On 2-group global symmetries and their anomalies

In general quantum field theories (QFTs), ordinary (0-form) global symmetries and 1-form symmetries can combine into 2-group global symmetries. We describe this phenomenon in detail using the language of symmetry defects. We exhibit a simple procedure to determine the (possible) 2-group global symmetry of a given QFT, and provide a classification of the related \u2019t Hooft anomalies (for symmetries not acting on spacetime). We also describe how QFTs can be coupled to extrinsic backgrounds for symmetry groups that differ from the intrinsic symmetry acting faithfully on the theory. Finally, we provide a variety of examples, ranging from TQFTs (gapped systems) to gapless QFTs. Along the way, we stress that the \u201cobstruction to symmetry fractionalization\u201d discussed in some condensed matter literature is really an instance of 2-group global symmetry

Holographic memory using beam steering

A method, apparatus, and system provide the ability for storing holograms at high speed. A single laser diode emits a collimated laser beam to both write to and read from a photorefractice crystal. One or more liquid crystal beam steering spatial light modulators (BSSLMs) steer a reference beam, split from the collimated laser beam, at high speed to the photorefractive crystal

Primes and composites in the determinant Hosoya triangle

In this paper, we look at numbers of the form $H_{r,k}:=F_{k-1}F_{r-k+2}+F_{k}F_{r-k}$. These numbers are the entries of a triangular array called the \emph{determinant Hosoya triangle} which we denote by ${\mathcal H}$. We discuss the divisibility properties of the above numbers and their primality. We give a small sieve of primes to illustrate the density of prime numbers in ${\mathcal H}$. Since the Fibonacci and Lucas numbers appear as entries in ${\mathcal H}$, our research is an extension of the classical questions concerning whether there are infinitely many Fibonacci or Lucas primes. We prove that ${\mathcal H}$ has arbitrarily large neighbourhoods of composite entries. Finally we present an abundance of data indicating a very high density of primes in ${\mathcal H}$.Comment: two figure

Ab initio theory and modeling of water

Water is of the utmost importance for life and technology. However, a genuinely predictive ab initio model of water has eluded scientists. We demonstrate that a fully ab initio approach, relying on the strongly constrained and appropriately normed (SCAN) density functional, provides such a description of water. SCAN accurately describes the balance among covalent bonds, hydrogen bonds, and van der Waals interactions that dictates the structure and dynamics of liquid water. Notably, SCAN captures the density difference between water and ice I{\it h} at ambient conditions, as well as many important structural, electronic, and dynamic properties of liquid water. These successful predictions of the versatile SCAN functional open the gates to study complex processes in aqueous phase chemistry and the interactions of water with other materials in an efficient, accurate, and predictive, ab initio manner

Lifshitz transition and van Hove singularity in a Topological Dirac Semimetal

A topological Dirac semimetal is a novel state of quantum matter which has recently attracted much attention as an apparent 3D version of graphene. In this paper, we report critically important results on the electronic structure of the 3D Dirac semimetal Na3Bi at a surface that reveals its nontrivial groundstate. Our studies, for the first time, reveal that the two 3D Dirac cones go through a topological change in the constant energy contour as a function of the binding energy, featuring a Lifshitz point, which is missing in a strict 3D analog of graphene (in other words Na3Bi is not a true 3D analog of graphene). Our results identify the first example of a band saddle point singularity in 3D Dirac materials. This is in contrast to its 2D analogs such as graphene and the helical Dirac surface states of a topological insulator. The observation of multiple Dirac nodes in Na3Bi connecting via a Lifshitz point along its crystalline rotational axis away from the Kramers point serves as a decisive signature for the symmetry-protected nature of the Dirac semimetal's topological groundstate.Comment: 5 pages, 4 Figures, Related papers on topological Fermi arcs and Weyl Semimetals (WSMs) are at http://physics.princeton.edu/zahidhasangroup/index.htm

Energy hole mitigation through cooperative transmission in wireless sensor networks

The energy balancing capability of cooperative communication is utilized to solve the energy hole problem in wireless sensor networks. We first propose a cooperative transmission strategy, where intermediate nodes participate in two cooperative multi-input single-output (MISO) transmissions with the node at the previous hop and a selected node at the next hop, respectively. Then, we study the optimization problems for power allocation of the cooperative transmission strategy by examining two different approaches: network lifetime maximization (NLM) and energy consumption minimization (ECM). For NLM, the numerical optimal solution is derived and a searching algorithm for suboptimal solution is provided when the optimal solution does not exist. For ECM, a closed-form solution is obtained. Numerical and simulation results show that both the approaches have much longer network lifetime than SISO transmission strategies and other cooperative communication schemes. Moreover, NLM which features energy balancing outperforms ECM which focuses on energy efficiency, in the network lifetime sense

