We present a scaling theory for unforced inviscid two-dimensional turbulence. Our model unifies existing spatial and temporal scaling theories. The theory is based on a self-similar distribution of vortices of different sizes $A$. Our model uniquely determines the spatial and temporal scaling of the associated vortex number density which allows the determination of the energy spectra and the vortex distributions. We find that the vortex number density scales as $n(A,t)\sim t^{-2/3}/A$, which implies an energy spectrum $\mathcal{E}\sim k^{-5}$, significantly steeper than the classical Batchelor-Kraichnan scaling. High-resolution numerical simulations corroborate the model.

Contact formation dynamics and electronic perturbations arising from the interaction of a metallic probe and a single molecule (1,3 cyclohexadiene) bound on the Si (100) surface are examined using a series of plane wave, density functional theory calculations. The approach of the probe induces a relaxation of the molecule that ultimately leads to the formation of an interface state due to a specific interaction between the probe apex atom and the $\mathrm{C}\mathrm{C}$ bond of the molecule. The calculated interface state is located 0.2 eV above the Fermi energy, in agreement with low temperature scanning tunneling spectroscopy local density of states data (0.35 eV), and is responsible for the contrast observed in low bias empty-state STM images.

The resistivity of ultraclean suspended graphene is strongly temperature ($T$) dependent for $5<T<240\mathrm{K}$. At $T\sim 5\mathrm{K}$ transport is near-ballistic in a device of $\sim 2\mu \mathrm{m}$ dimension and a mobility $\sim 170000{\mathrm{cm}}^2/\mathrm{V}\mathrm{s}$. At large carrier density, $n>0.5\times {10}^{11}{\mathrm{cm}}^{-2}$, the resistivity increases with increasing $T$ and is linear above 50 K, suggesting carrier scattering from acoustic phonons. At $T=240\mathrm{K}$ the mobility is $\sim 120000{\mathrm{cm}}^2/\mathrm{V}\mathrm{s}$, higher than in any known semiconductor. At the charge neutral point we observe a nonuniversal conductivity that decreases with decreasing $T$, consistent with a density inhomogeneity $<{10}^8{\mathrm{cm}}^{-2}$.

We provide a semiquantitative tool, derived from first-principles simulations, for answering the question of whether certain types of defects in solid ${}^4\mathrm{He}$ support mass superflow. Although ideal crystals of ${}^4\mathrm{He}$ are not supersolid, the gap for vacancy creation closes when applying a moderate stress. While a homogeneous system becomes unstable at this point, the stressed core of crystalline defects (dislocations and grain boundaries) can turn superfluid.

The interplay of strong interaction and strong disorder, as contained in the Anderson-Hubbard model, is addressed using two nonperturbative numerical methods: the Lanczos algorithm in the grand canonical ensemble at zero temperature and quantum Monte Carlo simulations. We find distinctive evidence for a zero-energy anomaly which is robust upon variation of doping, disorder, and interaction strength. Its similarities to, and differences from, pseudogap formation in other contexts, including perturbative treatments of interactions and disorder, classical theories of localized charges, and in the clean Hubbard model, are discussed.

The capability to control the type and amount of charge carriers in a material and, in the extreme case, the transition from metal to insulator, is one of the key challenges of modern electronics. By employing angle-resolved photoemission spectroscopy we find that a reversible metal to insulator transition and a fine-tuning of the charge carriers from electrons to holes can be achieved in epitaxial bilayer and single layer graphene by molecular doping. The effects of electron screening and disorder are also discussed. These results demonstrate that epitaxial graphene is suitable for electronics applications, as well as provide new opportunities for studying the hole doping regime of the Dirac cone in graphene.

We investigate the collapse dynamics of a dipolar condensate of ${}^{52}\mathrm{Cr}$ atoms when the $s$-wave scattering length characterizing the contact interaction is reduced below a critical value. A complex dynamics, involving an anisotropic, $d$-wave symmetric explosion of the condensate, is observed. The atom number decreases abruptly during the collapse. We find good agreement between our experimental results and those of a numerical simulation of the three-dimensional Gross-Pitaevskii equation, including contact and dipolar interactions as well as three-body losses. The simulation indicates that the collapse induces the formation of two vortex rings with opposite circulations.

