated noise

Growth in the complexity and capabilities of quantum information hardware mandates access to practical techniques for performance verification that function under realistic laboratory conditions. Here we experimentally characterise the impact of common temporally correlated noise processes on both randomised benchmarking (RB) and gate-set tomography (GST). We study these using an analytic toolkit based on a formalism mapping noise to errors for arbitrary sequences of unitary operations. This analysis highlights the role of sequence structure in enhancing or suppressing the sensitivity of quantum verification protocols to either slowly or rapidly varying noise, which we treat in the limiting cases of quasi-DC miscalibration and white noise power spectra. We perform experiments with a single trapped $^{171}$Yb$^{+}$ ion as a qubit and inject engineered noise ($\propto \sigma^z$) to probe protocol performance. Experiments on RB validate predictions that the distribution of measured fidelities over sequences is described by a gamma distribution varying between approximately Gaussian for rapidly varying noise, and a broad, highly skewed distribution for the slowly varying case. Similarly we find a strong gate set dependence of GST in the presence of correlated errors, leading to significant deviations between estimated and calculated diamond distances in the presence of correlated $\sigma^z$ errors. Numerical simulations demonstrate that expansion of the gate set to include negative rotations can suppress these discrepancies and increase reported diamond distances by orders of magnitude for the same error processes. Similar effects do not occur for correlated $\sigma^x$ or $\sigma^y$ errors or rapidly varying noise processes, highlighting the critical interplay of selected gate set and the gauge optimisation process on the meaning of the reported diamond norm in correlated noise environments.Comment: Expanded and updated analysis of GST, including detailed examination of the role of gauge optimization in GST. Full GST data sets and supplementary information available on request from the authors. Related results available from http://www.physics.usyd.edu.au/~mbiercuk/Publications.htm

Manifolds associated with (Z2)n(Z_2)^n-colored regular graphs

In this article we describe a canonical way to expand a certain kind of $(\mathbb Z_2)^{n+1}$-colored regular graphs into closed $n$-manifolds by adding cells determined by the edge-colorings inductively. We show that every closed combinatorial $n$-manifold can be obtained in this way. When $n\leq 3$, we give simple equivalent conditions for a colored graph to admit an expansion. In addition, we show that if a $(\mathbb Z_2)^{n+1}$-colored regular graph admits an $n$-skeletal expansion, then it is realizable as the moment graph of an $(n+1)$-dimensional closed $(\mathbb Z_2)^{n+1}$-manifold.Comment: 20 pages with 9 figures, in AMS-LaTex, v4 added a new section on reconstructing a space with a $(Z_2)^n$-action for which its moment graph is a given colored grap