On the number of representations providing noiseless subsystems

This paper studies the combinatoric structure of the set of all representations, up to equivalence, of a finite-dimensional semisimple Lie algebra. This has intrinsic interest as a previously unsolved problem in representation theory, and also has applications to the understanding of quantum decoherence. We prove that for Hilbert spaces of sufficiently high dimension, decoherence-free subspaces exist for almost all representations of the error algebra. For decoherence-free subsystems, we plot the function $f_d(n)$ which is the fraction of all $d$-dimensional quantum systems which preserve $n$ bits of information through DF subsystems, and note that this function fits an inverse beta distribution. The mathematical tools which arise include techniques from classical number theory.Comment: 17 pp, 4 figs, accepted for Physical Review

Constraints on Light Pseudoscalars Implied by Tests of the Gravitational Inverse-Square Law

The exchange of light pseudoscalars between fermions leads to a spin-independent potential in order g^4, where g is the Yukawa pseudoscalar-fermion coupling constant. This potential gives rise to detectable violations of both the weak equivalence principle (WEP) and the gravitational inverse-square law (ISL), even if g is quite small. We show that when previously derived WEP constraints are combined with those arisingfrom ISL tests, a direct experimental limit on the Yukawa coupling of light pseudoscalars to neutrons can be inferred for the first time (g_n^2/4pi < 1.6 \times 10^-7), along with a new (and significantly improved) limit on the coupling of light pseudoscalars to protons.Comment: 12 pages, Revtex, with 1 Postscript figure (submitted to Physical Review Letters

Anisotropic flow of strange particles at RHIC

Space-time picture of the anisotropic flow evolution in Au+Au collisions at BNL RHIC is studied for strange hadrons within the microscopic quark-gluon string model. The directed flow of both mesons and hyperons demonstrates wiggle structure with the universal antiflow slope at |y| < 2 for minimum bias events. This effect increases as the reaction becomes more peripheral. The development of both components of the anisotropic flow is closely related to particle freeze-out. Hadrons are emitted continuously, and different hadronic species are decoupled from the system at different times. These hadrons contribute differently to the formation and evolution of the elliptic flow, which can be decomposed onto three components: (i) flow created by hadrons emitted from the surface at the onset of the collision; (ii) flow produced by jets; (iii) hydrodynamic flow. Due to these features, the general trend in elliptic flow formation is that the earlier mesons are frozen, the weaker their elliptic flow. In contrast, baryons frozen at the end of the system evolution have stronger v2.Comment: proceedings of the conference SQM2004 (September 2004, Cape Town, South Africa

Computational science and re-discovery: open-source implementations of ellipsoidal harmonics for problems in potential theory

We present two open-source (BSD) implementations of ellipsoidal harmonic expansions for solving problems of potential theory using separation of variables. Ellipsoidal harmonics are used surprisingly infrequently, considering their substantial value for problems ranging in scale from molecules to the entire solar system. In this article, we suggest two possible reasons for the paucity relative to spherical harmonics. The first is essentially historical---ellipsoidal harmonics developed during the late 19th century and early 20th, when it was found that only the lowest-order harmonics are expressible in closed form. Each higher-order term requires the solution of an eigenvalue problem, and tedious manual computation seems to have discouraged applications and theoretical studies. The second explanation is practical: even with modern computers and accurate eigenvalue algorithms, expansions in ellipsoidal harmonics are significantly more challenging to compute than those in Cartesian or spherical coordinates. The present implementations reduce the "barrier to entry" by providing an easy and free way for the community to begin using ellipsoidal harmonics in actual research. We demonstrate our implementation using the specific and physiologically crucial problem of how charged proteins interact with their environment, and ask: what other analytical tools await re-discovery in an era of inexpensive computation?Comment: 25 pages, 3 figure

The Turn-On of Mass Transfer in AM CVn Binaries: Implications for RX J0806+1527 and RX J1914+2456

We report on evolutionary calculations of the onset of mass transfer in AM CVn binaries, treating the donor's evolution in detail. We show that during the early contact phase, while the mass transfer rate, \Mdot, is increasing, gravity wave (GW) emission continues to drive the binary to shorter orbital period, \Porb. We argue that the phase where \Mdot > 0 and \nudot > 0 (\nu = 1/\Porb) can last between $10^3$ and $10^6$ yrs, significantly longer than previously estimated. These results are applied to RX J0806+1527 (\Porb = 321 s) and RX J914+2456 (\Porb=569 s), both of which have measured \nudot > 0. \emph{Thus, a \nudot > 0 does not select between the unipolar inductor and accretion driven models proposed as the source of X-rays in these systems}. For the accretion model, we predict for RX J0806 that \ddot{\nu} \approx \ee{1.0-1.5}{-28} Hz s$^{-2}$ and argue that timing observations can probe $\ddot{\nu}$ at this level with a total $\approx 20$ yr baseline. We also place constraints on each system's initial parameters given current observational data.Comment: 5 pages, 3 figures, accepted to ApJ

Relativistic coupled-cluster single-double method applied to alkali-metal atoms

A relativistic version of the coupled-cluster single-double (CCSD) method is developed for atoms with a single valence electron. In earlier work, a linearized version of the CCSD method (with extensions to include a dominant class of triple excitations) led to accurate predictions for energies, transition amplitudes, hyperfine constants, and other properties of monovalent atoms. Further progress in high-precision atomic structure calculations for heavy atoms calls for improvement of the linearized coupled-cluster methodology. In the present work, equations for the single and double excitation coefficients of the Dirac-Fock wave function, including all non-linear coupled-cluster terms that contribute at the single-double level are worked out. Contributions of the non-linear terms to energies, electric-dipole matrix elements, and hyperfine constants of low-lying states in alkali-metal atoms from Li to Cs are evaluated and the results are compared with other calculations and with precise experiments.Comment: 12 page

Gamma radiation survey of the LDEF spacecraft

The retrieval of the Long Duration Exposure Facility spacecraft in January 1990 after nearly six years in orbit offered a unique opportunity to study the long term buildup of induced radioactivity in the variety of materials on board. We conducted the first complete gamma-ray survey of a large spacecraft on LDEF shortly after its return to earth. A surprising observation was the Be-7 activity which was seen primarily on the leading edge of the satellite, implying that it was picked up by LDEF in orbit. This is the first known evidence for accretion of a radioactive isotope onto an orbiting spacecraft. Other isotopes observed during the survey, the strongest being Na-22, are all attributed to activation of spacecraft components. Be-7 is a spallation product of cosmic rays on nitrogen and oxygen in the upper atmosphere. However, the observed density is much greater than expected due to cosmic-ray production in situ. This implies transport of Be-7 from much lower altitudes up to the LDEF orbit