Non-linear ground state representations and sharp Hardy inequalities - Frank, Rupert L; Robert Seiringer (Journal of Functional Analysis)
We determine the sharp constant in the Hardy inequality for fractional Sobolev spaces. To do so, we develop a non-linear and non-local version of the ground state representation, which even yields a remainder term. From the sharp Hardy inequality we deduce the sharp constant in a Sobolev embedding which is optimal in the Lorentz scale. In the appendix, we characterize the cases of equality in the rearrangement inequality in fractional Sobolev spaces.

The Lieb-Liniger model as a limit of dilute bosons in three dimensions - Robert Seiringer; Yin, Jun (Communications in Mathematical Physics)
We show that the Lieb-Liniger model for one-dimensional bosons with repulsive δ-function interaction can be rigorously derived via a scaling limit from a dilute three-dimensional Bose gas with arbitrary repulsive interaction potential of finite scattering length. For this purpose, we prove bounds on both the eigenvalues and corresponding eigenfunctions of three-dimensional bosons in strongly elongated traps and relate them to the corresponding quantities in the Lieb-Liniger model. In particular, if both the scattering length a and the radius r of the cylindrical trap go to zero, the Lieb-Liniger model with coupling constant g ∼ a/r 2 is derived. Our bounds are uniform in g in the whole parameter range 0 ≤ g ≤ ∞, and apply to the Hamiltonian for three-dimensional bosons in a spectral window of size ∼ r -2 above the ground state energy.

A nonlinear model for relativistic electrons at positive temperature - Hainzl, Christian; Lewin, Mathieu; Robert Seiringer (Reviews in Mathematical Physics)
We study the relativistic electron-positron field at positive temperature in the Hartree-Fock approximation. We consider both the case with and without exchange terms, and investigate the existence and properties of minimizers. Our approach is non-perturbative in the sense that the relevant electron subspace is determined in a self-consistent way. The present work is an extension of previous work by Hainzl, Lewin, Séré and Solovej where the case of zero temperature was considered.

k-Sets and k-facets - Uli Wagner (Surveys on Discrete and Computational Geometry: Twenty Years Later)

On center regions and balls containing many points - Smorodinsky, Shakhar; Sulovský, Marek; Uli Wagner
We study the disk containment problem introduced by Neumann-Lara and Urrutia and its generalization to higher dimensions. We relate the problem to centerpoints and lower centerpoints of point sets. Moreover, we show that for any set of n points in ℝd, there is a subset A ⊆ S of size [d+3/2] such that any ball containing A contains at least roughly 4/5ed 3n points of S. This improves previous bounds for which the constant was exponentially small in d. We also consider a generalization of the planar disk containment problem to families of pseudodisks.

Increased social interaction in mice deficient of the striatal medium spiny neuron-specific phosphodiesterase 10A2 - Sano, Hiromi; Nagai, Yumiko; Miyakawa, Tsuyoshi; Ryuichi Shigemoto; Yokoi, Mineto (Journal of Neurochemistry)
Cyclic nucleotide phosphodiesterase 10A (PDE10A) is a member of phosphodiesterase families that degrade cAMP and/or cGMP in distinct intracellular sites. PDE10A has a dual activity on hydrolysis of both cAMP and cGMP, and is prominently expressed in the striatum and the testis. Previous studies suggested that PDE10A is involved in regulation of locomotor activity and potentially related to psychosis, but concrete physiological roles of PDE10A remains elusive yet. In this study, we genetically inactivated PDE10A2, a prominent isoform of PDE10A in the brain, in mice, and demonstrate that PDE10A2 deficiency results in increased social interaction without any major influence on different other behaviors, along with increased levels of striatal cAMP. We also demonstrate that PDE10A2 is selectively distributed in medium spiny neurons, but not interneurons, of the striatal complex. Thus, our results establish a physiological role for PDE10A2 in regulating cAMP pathway and social interaction, and suggest that cAMP signaling cascade in striatal medium spiny neurons might be involved in regulating social interaction behavior in mice.

