18,592 research outputs found
Stringent Numerical Test of the Poisson Distribution for Finite Quantum Integrable Hamiltonians
Using a new class of exactly solvable models based on the pairing
interaction, we show that it is possible to construct integrable Hamiltonians
with a Wigner distribution of nearest neighbor level spacings. However, these
Hamiltonians involve many-body interactions and the addition of a small
integrable perturbation very quickly leads the system to a Poisson
distribution. Besides this exceptional cases, we show that the accumulated
distribution of an ensemble of random integrable two-body pairing hamiltonians
is in perfect agreement with the Poisson limit. These numerical results for
quantum integrable Hamiltonians provide a further empirical confirmation to the
work of the Berry and Tabor in the semiclassical limit.Comment: 5 pages, 4 figures, LaTeX (RevTeX 4) Content changed, References
added Accepted for publication in PR
Asymptotic analysis of displaced lunar orbits
The design of spacecraft trajectories is a crucial task in space mission design. Solar sail technology appears as a promising form of advanced spacecraft propulsion which can enable exciting new space science mission concepts such as solar system exploration and deep space observation. Although solar sailing has been considered as a practical means of spacecraft propulsion only relatively recently, the fundamental ideas are by no means new (see McInnes1 for a detailed description). A solar sail is propelled by reflecting solar photons and therefore can transform the momentum of the photons into a propulsive force. Solar sails can also be utilised for highly non-Keplerian orbits, such as orbits displaced high above the ecliptic plane (see Waters and McInnes2). Solar sails are especially suited for such non-Keplerian orbits, since they can apply a propulsive force continuously. In such trajectories, a sail can be used as a communication satellite for high latitudes. For example, the orbital plane of the sail can be displaced above the orbital plane of the Earth, so that the sail can stay fixed above the Earth at some distance, if the orbital periods are equal (see Forward3). Orbits around the collinear points of the Earth-Moon system are also of great interest because their unique positions are advantageous for several important applications in space mission design (see e.g. Szebehely4, Roy,5 Vonbun,6 Thurman et al.,7 Gomez et al.8, 9). Several authors have tried to determine more accurate approximations (quasi-Halo orbits) of such equilibrium orbits10. These orbits were first studied by Farquhar11, Farquhar and Kamel10, Breakwell and Brown12, Richardson13, Howell14, 15.If an orbit maintains visibility from Earth, a spacecraft on it (near the L2 point) can be used to provide communications between the equatorial regions of the Earth and the lunar poles. The establishment of a bridge for radio communications is crucial for forthcoming space missions, which plan to use the lunar poles.McInnes16 investigated a new family of displaced solar sail orbits near the Earth-Moon libration points.Displaced orbits have more recently been developed by Ozimek et al.17 using collocation methods. In Baoyin and McInnes18, 19, 20 and McInnes16, 21, the authors describe new orbits which are associated with artificial Lagrange points in the Earth-Sun system. These artificial equilibria have potential applications for future space physics and Earth observation missions. In McInnes and Simmons22, the authors investigate large new families of solar sail orbits, such as Sun-centered halo-type trajectories, with the sail executing a circular orbit of a chosen period above the ecliptic plane. We have recently investigated displaced periodic orbits at linear order in the Earth-Moon restricted three-body system, where the third massless body is a solar sail (see Simo and McInnes23). These highly non-Keplerian orbits are achieved using an extremely small sail acceleration. It was found that for a given displacement distance above/below the Earth-Moon plane it is easier by a factor of order 3.19 to do so at L4=L5 compared to L1=L2 - ie. for a fixed sail acceleration the displacement distance at L4=L5 is greater than that at L1=L2. In addition, displaced L4=L5 orbits are passively stable, making them more forgiving to sail pointing errors than highly unstable orbits at L1=L2.The drawback of the new family of orbits is the increased telecommunications path-length, particularly the Moon-L4 distance compared to the Moon-L2 distance
First clear evidence of quantum chaos in the bound states of an atomic nucleus
We study the spectral fluctuations of the Pb nucleus using the
complete experimental spectrum of 151 states up to excitation energies of
MeV recently identified at the Maier-Leibnitz-Laboratorium at Garching,
Germany. For natural parity states the results are very close to the
predictions of Random Matrix Theory (RMT) for the nearest-neighbor spacing
distribution. A quantitative estimate of the agreement is given by the Brody
parameter , which takes the value for regular systems and
for chaotic systems. We obtain which
is, to our knowledge, the closest value to chaos ever observed in experimental
bound states of nuclei. By contrast, the results for unnatural parity states
are far from RMT behavior. We interpret these results as a consequence of the
strength of the residual interaction in Pb, which, according to
experimental data, is much stronger for natural than for unnatural parity
states. In addition our results show that chaotic and non-chaotic nuclear
