On the Cauchy problem for Gross-Pitaevskii hierarchies

The purpose of this paper is to investigate the Cauchy problem for the Gross-Pitaevskii infinite linear hierarchy of equations on $\mathbb{R}^n,$ $n \geq 1.$ We prove local existence and uniqueness of solutions in certain Sobolev type spaces $\mathrm{H}^{\alpha}_{\xi}$ of sequences of marginal density operators with $\alpha > n/2.$ In particular, we give a clear discussion of all cases $\alpha > n/2,$ which covers the local well-posedness problem for Gross-Pitaevskii hierarchy in this situation.Comment: 17 pages. The referee's comments and suggestions have been incorporated into this version of the pape

Discriminative Cooperative Networks for Detecting Phase Transitions

The classification of states of matter and their corresponding phase transitions is a special kind of machine-learning task, where physical data allow for the analysis of new algorithms, which have not been considered in the general computer-science setting so far. Here we introduce an unsupervised machine-learning scheme for detecting phase transitions with a pair of discriminative cooperative networks (DCN). In this scheme, a guesser network and a learner network cooperate to detect phase transitions from fully unlabeled data. The new scheme is efficient enough for dealing with phase diagrams in two-dimensional parameter spaces, where we can utilize an active contour model -- the snake -- from computer vision to host the two networks. The snake, with a DCN "brain", moves and learns actively in the parameter space, and locates phase boundaries automatically

Evolution of SU(4) Transport Regimes in Carbon Nanotube Quantum Dots

We study the evolution of conductance regimes in carbon nanotubes with doubly degenerate orbitals (``shells'') by controlling the contact transparency within the same sample. For sufficiently open contacts, Kondo behavior is observed for 1, 2, and 3 electrons in the topmost shell. As the contacts are opened more, the sample enters the ``mixed valence'' regime, where different charge states are strongly hybridized by electron tunneling. Here, the conductance as a function of gate voltage shows pronounced modulations with a period of four electrons, and all single-electron features are washed away at low temperature. We successfully describe this behavior by a simple formula with no fitting parameters. Finally, we find a surprisingly small energy scale that controls the temperature evolution of conductance and the tunneling density of states in the mixed valence regime.Comment: 4 pages + supplementary info. The second part of the original submission is now split off as a separate paper (0709.1288

Understanding the different rotational behaviors of 252^{252}No and 254^{254}No

Total Routhian surface calculations have been performed to investigate rapidly rotating transfermium nuclei, the heaviest nuclei accessible by detailed spectroscopy experiments. The observed fast alignment in $^{252}$No and slow alignment in $^{254}$No are well reproduced by the calculations incorporating high-order deformations. The different rotational behaviors of $^{252}$No and $^{254}$No can be understood for the first time in terms of $\beta_6$ deformation that decreases the energies of the $\nu j_{15/2}$ intruder orbitals below the N=152 gap. Our investigations reveal the importance of high-order deformation in describing not only the multi-quasiparticle states but also the rotational spectra, both providing probes of the single-particle structure concerning the expected doubly-magic superheavy nuclei.Comment: 5 pages, 4 figures, the version accepted for publication in Phys. Rev.

Electromagnetic Force in Dispersive and Transparent Media

A hydrodynamic-type, macroscopic theory was set up recently to simultaneously account for dissipation and dispersion of electromagnetic field, in nonstationary condensed systems of nonlinear constitutive relations~\cite{JL}. Since it was published in the letter format, some algebra and the more subtle reasonings had to be left out. Two of the missing parts are presented in this paper: How algebraically the new results reduce to the known old ones; and more thoughts on the range of validity of the new theory, especially concerning the treatment of dissipation.Comment: 10 pages, 0 figur

Observations of Feedback from Radio-Quiet Quasars: I. Extents and Morphologies of Ionized Gas Nebulae

Black hole feedback -- the strong interaction between the energy output of supermassive black holes and their surrounding environments -- is routinely invoked to explain the absence of overly luminous galaxies, the black hole vs. bulge correlations and the similarity of black hole accretion and star formation histories. Yet direct probes of this process in action are scarce and limited to small samples of active nuclei. We present Gemini IFU observations of the distribution of ionized gas around luminous, obscured, radio-quiet (RQ) quasars at z~0.5. We detect extended ionized gas nebulae via [O III]5007 emission in every case, with a mean diameter of 28 kpc. These nebulae are nearly perfectly round. The regular morphologies of nebulae around RQ quasars are in striking contrast with lumpy or elongated nebulae seen around radio galaxies at low and high redshifts. We present the uniformly measured size-luminosity relationship of [O III] nebulae around Seyfert 2 galaxies and type 2 quasars spanning 6 orders of magnitude in luminosity and confirm the flat slope of the correlation (R ~ L^{0.25+/-0.02}). We find a universal behavior of the [O III]/H-beta ratio in our entire RQ quasar sample: it persists at a constant value (~10) in the central regions, until reaching a "break" isophotal radius ranging from 4 to 11 kpc where it starts to decrease. We propose a model of clumpy nebulae in which clouds that produce line emission transition from being ionization-bounded at small distances from the quasar to being matter-bounded in the outer parts of the nebula, which qualitatively explains the observed line ratio and surface brightness profiles. It is striking that we see such smooth and round large-scale gas nebulosities in this sample, which are inconsistent with illuminated merger debris and which we suggest may be the signature of accretion energy from the nucleus reaching gas at large scales.Comment: 44 pages, 11 figures, 3 tables. Accepted for publication in MNRA