We carry out first-principles calculations of the nonlinear dielectric response of short-period ferroelectric superlattices. We compute and store not only the total polarization, but also the Wannier-based polarizations of individual atomic layers, as a function of the electric displacement field, and use this information to construct a model capable of predicting the nonlinear dielectric response of an arbitrary superlattice sequence. We demonstrate the successful application of our approach to superlattices composed of ${\mathrm{SrTiO}}_3$, ${\mathrm{CaTiO}}_3$, and ${\mathrm{BaTiO}}_3$ layers.

We demonstrate spin squeezing in a room temperature ensemble of $\approx {10}^{12}$ cesium atoms using their internal structure, where the necessary entanglement is created between nuclear and electronic spins of each individual atom. This state provides improvement in measurement sensitivity beyond the standard quantum limit for quantum memory experiments and applications in quantum metrology and is thus a complementary alternative to spin squeezing obtained via interatom entanglement. Squeezing of the collective spin is verified by quantum state tomography.

We use ultrafast electron crystallography to study structural changes induced in graphite by a femtosecond laser pulse. At moderate fluences of $\le 21\mathrm{mJ}/{\mathrm{cm}}^2$, lattice vibrations are observed to thermalize on a time scale of $\approx 8\mathrm{ps}$. At higher fluences approaching the damage threshold, lattice vibration amplitudes saturate. Following a marked initial contraction, graphite is driven nonthermally into a transient state with $s{p}^3$-like character, forming interlayer bonds. Using ab initio density functional calculations, we trace the governing mechanism back to electronic structure changes following the photoexcitation.

We report the results of a search for the bottomonium ground state ${\eta }_b(1S)$ in the photon energy spectrum with a sample of $(109\pm 1)$ million of ${\rm Y}(3S)$ recorded at the ${\rm Y}(3S)$ energy with the BABAR detector at the PEP-II $B$ factory at SLAC. We observe a peak in the photon energy spectrum at $E_{\gamma }={921.2}_{-2.8}^{+2.1}(\mathrm{stat})\pm 2.4(\mathrm{syst})\mathrm{MeV}$ with a significance of 10 standard deviations. We interpret the observed peak as being due to monochromatic photons from the radiative transition ${\rm Y}(3S)\to \gamma {\eta }_b(1S)$. This photon energy corresponds to an ${\eta }_b(1S)$ mass of ${9388.9}_{-2.3}^{+3.1}(\mathrm{stat})\pm 2.7(\mathrm{syst})\mathrm{MeV}/c^2$. The hyperfine ${\rm Y}(1S)$-${\eta }_b(1S)$ mass splitting is ${71.4}_{-3.1}^{+2.3}(\mathrm{stat})\pm 2.7(\mathrm{syst})\mathrm{MeV}/{\mathrm{c}}^2$. The branching fraction for this radiative ${\rm Y}(3S)$ decay is estimated to be $[4.8\pm 0.5(\mathrm{stat})\pm 1.2(\mathrm{syst})]\times {10}^{-4}$.

Reaction mechanism analyses performed with a $4\pi$ detector for the systems ${}^{208}\mathrm{Pb}+\mathrm{Ge}$, ${}^{238}\mathrm{U}+\mathrm{Ni}$ and ${}^{238}\mathrm{U}+\mathrm{Ge}$, combined with analyses of the associated reaction time distributions, provide us with evidence for nuclei with $Z=120$ and 124 living longer than ${10}^{-18}\mathrm{s}$ and arising from highly excited compound nuclei. By contrast, the neutron deficient nuclei with $Z=114$ possibly formed in ${}^{208}\mathrm{Pb}+\mathrm{Ge}$ reactions have shorter lifetimes, close to or below the sensitivity limit of the experiment.

We investigate disease extinction in an epidemic model described by a birth-death process. We show that, in the absence of vaccination, the effective entropic barrier for extinction displays scaling with the distance to the bifurcation point, with an unusual critical exponent. Even a comparatively weak Poisson-distributed random vaccination leads to an exponential increase in the extinction rate, with the exponent that strongly depends on the vaccination parameters.