The Decapentaplegic morphogen gradient a precise definition - Anna Kicheva; González-Gaitán, Marcos A (Current Opinion in Cell Biology)
Two key processes are in the basis of morphogenesis: the spatial allocation of cell types in fields of naïve cells and the regulation of growth. Both are controlled by morphogens, which activate target genes in the growing tissue in a concentration-dependent manner. Thus the morphogen model is an intrinsically quantitative concept. However, quantitative studies were performed only in recent years on two morphogens: Bicoid and Decapentaplegic. This review covers quantitative aspects of the formation and precision of the Decapentaplegic morphogen gradient. The morphogen gradient concept is transitioning from a soft definition to a precise idea of what the gradient could really do.

Dynamics of anisotropic tissue growth - Bittig, Thomas; Wartlick, Ortrud; Anna Kicheva; González-Gaitárr, Marcos; Julicher, Frank (New Journal of Physics)
We study the mechanics of tissue growth via cell division and cell death (apoptosis). The rearrangements of cells can on large scales and times be captured by a continuum theory which describes the tissue as an effective viscous material with active stresses generated by cell division. We study the effects of anisotropies of cell division on cell rearrangements and show that average cellular trajectories exhibit anisotropic scaling behaviors. If cell division and apoptosis balance, there is no net growth, but for anisotropic cell division the tissue undergoes spontaneous shear deformations. Our description is relevant for the study of developing tissues such as the imaginal disks of the fruit fly Drosophila melanogaster, which grow anisotropically.

Three-dimensional composition profiles of single quantum dots determined by scanning-probe-microscopy-based nanotomography - Rastelli, Armando; Stoffel, Mathieu; Malachias, Ângelo S; Merdzhanova, Tsvetelina; Georgios Katsaros; Kern, Klaus; Metzger, Till H; Schmidt, Oliver G (Nano Letters)
Scanning probe microscopy; Semiconductor quantum dots; Composition gradients; Composition profiles; Nanotomography; Single quantum dots; Strained sige/si; Three-dimensional (3D); Wet-chemical etchings; X-ray scattering measurements; quantum dot; methodology; nanotechnology; optical tomography; scanning probe microscopy; three dimensional imaging; Imaging, Three-Dimensional; Materials Testing; Microscopy, Scanning Probe; Nanotechnology; Quantum Dots; Tomography,

Positioning of strained islands by interaction with surface nanogrooves - Georgios Katsaros; Tersoff, Jerry; Stoffel, Mathieu; Rastelli, Armando; Acosta-Diaz, P; Kar, Gouranga S; Costantini, Giovanni; Schmidt, Oliver G; Kern, Klaus (Physical Review Letters)
When strained Stranski-Krastanow islands are used as "self-assembled quantum dots," a key goal is to control the island position. Here we show that nanoscale grooves can control the nucleation of epitaxial Ge islands on Si(001), and can drive lateral motion of existing islands onto the grooves, even when the grooves are very narrow and shallow compared to the islands. A position centered on the groove minimizes energy. We use as prototype grooves the trenches which form naturally around islands. During coarsening, the shrinking islands move laterally to sit directly astride that trench. In subsequent growth, we demonstrate that islands nucleate on the "empty trenches" which remain on the surface after complete dissolution of the original islands.

Climbing the Jaynes-Cummings ladder and observing its √n nonlinearity in a cavity QED system - Johannes Fink; Göppl, M; Baur, Matthias P; Bianchetti, R; Leek, Peter J; Blais, Alexandre; Wallraff, Andreas (Nature)
The field of cavity quantum electrodynamics (QED), traditionally studied in atomic systems, has gained new momentum by recent reports of quantum optical experiments with solid-state semiconducting and superconducting systems. In cavity QED, the observation of the vacuum Rabi mode splitting is used to investigate the nature of matter-light interaction at a quantum-mechanical level. However, this effect can, at least in principle, be explained classically as the normal mode splitting of two coupled linear oscillators. It has been suggested that an observation of the scaling of the resonant atom-photon coupling strength in the Jaynes-Cummings energy ladder with the square root of photon number n is sufficient to prove that the system is quantum mechanical in nature. Here we report a direct spectroscopic observation of this characteristic quantum nonlinearity. Measuring the photonic degree of freedom of the coupled system, our measurements provide unambiguous spectroscopic evidence for the quantum nature of the resonant atom-field interaction in cavity QED. We explore atom-photon superposition states involving up to two photons, using a spectroscopic pump and probe technique. The experiments have been performed in a circuit QED set-up, in which very strong coupling is realized by the large dipole coupling strength and the long coherence time of a superconducting qubit embedded in a high-quality on-chip microwave cavity. Circuit QED systems also provide a natural quantum interface between flying qubits (photons) and stationary qubits for applications in quantum information processing and communication.

