Equation of state of low--density neutron matter and the 1S0^1S_0 pairing gap

We report results of the equation of state of neutron matter in the low--density regime, where the Fermi wave vector ranges from $0.4 fm^{-1} \leq k_F \leq 1.0 fm^{-1}$. Neutron matter in this regime is superfluid because of the strong and attractive interaction in the $^1S_0$ channel. The properties of this superfluid matter are calculated starting from a realistic Hamiltonian that contains modern two-- and three--body interactions. The ground state energy and the $^1S_0$ superfluid energy gap are calculated using the Auxiliary Field Diffusion Monte Carlo method. We study the structure of the ground state by looking at pair distribution functions as well as the Cooper-pair wave function used in the calculations.Comment: 12 pages, 7 figure

Inherited crustal deformation along the East Gondwana margin revealed by seismic anisotropy tomography

Acknowledgments We thank Mallory Young for providing phase velocity measurements in mainland Australia and Tasmania. Robert Musgrave is thanked for making available his tilt-filtered magnetic intensity map. In the short term, data may be made available by contacting the authors (S.P. or N.R.). A new database of passive seismic data recorded in Australia is planned as part of a national geophysics data facility for easy access download. Details on the status of this database may be obtained from the authors (S.P., N.R., or A.M.R.). There are no restrictions on access for noncommercial use. Commercial users should seek written permission from the authors (S.P. or N.R.). Ross Cayley publishes with the permission of the Director of the Geological Survey of Victoria.Peer reviewedPublisher PD

E_7 and the tripartite entanglement of seven qubits

In quantum information theory, it is well known that the tripartite entanglement of three qubits is described by the group [SL(2,C)]^3 and that the entanglement measure is given by Cayley's hyperdeterminant. This has provided an analogy with certain N=2 supersymmetric black holes in string theory, whose entropy is also given by the hyperdeterminant. In this paper, we extend the analogy to N=8. We propose that a particular tripartite entanglement of seven qubits, encoded in the Fano plane, is described by the exceptional group E_7(C) and that the entanglement measure is given by Cartan's quartic E_7 invariant.Comment: Minor improvements. 15 page late

The frequency map for billiards inside ellipsoids

The billiard motion inside an ellipsoid Q \subset \Rset^{n+1} is completely integrable. Its phase space is a symplectic manifold of dimension $2n$, which is mostly foliated with Liouville tori of dimension $n$. The motion on each Liouville torus becomes just a parallel translation with some frequency $\omega$ that varies with the torus. Besides, any billiard trajectory inside $Q$ is tangent to $n$ caustics $Q_{\lambda_1},...,Q_{\lambda_n}$, so the caustic parameters $\lambda=(\lambda_1,...,\lambda_n)$ are integrals of the billiard map. The frequency map $\lambda \mapsto \omega$ is a key tool to understand the structure of periodic billiard trajectories. In principle, it is well-defined only for nonsingular values of the caustic parameters. We present four conjectures, fully supported by numerical experiments. The last one gives rise to some lower bounds on the periods. These bounds only depend on the type of the caustics. We describe the geometric meaning, domain, and range of $\omega$. The map $\omega$ can be continuously extended to singular values of the caustic parameters, although it becomes "exponentially sharp" at some of them. Finally, we study triaxial ellipsoids of \Rset^3. We compute numerically the bifurcation curves in the parameter space on which the Liouville tori with a fixed frequency disappear. We determine which ellipsoids have more periodic trajectories. We check that the previous lower bounds on the periods are optimal, by displaying periodic trajectories with periods four, five, and six whose caustics have the right types. We also give some new insights for ellipses of \Rset^2.Comment: 50 pages, 13 figure