The structures of heavy and light water at ambient conditions are investigated with the combined techniques of x-ray diffraction, neutron diffraction, and computer simulation. It is found that heavy water is a more structured liquid than light water. We find the OH bond length in ${\mathrm{H}}_2\mathrm{O}$ is $\sim 3\%$ longer than the OD bond length in ${\mathrm{D}}_2\mathrm{O}$. This is a much larger change than current predictions. Corresponding to this, the hydrogen bond in light water is $\sim 4\%$ shorter than in heavy water, while the intermolecular HH distance is $\sim 2\%$ longer.

We consider a heterostructure of a metal and a paramagnetic Mott insulator using an adaptation of dynamical mean-field theory to describe inhomogeneous systems. The metal can penetrate into the insulator via the Kondo effect. We investigate the scaling properties of the metal-insulator interface close to the critical point of the Mott insulator. At criticality, the quasiparticle weight decays as $1/x^2$ with distance $x$ from the metal within our mean-field theory. Our numerical results (using the numerical renormalization group as an impurity solver) show that the prefactor of this power law is extremely small.

We propose a scheme to construct the most prominent Abelian and non-Abelian fractional quantum Hall states from $K$-component Halperin wave functions. In order to account for a one-component quantum Hall system, these $\mathrm{SU}(K)$ colors are distributed over all particles by an appropriate symmetrization. Numerical calculations corroborate the picture that $K$-component Halperin wave functions may be a common basis for both Abelian and non-Abelian trial wave functions in the study of one-component quantum Hall systems.

Recently, much attention has been given to a noteworthy property of some soft tissues: their ability to grow. Many attempts have been made to model this behavior in biology, chemistry, and physics. Using the theory of finite elasticity, Rodriguez has postulated a multiplicative decomposition of the geometric deformation gradient into a growth-induced part and an elastic one needed to ensure compatibility of the body. In order to fully explore the consequences of this hypothesis, the equations describing thin elastic objects under finite growth are derived. Under appropriate scaling assumptions for the growth rates, the proposed model is of the Föppl–von Kármán type. As an illustration, the circumferential growth of a free hyperelastic disk is studied.

The energy spectrum of cosmic rays above $2.5\times {10}^{18}\mathrm{eV}$, derived from 20 000 events recorded at the Pierre Auger Observatory, is described. The spectral index $\gamma$ of the particle flux, $J\propto E^{-\gamma }$, at energies between $4\times {10}^{18}\mathrm{eV}$ and $4\times {10}^{19}\mathrm{eV}$ is $2.69\pm 0.02(\mathrm{stat})\pm 0.06(\mathrm{syst})$, steepening to $4.2\pm 0.4(\mathrm{stat})\pm 0.06(\mathrm{syst})$ at higher energies. The hypothesis of a single power law is rejected with a significance greater than 6 standard deviations. The data are consistent with the prediction by Greisen and by Zatsepin and Kuz’min.

We attempt to generalize the anti–de Sitter/conformal field theory correspondence to nonrelativistic conformal field theories which are invariant under Galilean transformations. Such systems govern ultracold atoms at unitarity, nucleon scattering in some channels, and, more generally, a family of universality classes of quantum critical behavior. We construct a family of metrics which realize these symmetries as isometries. They are solutions of gravity with a negative cosmological constant coupled to pressureless dust. We discuss realizations of the dust, which include a bulk superconductor. We develop the holographic dictionary and find two-point correlators of the correct form. A strange aspect of the correspondence is that the bulk geometry has two extra noncompact dimensions.

Phase singularities of wave-front-like screw dislocations or vortices possess a well-defined quantity that can only take integer value: the topological charge. In the nonlinear regime, it has been demonstrated that optical or acoustical vortices interact and the topological charge follows a conservation law. Here this facility is used in nonlinear parametric interaction of two vortices shifted in frequency to perform sums and subtractions of the topological charge. Thus, we experimentally demonstrate a new technique to perform wave computation in the group of integer $\mathbb{Z}$. When the two vortices have commensurable frequencies, different combinations give the same frequencies but different tolopological charges may occur. We show that an energy criterion can be used to predict the outcome. A corollary is that a modulation of amplitude of the vortices switches from one result to the other.