Resolving vacuum fluctuations in an electrical circuit by measuring the lamb shift - Fragner, A; Göppl, M; Johannes Fink; Baur, Matthias P; Bianchetti, R; Leek, Peter J; Blais, Alexandre; Wallraff, Andreas (Science)
Quantum theory predicts that empty space is not truly empty. Even in the absence of any particles or radiation, in pure vacuum, virtual particles are constantly created and annihilated. In an electromagnetic field, the presence of virtual photons manifests itself as a small renormalization of the energy of a quantum system, known as the Lamb shift. We present an experimental observation of the Lamb shift in a solid-state system. The strong dispersive coupling of a superconducting electronic circuit acting as a quantum bit (qubit) to the vacuum field in a transmission-line resonator leads to measurable Lamb shifts of up to 1.4% of the qubit transition frequency. The qubit is also observed to couple more strongly to the vacuum field than to a single photon inside the cavity, an effect that is explained by taking into account the limited anharmonicity of the higher excited qubit states.

Coplanar waveguide resonators for circuit quantum electrodynamics - Göppl, M; Fragner, A; Baur, Matthias P; Bianchetti, R; Filipp, Stefan; Johannes Fink; Leek, Peter J; Puebla, G; Steffen, L. Kraig; Wallraff, Andreas (Journal of Applied Physics)
High quality on-chip microwave resonators have recently found prominent new applications in quantum optics and quantum information processing experiments with superconducting electronic circuits, a field now known as circuit quantum electrodynamics (QED). They are also used as single photon detectors and parametric amplifiers. Here we analyze the physical properties of coplanar waveguide resonators and their relation to the materials properties for use in circuit QED. We have designed and fabricated resonators with fundamental frequencies from 2 to 9 GHz and quality factors ranging from a few hundreds to a several hundred thousands controlled by appropriately designed input and output coupling capacitors. The microwave transmission spectra measured at temperatures of 20 mK are shown to be in good agreement with theoretical lumped element and distributed element transmission matrix models. In particular, the experimentally determined resonance frequencies, quality factors, and insertion losses are fully and consistently explained by the two models for all measured devices. The high level of control and flexibility in design renders these resonators ideal for storing and manipulating quantum electromagnetic fields in integrated superconducting electronic circuits.

The thickness of high-redshift quasar ionization fronts as a constraint on the ionizing spectral energy distribution - Kramer, R. H.; Haiman, Zoltán (Monthly Notices of the Royal Astronomical Society)
High-redshift quasars (z >~ 6) drive ionization fronts into the intergalactic medium (IGM). If the thickness of the front can be measured, it can provide a novel constraint on the ionizing spectral energy distribution (SED). Here we follow the propagation of an I-front into a uniform IGM, and compute its thickness for a range of possible quasar spectra and ages. We also explore the effects of uniform and non-uniform ionizing backgrounds. We find that even for hard spectra, the fronts are initially thin, with a thickness much smaller than the mean free path of ionizing photons, but the thickness increases as the front approaches equilibrium in 10^8 - 10^9 years, and can eventually significantly exceed simple estimates based on the mean free path. With a high intrinsic hydrogen column density obscuring the source (log(N_H/cm^-2) >~ 19.2) or a hard power-law spectrum combined with some obscuration (e.g. dlog(F_ν)/dlog(ν) >~ -1.2 at log(N_H/cm^-2) >~ 18.0), the thickness of the front exceeds ~1 physical Mpc and may be measurable from the morphology of its redshifted 21cm signal. We find that the highly ionized inner part of the front, which may be probed by Lyman line absorption spectra, remains sharp for bright quasars unless a large obscuring column (log(N_H/cm^-2) >~ 19.2) removes most of their ionizing photons up to ~40 eV. For obscured sources with log(N_H/cm^-2) >~ 19.8, embedded in a significantly neutral IGM, the black Lyman-alpha trough (where the neutral fraction is ~10^-3) underestimates the size of the HII region by a factor of >~4.