states coexist in the same energy region of the spectrum.Comment: 9 pages, 1 figur
Electron concentration effects on the Shastry-Sutherland phase stability in Ce_{2-x}Pd_{2+y}In_{1-z} solid solutions
The stability of a Shastry-Sutherland ShSu phase as a function of electron
concentration is investigated through the field dependence of thermal and
magnetic properties of the solid solution Ce_{2-x}Pd_{2+y}In_{1-z} in the
antiferromagnetic branch. In these alloys the electronic (holes) variation is
realized by increasing concentration. The AF transition T_M decreases from
3.5K to 2.8K as concentration increases from y=0.2 to y=0.4. By applying
magnetic field, the ShSu phase is suppressed once the field induced
ferromagnetic polarization takes over at a critical field B_{cr} which
increases with content. A detailed analysis around the critical point
reveals a structure in the maximum of the dM/dB derivative, which is related
with incipient steps in the magnetization M(B) as predicted by the theory for
the ShSu lattice. The crossing of M(B) isotherms, observed in ShSu prototype
compounds, is also analyzed. The effect of substitution by is
interpreted as an increase of the number of 'holes' in the conduction band and
results in a unique parameter able to describe the variation of the magnetic
properties along the studied range of concentration.Comment: 8 pages, 11 figure
Mission design for LISA Pathfinder
Here we describe the mission design for SMART-2/LISA Pathfinder. The best
trade-off between the requirements of a low-disturbance environment and
communications distance is found to be a free-insertion Lissajous orbit around
the first co-linear Lagrange point of the Sun-Earth system L1, 1.5x 10^6 km
from Earth. In order to transfer SMART-2/LISA Pathfinder from a low Earth
orbit, where it will be placed by a small launcher, the spacecraft carries out
a number of apogee-raise manoeuvres, which ultimatively place it to a parabolic
escape trajectory towards L1. The challenges of the design of a small mission
are met, fulfilling the very demanding technology demonstration requirements
without creating excessive requirements on the launch system or the ground
segment.Comment: 7 pages, 6 figures, 5th International LISA Symposium, see
http://www.landisoft.de/Markus-Landgra
Long-range ferromagnetism of Mn12 acetate single-molecule magnets under a transverse magnetic field
We use neutron diffraction to probe the magnetization components of a crystal
of Mn12 single-molecule magnets. Each of these molecules behaves, at low
temperatures, as a nanomagnet with spin S = 10 and strong anisotropy along the
crystallographic c axis. Application of a magnetic field perpendicular to c
induces quantum tunneling between opposite spin orientations, enabling the
spins to attain thermal equilibrium. Below approximately 0.9 K, intermolecular
interactions turn this equilibrium state into a ferromagnetically ordered
phase. However, long range ferromagnetic correlations nearly disappear for
fields larger 5.5 T, possibly suggesting the existence of a quantum critical
point.Comment: 4 pages, 4 figure
Designing displaced lunar orbits using low-thrust propulsion
The design of spacecraft trajectories is a crucial task in space mission design. Solar sail technology appears as a promising form of advanced spacecraft propulsion which can enable exciting new space science mission concepts such as solar system exploration and deep space observation. Although solar sailing has been considered as a practical means of spacecraft propulsion only relatively recently, the fundamental ideas are by no means new (see McInnes1 for a detailed description). A solar sail is propelled by re ecting solar photons and therefore can transform the momentum of the photons into a propulsive force. This article focuses on designing displaced lunar orbits using low-thrust propulsion
Imperfect bifurcations via topological methods in superlinear indefinite problems
In [5] the structure of the bifurcation diagrams of a class of superlinear
indefinite problems with a symmetric weight was ascertained, showing that they
consist of a primary branch and secondary loops bifurcating from it. In [4] it
has been proved that, when the weight is asymmetric, the bifurcation diagrams
are no longer connected since parts of the primary branch and loops of the
symmetric case form an arbitrarily high number of isolas. In this work we give
a deeper insight on this phenomenon, studying how the secondary bifurcations
break as the weight is perturbed from the symmetric situation. Our proofs rely
on the approach of [5,4], i.e. on the construction of certain Poincar\'e maps
and the study of how they vary as some of the parameters of the problems
change, constructing in this way the bifurcation diagrams.Comment: 13 pages, 7 figure
Invariant Manifolds, the Spatial Three-Body Problem and Space Mission Design
The invariant manifold structures of the collinear libration points for the
spatial restricted three-body problem provide the framework for understanding
complex dynamical phenomena from a geometric point of view.
In particular, the stable and unstable invariant manifold \tubes" associated
to libration point orbits are the phase space structures that provide a
conduit for orbits between primary bodies for separate three-body systems.
These invariant manifold tubes can be used to construct new spacecraft
trajectories, such as a \Petit Grand Tour" of the moons of Jupiter. Previous
work focused on the planar circular restricted three-body problem.
The current work extends the results to the spatial case
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