On the Maximal Excess Charge of the Chandrasekhar-Coulomb Hamiltonian in Two Dimensions

We show that for the straightforward quantized relativistic Coulomb Hamiltonian of a two-dimensional atom -- or the corresponding magnetic quantum dot -- the maximal number of electrons does not exceed twice the nuclear charge. It result is then generalized to the presence of external magnetic fields and atomic Hamiltonians. This is based on the positivity of |\bx| T(\bp) + T(\bp) |\bx| which -- in two dimensions -- is false for the non-relativistic case T(\bp) = \bp^2, but is proven in this paper for T(\bp) = |\bp|, i.e., the ultra-relativistic kinetic energy

Semiclassical Moser--Trudinger inequalities

We extend the Moser--Trudinger inequality of one function to systems of orthogonal functions. Our results are asymptotically sharp when applied to the collective behavior of eigenfunctions of Schr\"odinger operators on bounded domains.Comment: 18 page

Memory and superposition in a spin glass

Non-equilibrium dynamics in a Ag(Mn) spin glass are investigated by measurements of the temperature dependence of the remanent magnetisation. Using specific cooling protocols before recording the thermo- or isothermal remanent magnetisations on re-heating, it is found that the measured curves effectively disclose non-equilibrium spin glass characteristics such as ageing and memory phenomena as well as an extended validity of the superposition principle for the relaxation. The usefulness of this "simple" dc-method is discussed, as well as its applicability to other disordered magnetic systems.Comment: REVTeX style; 8 pages, 4 figure

Optimal Upper Bound for the Correlation Energy of a Fermi Gas in the Mean-Field Regime

While Hartree\u2013Fock theory is well established as a fundamental approximation for interacting fermions, it has been unclear how to describe corrections to it due to many-body correlations. In this paper we start from the Hartree\u2013Fock state given by plane waves and introduce collective particle\u2013hole pair excitations. These pairs can be approximately described by a bosonic quadratic Hamiltonian. We use Bogoliubov theory to construct a trial state yielding a rigorous Gell-Mann\u2013Brueckner\u2013type upper bound to the ground state energy. Our result justifies the random-phase approximation in the mean-field scaling regime, for repulsive, regular interaction potentials

Memory and chaos in an Ising spin glass

The non-equilibrium dynamics of the model 3d-Ising spin glass - Fe$_{0.55}$Mn$_{0.45}$TiO$_3$ - has been investigated from the temperature and time dependence of the zero field cooled magnetization recorded under certain thermal protocols. The results manifest chaos, rejuvenation and memory features of the equilibrating spin configuration that are very similar to those observed in corresponding studies of the archetypal RKKY spin glass Ag(Mn). The sample is rapidly cooled in zero magnetic field, and the magnetization recorded on re-heating. When a stop at constant temperature $T_s$ is made during the cooling, the system evolves toward its equilibrium state at this temperature. The equilibrated state established during the stop becomes frozen in on further cooling and is retrieved on re-heating. The memory of the aging at $T_s$ is not affected by a second stop at a lower temperature $T'_s$. Reciprocally, the first equilibration at $T_s$ has no influence on the relaxation at $T'_s$, as expected within the droplet model for domain growth in a chaotic landscape.Comment: REVTeX style; 4 pages, 4 figure

The Cosmic Infrared Background Experiment (CIBER): Instrumentation and First Results

Ultraviolet emission from the first generation of stars in the Universe ionized the intergalactic medium in a process which was completed by z similar to 6; the wavelength of these photons has been redshifted by (1 + z) into the near infrared today and can be measured using instruments situated above the Earth's atmosphere. First flying in February 2009, the Cosmic Infrared Background ExpeRiment (CIBER) comprises four instruments housed in a single reusable sounding rocket borne payload. CIBER will measure spatial anisotropies in the extragalactic IR background caused by cosmological structure from the epoch of reionization using two broadband imaging instruments, make a detailed characterization of the spectral shape of the IR background using a low resolution spectrometer, and measure the absolute brightness of the Zodiacal light foreground with a high resolution spectrometer in each of our six science fields. The scientific motivation for CIBER and details of its first and second flight instrumentation will be discussed. First flight results on the color of the zodiacal light around 1 mu m and plans for the future will also be presented