Premerger localization of gravitational wave standard sirens with LISA: Triggered search for an electromagnetic counterpart - Kocsis, Bence; Haiman, Zoltán; Menou, Kristen (The Astrophysical Journal)
Electromagnetic (EM) counterparts to supermassive black hole binary mergers observed by LISA can be localized to within the field of view of astronomical instruments ~10 deg^2 hours to weeks prior to coalescence. The temporal coincidence of any prompt EM counterpart with a gravitationally-timed merger may offer the best chance of identifying a unique host galaxy. We discuss the challenges posed by searches for prompt EM counterparts and propose novel observational strategies to address them. In particular, we discuss the size and shape evolution of the LISA localization error ellipses on the sky, and quantify the requirements for dedicated EM surveys of the area prior to coalescence. A triggered EM counterpart search campaign will require monitoring a several-square degree area. It could aim for variability at the 24-27 mag level in optical bands, for example, which corresponds to 1-10% of the Eddington luminosity of the prime LISA sources of 10^6-10^7 Msun BHs at z=1-2, on time-scales of minutes to hours, the orbital time-scale of the binary in the last 2-4 weeks. A cross-correlation of the period of any variable EM signal with the quasi-periodic gravitational waveform over 10-1000 cycles may aid the detection. Alternatively, EM searches can detect a transient signal accompanying the coalescence. We highlight the measurement of differences in the arrival times of photons and gravitons from the same cosmological source as a valuable independent test of the massive character of gravity, and of possible violations of Lorentz invariance in the gravity sector.

Feedback effects on population III star formation - Bryan, Greg L.; McGreer, Ian D.; Mesinger, Andrei; Haiman, Zoltán (AIP Conference Proceedings)
With the help of numerical simulations, we examine two aspects of feedback from the first generation of stars on later star formation. First, we investigate the impact of relic HII regions on forming halos. We find that the positive and negative effects of such feedback nearly cancel because the increase in entropy due to heating is balanced by the increase in the H 2 fraction due to the free electrons. However, these halos can be delayed more easily by a background Lyman-Werner flux. Second, we show that HD cooling is important in halos which have been ionized and allowed to recombine. Gas is allowed to cool to the CMB temperature at densities around n∼10 4cm-3, reducing the accreted mass by a factor of a few. However, as the collapse proceeds, the central gas density exceeds the critical density of HD and heats until HD cooling is no longer important. Therefore the behaviour of the (smaller mass) core is relatively unaffected by HD cooling.

Prompt shocks in the gas disk around a recoiling supermassive black hole binary - Lippai, Zoltán; Frei, Zsolt; Haiman, Zoltán (The Astrophysical Journal)
Supermassive black hole binaries (BHBs) produced in galaxy mergers recoil at the time of their coalescence due to the emission of gravitational waves (GWs). We simulate the response of a thin, 2D disk of collisionless particles, initially on circular orbits around a 10^6 M_sun BHB, to kicks that are either parallel or perpendicular to the initial orbital plane. Typical kick velocities (v_k) can exceed the sound speed in a circumbinary gas disk. While the inner disk is strongly bound to the recoiling binary, the outer disk is only weakly bound or unbound. This leads to differential motions in the disturbed disk that increase with radius and can become supersonic at ~700 Schwarzschild radii for v_k ~500 km/s, implying that shocks form beyond this radius. We indeed find that kicks in the disk plane lead to immediate strong density enhancements (within weeks) in a tightly wound spiral caustic, propagating outward at the speed v_k. Concentric density enhancements are also observed for kicks perpendicular to the disk, but are weaker and develop into caustics only after a long delay (>1 year). Unless both BH spins are low or precisely aligned with the orbital angular momentum, a significant fraction (> several %) of kicks are sufficiently large and well aligned with the orbital plane for strong shocks to be produced. The shocks could result in an afterglow whose characteristic photon energy increases with time, from the UV (~10eV) to the soft X-ray (~100eV) range, between one month and one year after the merger. This could help identify EM counterparts to GW sources discovered by LISA.