Scalar-Torsion Mode in a Cosmological Model of the Poincar\'{e} Gauge Theory of Gravity

We investigate the equation of state (EoS) of the scalar-torsion mode in Poincar\'{e} gauge theory of gravity. We concentrate on two cases with the constant curvature solution and positive kinetic energy, respectively. In the former, we find that the torsion EoS has different values in the various stages of the universe. In particular, it behaves like the radiation (matter) EoS of $w_r=1/3$ ($w_m=0$) in the radiation (matter) dominant epoch, while in the late time the torsion density is supportive for the accelerating universe. In the latter, our numerical analysis shows that in general the EoS has an asymptotic behavior in the high redshift regime, while it could cross the phantom divide line in the low redshift regime.Comment: 12 pages, 2 figures, title changed, revised version accepted for publication in JCA

Supercooled Water and the Kinetic Glass Transition II: Collective Dynamics

In this article we study in detail the Q-vector dependence of the collective dynamics in simulated deeply supercooled SPC/E water. The evolution of the system has been followed for 250 ns at low T, allowing a clear identification of a two step relaxation process. We present evidence in favor of the use of the mode coupling theory for supercooled liquid as framework for the description of the slow alpha-relaxation dynamics in SPC/E water, notwithstanding the fact that the cage formation in this system is controlled by the formation of an open network of hydrogen bonds as opposed to packing constraints, as in the case of simple liquids.Comment: rev-tex + 9 figure

Mass Determination in SUSY-like Events with Missing Energy

We describe a kinematic method which is capable of determining the overall mass scale in SUSY-like events at a hadron collider with two missing (dark matter) particles. We focus on the kinematic topology in which a pair of identical particles is produced with each decaying to two leptons and an invisible particle (schematically, $pp\to YY+jets$ followed by each $Y$ decaying via $Y\to \ell X\to \ell\ell'N$ where $N$ is invisible). This topology arises in many SUSY processes such as squark and gluino production and decay, not to mention t\anti t di-lepton decays. In the example where the final state leptons are all muons, our errors on the masses of the particles $Y$, $X$ and $N$ in the decay chain range from 4 GeV for 2000 events after cuts to 13 GeV for 400 events after cuts. Errors for mass differences are much smaller. Our ability to determine masses comes from considering all the kinematic information in the event, including the missing momentum, in conjunction with the quadratic constraints that arise from the $Y$, $X$ and $N$ mass-shell conditions. Realistic missing momentum and lepton momenta uncertainties are included in the analysis.Comment: 41 pages, 14 figures, various clarifications and expanded discussion included in revised version that conforms to the version to be publishe

Herschel HIFI observations of O2_2 toward Orion: special conditions for shock enhanced emission

We report observations of molecular oxygen (O$_2$) rotational transitions at 487 GHz, 774 GHz, and 1121 GHz toward Orion Peak A. The O2 lines at 487 GHz and 774 GHz are detected at velocities of 10-12 km/s with line widths 3 km/s; however, the transition at 1121 GHz is not detected. The observed line characteristics, combined with the results of earlier observations, suggest that the region responsible for the O$_2$ emission is 9" (6e16 cm) in size, and is located close to the H2 Peak 1position (where vibrationally-excited H$_2$ emission peaks), and not at Peak A, 23" away. The peak O2 column density is 1.1e18/cm2. The line velocity is close to that of 621 GHz water maser emission found in this portion of the Orion Molecular Cloud, and having a shock with velocity vector lying nearly in the plane of the sky is consistent with producing maximum maser gain along the line-of-sight. The enhanced O$_2$ abundance compared to that generally found in dense interstellar clouds can be explained by passage of a low-velocity C-shock through a clump with preshock density 2e4/cm3, if a reasonable flux of UV radiation is present. The postshock O$_2$ can explain the emission from the source if its line of sight dimension is ~10 times larger than its size on the plane of the sky. The special geometry and conditions required may explain why O$_2$ emission has not been detected in the cores of other massive star-forming molecular clouds.Comment: 28 pages, 13 figure