Designers manual for circuit design by analog/digital techniques Final report

Manual for designing circuits by hybrid compute

Specific heat and entropy of NN-body nonextensive systems

We have studied finite $N$-body $D$-dimensional nonextensive ideal gases and harmonic oscillators, by using the maximum-entropy methods with the $q$- and normal averages ($q$: the entropic index). The validity range, specific heat and Tsallis entropy obtained by the two average methods are compared. Validity ranges of the $q$- and normal averages are $0 q_L$, respectively, where $q_U=1+(\eta DN)^{-1}$, $q_L=1-(\eta DN+1)^{-1}$ and $\eta=1/2$ ($\eta=1$) for ideal gases (harmonic oscillators). The energy and specific heat in the $q$- and normal averages coincide with those in the Boltzmann-Gibbs statistics, % independently of $q$, although this coincidence does not hold for the fluctuation of energy. The Tsallis entropy for $N |q-1| \gg 1$ obtained by the $q$-average is quite different from that derived by the normal average, despite a fairly good agreement of the two results for $|q-1 | \ll 1$. It has been pointed out that first-principles approaches previously proposed in the superstatistics yield $additive$ $N$-body entropy ($S^{(N)}= N S^{(1)}$) which is in contrast with the $nonadditive$ Tsallis entropy.Comment: 27 pages, 8 figures: augmented the tex

Transport in ultradilute solutions of 3^3He in superfluid 4^4He

We calculate the effect of a heat current on transporting $^3$He dissolved in superfluid $^4$He at ultralow concentration, as will be utilized in a proposed experimental search for the electric dipole moment of the neutron (nEDM). In this experiment, a phonon wind will generated to drive (partly depolarized) $^3$He down a long pipe. In the regime of $^3$He concentrations $\tilde < 10^{-9}$ and temperatures $\sim 0.5$ K, the phonons comprising the heat current are kept in a flowing local equilibrium by small angle phonon-phonon scattering, while they transfer momentum to the walls via the $^4$He first viscosity. On the other hand, the phonon wind drives the $^3$He out of local equilibrium via phonon-$^3$He scattering. For temperatures below $0.5$ K, both the phonon and $^3$He mean free paths can reach the centimeter scale, and we calculate the effects on the transport coefficients. We derive the relevant transport coefficients, the phonon thermal conductivity and the $^3$He diffusion constants from the Boltzmann equation. We calculate the effect of scattering from the walls of the pipe and show that it may be characterized by the average distance from points inside the pipe to the walls. The temporal evolution of the spatial distribution of the $^3$He atoms is determined by the time dependent $^3$He diffusion equation, which describes the competition between advection by the phonon wind and $^3$He diffusion. As a consequence of the thermal diffusivity being small compared with the $^3$He diffusivity, the scale height of the final $^3$He distribution is much smaller than that of the temperature gradient. We present exact solutions of the time dependent temperature and $^3$He distributions in terms of a complete set of normal modes.Comment: NORDITA PREPRINT 2015-37, 9 pages, 6 figure

Transport in very dilute solutions of 3^3He in superfluid 4^4 He

Motivated by a proposed experimental search for the electric dipole moment of the neutron (nEDM) utilizing neutron-$^3$He capture in a dilute solution of $^3$He in superfluid $^4$He, we derive the transport properties of dilute solutions in the regime where the $^3$He are classically distributed and rapid $^3$He-$^3$He scatterings keep the $^3$He in equilibrium. Our microscopic framework takes into account phonon-phonon, phonon-$^3$He, and $^3$He-$^3$He scatterings. We then apply these calculations to measurements by Rosenbaum et al. [J.Low Temp.Phys. {\bf 16}, 131 (1974)] and by Lamoreaux et al. [Europhys.Lett. {\bf 58}, 718 (2002)] of dilute solutions in the presence of a heat flow. We find satisfactory agreement of theory with the data, serving to confirm our understanding of the microscopics of the helium in the future nEDM experiment.Comment: 10 pages, 5 figures, v

Low Temperature Transport Properties of Very Dilute Classical Solutions of 3^3He in Superfluid 4^4He