Topics in Cubic Special Geometry

We reconsider the sub-leading quantum perturbative corrections to N=2 cubic special Kaehler geometries. Imposing the invariance under axion-shifts, all such corrections (but the imaginary constant one) can be introduced or removed through suitable, lower unitriangular symplectic transformations, dubbed Peccei-Quinn (PQ) transformations. Since PQ transformations do not belong to the d=4 U-duality group G4, in symmetric cases they generally have a non-trivial action on the unique quartic invariant polynomial I4 of the charge representation R of G4. This leads to interesting phenomena in relation to theory of extremal black hole attractors; namely, the possibility to make transitions between different charge orbits of R, with corresponding change of the supersymmetry properties of the supported attractor solutions. Furthermore, a suitable action of PQ transformations can also set I4 to zero, or vice versa it can generate a non-vanishing I4: this corresponds to transitions between "large" and "small" charge orbits, which we classify in some detail within the "special coordinates" symplectic frame. Finally, after a brief account of the action of PQ transformations on the recently established correspondence between Cayley's hyperdeterminant and elliptic curves, we derive an equivalent, alternative expression of I4, with relevant application to black hole entropy.Comment: 1+39 page

Classification of symmetric periodic trajectories in ellipsoidal billiards

We classify nonsingular symmetric periodic trajectories (SPTs) of billiards inside ellipsoids of R^{n+1} without any symmetry of revolution. SPTs are defined as periodic trajectories passing through some symmetry set. We prove that there are exactly 2^{2n}(2^{n+1}-1) classes of such trajectories. We have implemented an algorithm to find minimal SPTs of each of the 12 classes in the 2D case (R^2) and each of the 112 classes in the 3D case (R^3). They have periods 3, 4 or 6 in the 2D case; and 4, 5, 6, 8 or 10 in the 3D case. We display a selection of 3D minimal SPTs. Some of them have properties that cannot take place in the 2D case.Comment: 26 pages, 77 figures, 17 table

Evidence of micro-continent entrainment during crustal accretion

Peer reviewe

On the role of a new type of correlated disorder in extended electronic states in the Thue-Morse lattice

A new type of correlated disorder is shown to be responsible for the appearance of extended electronic states in one-dimensional aperiodic systems like the Thue-Morse lattice. Our analysis leads to an understanding of the underlying reason for the extended states in this system, for which only numerical evidence is available in the literature so far. The present work also sheds light on the restrictive conditions under which the extended states are supported by this lattice.Comment: 11 pages, LaTeX V2.09, 1 figure (available on request), to appear in Physical Review Letter

Partial separability revisited: Necessary and sufficient criteria

We extend the classification of mixed states of quantum systems composed of arbitrary number of subsystems of arbitrary dimensions. This extended classification is complete in the sense of partial separability and gives 1+18+1 partial separability classes in the tripartite case contrary to a former 1+8+1. Then we give necessary and sufficient criteria for these classes, which make it possible to determine to which class a mixed state belongs. These criteria are given by convex roof extensions of functions defined on pure states. In the special case of three-qubit systems, we define a different set of such functions with the help of the Freudenthal triple system approach of three-qubit entanglement.Comment: v3: 22 pages, 5 tables, 1 figure, minor corrections (typos), clarification in the Introduction. Accepted in Phys. Rev. A. Comments are welcom

A Hamiltonian approach for explosive percolation

We introduce a cluster growth process that provides a clear connection between equilibrium statistical mechanics and an explosive percolation model similar to the one recently proposed by Achlioptas et al. [Science 323, 1453 (2009)]. We show that the following two ingredients are essential for obtaining an abrupt (first-order) transition in the fraction of the system occupied by the largest cluster: (i) the size of all growing clusters should be kept approximately the same, and (ii) the inclusion of merging bonds (i.e., bonds connecting vertices in different clusters) should dominate with respect to the redundant bonds (i.e., bonds connecting vertices in the same cluster). Moreover, in the extreme limit where only merging bonds are present, a complete enumeration scheme based on tree-like graphs can be used to obtain an exact solution of our model that displays a first-order transition. Finally, the proposed mechanism can be viewed as a generalization of standard percolation that discloses an entirely new family of models with potential application in growth and fragmentation processes of real network systems.Comment: 4 pages, 4 figure