602 research outputs found
Equation of state of low--density neutron matter and the 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 . Neutron matter in this regime is superfluid because of
the strong and attractive interaction in the 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 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 , which
is mostly foliated with Liouville tori of dimension . The motion on each
Liouville torus becomes just a parallel translation with some frequency
that varies with the torus. Besides, any billiard trajectory inside
is tangent to caustics , so the
caustic parameters are integrals of the
billiard map. The frequency map 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
. The map 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
Small Orbits
We study both the "large" and "small" U-duality charge orbits of extremal
black holes appearing in D = 5 and D = 4 Maxwell-Einstein supergravity theories
with symmetric scalar manifolds. We exploit a formalism based on cubic Jordan
algebras and their associated Freudenthal triple systems, in order to derive
the minimal charge representatives, their stabilizers and the associated
"moduli spaces". After recalling N = 8 maximal supergravity, we consider N = 2
and N = 4 theories coupled to an arbitrary number of vector multiplets, as well
as N = 2 magic, STU, ST^2 and T^3 models. While the STU model may be considered
as part of the general N = 2 sequence, albeit with an additional triality
symmetry, the ST^2 and T^3 models demand a separate treatment, since their
representative Jordan algebras are Euclidean or only admit non-zero elements of
rank 3, respectively. Finally, we also consider minimally coupled N = 2, matter
coupled N = 3, and "pure" N = 5 theories.Comment: 40 pages, 9 tables. References added. Expanded comments added to
sections III. C. 1. and III. F.
The falling chain of Hopkins, Tait, Steele and Cayley
A uniform, flexible and frictionless chain falling link by link from a heap
by the edge of a table falls with an acceleration if the motion is
nonconservative, but if the motion is conservative, being the
acceleration due to gravity. Unable to construct such a falling chain, we use
instead higher-dimensional versions of it. A home camcorder is used to measure
the fall of a three-dimensional version called an -slider. After
frictional effects are corrected for, its vertical falling acceleration is
found to be . This result agrees with the theoretical
value of for an ideal energy-conserving -slider.Comment: 17 pages, 5 figure
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
- âŠ