We report microscopic calculations of the thermal conductivity, diffusion constant and thermal diffusion constant for classical solutions of $^3$He in superfluid $^4$He at temperatures T \la 0.6~K, where phonons are the dominant excitations of the $^4$He. We focus on solutions with $^3$He concentrations \la \,10^{-3}, for which the main scattering mechanisms are phonon-phonon scattering via 3-phonon Landau and Beliaev processes, which maintain the phonons in a drifting equilibrium distribution, and the slower process of $^3$He-phonon scattering, which is crucial for determining the $^3$He distribution function in transport. We use the fact that the relative changes in the energy and momentum of a $^3$He atom in a collision with a phonon are small to derive a Fokker-Planck equation for the $^3$He distribution function, which we show has an analytical solution in terms of Sonine polynomials. We also calculate the corrections to the Fokker-Planck results for the transport coefficients.Comment: 29 pages, 2 figure

The Infrared Nucleus of the Wolf-Rayet Galaxy Henize 2-10

We have obtained near-infrared images and mid-infrared spectra of the starburst core of the dwarf Wolf-Rayet galaxy He 2-10. We find that the infrared continuum and emission lines are concentrated in a flattened ellipse 3-4'' or 150 pc across which may show where a recent accretion event has triggered intense star formation. The ionizing radiation from this cluster has an effective temperature of 40,000 K, corresponding to $30M_\odot$ stars, and the starburst is $0.5-1.5 \times 10^7$ years old.Comment: 17 pages Latex, 7 postscript figures, 1 postscript table, accepted to A

Near-infrared spectropolarimetry of a delta-spot

Sunspots harboring umbrae of both magnetic polarities within a common penumbra (delta-spots) are often but not always related to flares. We present first near-infrared (NIR) observations (Fe I 1078.3 nm and Si I 1078.6 nm spectra) obtained with the Tenerife Infrared Polarimeter (TIP) at the Vacuum Tower Telescope (VTT) in Tenerife on 2012 June 17, which afford accurate and sensitive diagnostics to scrutinize the complex fields along the magnetic neutral line of a delta-spot within active region NOAA 11504. We examine the vector magnetic field, line-of-sight (LOS) velocities, and horizontal proper motions of this rather inactive delta-spot. We find a smooth transition of the magnetic vector field from the main umbra to that of opposite polarity (delta-umbra), but a discontinuity of the horizontal magnetic field at some distance from the delta-umbra on the polarity inversion line. The magnetic field decreases faster with height by a factor of two above the delta-umbra. The latter is surrounded by its own Evershed flow. The Evershed flow coming from the main umbra ends at a line dividing the spot into two parts. This line is marked by the occurrence of central emission in the Ca II 854.2 nm line. Along this line, high chromospheric LOS-velocities of both signs appear. We detect a shear flow within the horizontal flux transport velocities parallel to the dividing line.Comment: 4 pages, will appear as Letter in Astronomy & Astrophysic

Spin lifetimes and strain-controlled spin precession of drifting electrons in zinc blende type semiconductors

We study the transport of spin polarized electrons in n-GaAs using spatially resolved continuous wave Faraday rotation. From the measured steady state distribution, we determine spin relaxation times under drift conditions and, in the presence of strain, the induced spin splitting from the observed spin precession. Controlled variation of strain along [110] allows us to deduce the deformation potential causing this effect, while strain along [100] has no effect. The electric field dependence of the spin lifetime is explained quantitatively in terms of an increase of the electron temperature.Comment: 5 pages, 6 figure

Tsallis' q index and Mori's q phase transitions at edge of chaos

We uncover the basis for the validity of the Tsallis statistics at the onset of chaos in logistic maps. The dynamics within the critical attractor is found to consist of an infinite family of Mori's $q$-phase transitions of rapidly decreasing strength, each associated to a discontinuity in Feigenbaum's trajectory scaling function $\sigma$. The value of $q$ at each transition corresponds to the same special value for the entropic index $q$, such that the resultant sets of $q$-Lyapunov coefficients are equal to the Tsallis rates of entropy evolution.Comment: Significantly enlarged version, additional figures and references. To be published in Physical Review