Oxygen pumping. II. Probing the inhomogeneous metal enrichment at the epoch of reionization with high‐frequency CMB observations - Hernandez‐Monteagudo, Carlos; Haiman, Zoltán; Verde, Licia; Jimenez, Raul (The Astrophysical Journal)
At the epoch of reionization, when the high-redshift inter-galactic medium (IGM) is being enriched with metals, the 63.2 micron fine structure line of OI is pumped by the ~ 1300 AA soft UV background and introduces a spectral distortion in the Cosmic Microwave Background (CMB). Here we use a toy model for the spatial distribution of neutral oxygen, assuming metal bubbles surround dark matter halos, and compute the fluctuations of this distortion, and the angular power spectrum it imprints on the CMB. We discuss the dependence of the power spectrum on the velocity of the winds polluting the IGM with metals, the minimum mass of the halos producing these winds, and on the cosmic epoch when the OI pumping occurs. We find that, although the clustering signal of the CMB distortion is weak δ y_{rms} ~ 10^{-7} (roughly corresponding to a temperature anisotropy of few nK), it may be reachable in deep integrations with high-sensitivity infrared detectors. Even without a detection, these instruments should be able to useful constraints on the heavy element enrichment history of the IGM.

Challenges to the DGP model from horizon-scale growth and geometry - Fang, Wenjuan; Wang, Sheng; Hu, Wayne; Haiman, Zoltán; Hui, Lam; May, Morgan (Physical Review D)
We conduct a Markov Chain Monte Carlo study of the Dvali-Gabadadze-Porrati self-accelerating braneworld scenario given the cosmic microwave background (CMB) anisotropy, supernovae and Hubble constant data by implementing an effective dark energy prescription for modified gravity into a standard Einstein-Boltzmann code. We find no way to alleviate the tension between distance measures and horizon-scale growth in this model. Growth alterations due to perturbations propagating into the bulk appear as excess CMB anisotropy at the lowest multipoles. In a flat cosmology, the maximum likelihood Dvali-Gabadadze-Porrati model is nominally a 5.3⁢𝜎 poorer fit than 𝛬⁢CDM. Curvature can reduce the tension between distance measures but only at the expense of exacerbating the problem with growth leading to a 4.8⁢𝜎 result that is dominated by the low multipole CMB temperature spectrum. While changing the initial conditions to reduce large-scale power can flatten the temperature spectrum, this also suppresses the large angle polarization spectrum in violation of recent results from the five-year Wilkinson Microwave Anisotropy Probe. The failure of this model highlights the power of combining growth and distance measures in cosmology as a test of gravity on the largest scales.

Cosmological physics with black holes (and possibly white dwarfs) - Menou, Kristen; Haiman, Zoltán; Kocsis, Bence (New Astronomy Reviews)
The notion that microparsec-scale black holes can be used to probe gigaparsec-scale physics may seem counterintuitive, at first. Yet, the gravitational observatory LISA will detect cosmologically-distant coalescing pairs of massive black holes, accurately measure their luminosity distance and help identify an electromagnetic counterpart or a host galaxy. A wide variety of new black hole studies and a gravitational version of Hubble’s diagram become possible, if host galaxies are successfully identified. Furthermore, if dark energy is a manifestation of large-scale modified gravity, deviations from general relativistic expectations could become apparent in a gravitational signal propagated over cosmological scales, especially when compared to the electromagnetic signal from a same source. Finally, since inspirals of white dwarfs into massive black holes at cosmological distances may permit pre-merger localizations, we suggest that careful monitoring of these events and any associated electromagnetic counterpart could lead to high-precision cosmological measurements with LISA.