Spin-Spin Interaction In Matrix Theory

We calculate the spin dependent static force between two D0-branes in Matrix theory. Supersymmetry relates velocity dependent potentials to spin dependent potentials. The well known v^4/r^7 term is related to a theta^8/r^11 term, where theta is the relative spin of the D0-branes. We calculate this term, confirming that it is the lowest order contribution to the static potential, and find its structure consistent with supergravity.Comment: 15 pages, LaTeX, uses feynmf.sty for diagrams. Reference added and some labels on the diagrams restore

Jupiter as a Giant Cosmic Ray Detector

We explore the feasibility of using the atmosphere of Jupiter to detect Ultra-High-Energy Cosmic Rays (UHECR's). The large surface area of Jupiter allows us to probe cosmic rays of higher energies than previously accessible. Cosmic ray extensive air showers in Jupiter's atmosphere could in principle be detected by the Large Area Telescope (LAT) on the Fermi observatory. In order to be observed, these air showers would need to be oriented toward the Earth, and would need to occur sufficiently high in the atmosphere that the gamma rays can penetrate. We demonstrate that, under these assumptions, Jupiter provides an effective cosmic ray "detector" area of $3.3 \times 10^7$ km$^2$. We predict that Fermi-LAT should be able to detect events of energy $>10^{21}$ eV with fluence $10^{-7}$ erg cm$^{-2}$ at a rate of about one per month. The observed number of air showers may provide an indirect measure of the flux of cosmic rays $\gtrsim 10^{20}$ eV. Extensive air showers also produce a synchrotron signature that may be measurable by ALMA. Simultaneous observations of Jupiter with ALMA and Fermi-LAT could be used to provide broad constraints on the energies of the initiating cosmic rays.Comment: 8 pages, 5 figures. Accepted for publication in the Astrophysical Journal Letter

A Special Case Of A Conjecture By Widom With Implications To Fermionic Entanglement Entropy

We prove a special case of a conjecture in asymptotic analysis by Harold Widom. More precisely, we establish the leading and next-to-leading term of a semi-classical expansion of the trace of the square of certain integral operators on the Hilbert space $L^2(\R^d)$. As already observed by Gioev and Klich, this implies that the bi-partite entanglement entropy of the free Fermi gas in its ground state grows at least as fast as the surface area of the spatially bounded part times a logarithmic enhancement.Comment: 20 pages, 3 figures, improvement of the presentation, some references added or updated, proof of Theorem 12 (formerly Lemma 11) adde

Groups of Fibonacci type revisited

This article concerns a class of groups of Fibonacci type introduced by Johnson and Mawdesley that includes Conway?s Fibonacci groups, the Sieradski groups, and the Gilbert-Howie groups. This class of groups provides an interesting focus for developing the theory of cyclically presented groups and, following questions by Bardakov and Vesnin and by Cavicchioli, Hegenbarth, and Repov?s, they have enjoyed renewed interest in recent years. We survey results concerning their algebraic properties, such as isomorphisms within the class, the classification of the finite groups, small cancellation properties, abelianizations, asphericity, connections with Labelled Oriented Graph groups, and the semigroups of Fibonacci type. Further, we present a new method of proving the classification of the finite groups that deals with all but three groups

Entanglement and particle correlations of Fermi gases in harmonic traps

We investigate quantum correlations in the ground state of noninteracting Fermi gases of N particles trapped by an external space-dependent harmonic potential, in any dimension. For this purpose, we compute one-particle correlations, particle fluctuations and bipartite entanglement entropies of extended space regions, and study their large-N scaling behaviors. The half-space von Neumann entanglement entropy is computed for any dimension, obtaining S_HS = c_l N^(d-1)/d ln N, analogously to homogenous systems, with c_l=1/6, 1/(6\sqrt{2}), 1/(6\sqrt{6}) in one, two and three dimensions respectively. We show that the asymptotic large-N relation S_A\approx \pi^2 V_A/3, between the von Neumann entanglement entropy S_A and particle variance V_A of an extended space region A, holds for any subsystem A and in any dimension, analogously to homogeneous noninteracting Fermi gases.Comment: 15 pages, 22 fig

Hamiltonian and physical Hilbert space in polymer quantum mechanics

In this paper, a version of polymer quantum mechanics, which is inspired by loop quantum gravity, is considered and shown to be equivalent, in a precise sense, to the standard, experimentally tested, Schroedinger quantum mechanics. The kinematical cornerstone of our framework is the so called polymer representation of the Heisenberg-Weyl (H-W) algebra, which is the starting point of the construction. The dynamics is constructed as a continuum limit of effective theories characterized by a scale, and requires a renormalization of the inner product. The result is a physical Hilbert space in which the continuum Hamiltonian can be represented and that is unitarily equivalent to the Schroedinger representation of quantum mechanics. As a concrete implementation of our formalism, the simple harmonic oscillator is fully developed.Comment: 19 pages, 2 figures. Comments and references added. Version to be published in CQ

Ionisation and discharge in cloud-forming atmospheres of brown dwarfs and extrasolar planets

Brown dwarfs and giant gas extrasolar planets have cold atmospheres with rich chemical compositions from which mineral cloud particles form. Their properties, like particle sizes and material composition, vary with height, and the mineral cloud particles are charged due to triboelectric processes in such dynamic atmospheres. The dynamics of the atmospheric gas is driven by the irradiating host star and/or by the rotation of the objects that changes during its lifetime. Thermal gas ionisation in these ultra-cool but dense atmospheres allows electrostatic interactions and magnetic coupling of a substantial atmosphere volume. Combined with a strong magnetic field , a chromosphere and aurorae might form as suggested by radio and x-ray observations of brown dwarfs. Non-equilibrium processes like cosmic ray ionisation and discharge processes in clouds will increase the local pool of free electrons in the gas. Cosmic rays and lighting discharges also alter the composition of the local atmospheric gas such that tracer molecules might be identified. Cosmic rays affect the atmosphere through air showers in a certain volume which was modelled with a 3D Monte Carlo radiative transfer code to be able to visualise their spacial extent. Given a certain degree of thermal ionisation of the atmospheric gas, we suggest that electron attachment to charge mineral cloud particles is too inefficient to cause an electrostatic disruption of the cloud particles. Cloud particles will therefore not be destroyed by Coulomb explosion for the local temperature in the collisional dominated brown dwarf and giant gas planet atmospheres. However, the cloud particles are destroyed electrostatically in regions with strong gas ionisation. The potential size of such cloud holes would, however, be too small and might occur too far inside the cloud to mimic the effect of, e.g. magnetic field induced star spots

Intergenerational Continuity of the Family Farm: Influence of Parental Aspirations and Expectations for Their Children

The decline in the number of young people entering the farming occupation was investigated. Specifically, whether parents are encouraging their children to farm, and the links between encouragement and parental experience on the farm were explored. In-depth interviews with adult junior members of farming families were conducted regarding their experiences with farming, their attitudes about farming, and their goals for their own children. Results give preliminary support for the hypothesis that parental aspirations and expectations for their children are linked to parents\u27 experiences and attitudes towards farming

Polymer state approximations of Schroedinger wave functions

It is shown how states of a quantum mechanical particle in the Schroedinger representation can be approximated by states in the so-called polymer representation. The result may shed some light on the semiclassical limit of loop quantum gravity.Comment: 11 pages, 1 figure, Conclusions section adde