Phase diagrams of the 2D t-t'-U Hubbard model from an extended mean field method

It is well-known from unrestricted Hartree-Fock computations that the 2D Hubbard model does not have homogeneous mean field states in significant regions of parameter space away from half filling. This is incompatible with standard mean field theory. We present a simple extension of the mean field method that avoids this problem. As in standard mean field theory, we restrict Hartree-Fock theory to simple translation invariant states describing antiferromagnetism (AF), ferromagnetism (F) and paramagnetism (P), but we use an improved method to implement the doping constraint allowing us to detect when a phase separated state is energetically preferred, e.g. AF and F coexisting at the same time. We find that such mixed phases occur in significant parts of the phase diagrams, making them much richer than the ones from standard mean field theory. Our results for the 2D t-t'-U Hubbard model demonstrate the importance of band structure effects.Comment: 6 pages, 5 figure

The BCS Functional for General Pair Interactions

The Bardeen-Cooper-Schrieffer (BCS) functional has recently received renewed attention as a description of fermionic gases interacting with local pairwise interactions. We present here a rigorous analysis of the BCS functional for general pair interaction potentials. For both zero and positive temperature, we show that the existence of a non-trivial solution of the nonlinear BCS gap equation is equivalent to the existence of a negative eigenvalue of a certain linear operator. From this we conclude the existence of a critical temperature below which the BCS pairing wave function does not vanish identically. For attractive potentials, we prove that the critical temperature is non-zero and exponentially small in the strength of the potential.Comment: Revised Version. To appear in Commun. Math. Phys

Herschel/HIFI deepens the circumstellar NH3 enigma

Circumstellar envelopes (CSEs) of a variety of evolved stars have been found to contain ammonia (NH3) in amounts that exceed predictions from conventional chemical models by many orders of magnitude. The observations reported here were performed in order to better constrain the NH3 abundance in the CSEs of four, quite diverse, oxygen-rich stars using the NH3 ortho J_K = 1_0 - 0_0 ground-state line. We used the Heterodyne Instrument for the Far Infrared aboard Herschel to observe the NH3 J_K = 1_0 - 0_0 transition near 572.5 GHz, simultaneously with the ortho-H2O J_Ka,Kc = 1_1,0 -1_0,1 transition, toward VY CMa, OH 26.5+0.6, IRC+10420, and IK Tau. We conducted non-LTE radiative transfer modeling with the goal to derive the NH3 abundance in these objects' CSEs. For the latter two stars, Very Large Array imaging of NH3 radio-wavelength inversion lines were used to provide further constraints, particularly on the spatial extent of the NH3-emitting regions. Results. We find remarkably strong NH3 emission in all of our objects with the NH3 line intensities rivaling those obtained for the ground state H2O line. The NH3 abundances relative to H2 are very high and range from 2 x 10-7 to 3 x 10-6 for the objects we have studied. Our observations confirm and even deepen the circumstellar NH3 enigma. While our radiative transfer modeling does not yield satisfactory fits to the observed line profiles, it leads to abundance estimates that confirm the very high values found in earlier studies. New ways to tackle this mystery will include further Herschel observations of more NH3 lines and imaging with the Expanded Very Large Array.Comment: 4+2 page

Numerical Investigation of Boundary Conditions for Moving Contact Line Problems

When boundary conditions arising from the usual hydrodynamic assumptions are applied, analyses of dynamic wetting processes lead to a well-known nonintegrable stress singularity at the dynamic contact line, necessitating new ways to model this problem. In this paper, numerical simulations for a set of representative problems are used to explore the possibility of providing material boundary conditions for predictive models of inertialess moving contact line processes. The calculations reveal that up to Capillary number Ca=0.15, the velocity along an arc of radius 10Li (Li is an inner, microscopic length scale! from the dynamic contact line is independent of the macroscopic length scale a for a.103Li , and compares well to the leading order analytical ‘‘modulated-wedge’’ flow field [R. G. Cox, J. Fluid Mech. 168, 169 (1986)] for Capillary number Ca,0.1. Systematic deviations between the numerical and analytical velocity field occur for 0.1168, 169 (1986)] is used as a boundary condition along an arc of radius R=10-2a from the dynamic contact line, agree well with those using two inner slip models for Ca\u3c0.1, with a breakdown at higher Ca. Computations in a cylindrical geometry reveal the role of azimuthal curvature effects on velocity profiles in this vicinity of dynamic contact lines. These calculations show that over an appropriate range of Ca, the velocity field and the meniscus slope in a geometry-independent region can potentially serve as material boundary conditions for models of processes containing dynamic contact lines

Low-Rank Network Decomposition Reveals Structural Characteristics Of Small-World Networks

Small-world networks occur naturally throughout biological, technological, and social systems. With their prevalence, it is particularly important to prudently identify small-world networks and further characterize their unique connection structure with respect to network function. In this work we develop a formalism for classifying networks and identifying small-world structure using a decomposition of network connectivity matrices into low-rank and sparse components, corresponding to connections within clusters of highly connected nodes and sparse interconnections between clusters, respectively. We show that the network decomposition is independent of node indexing and define associated bounded measures of connectivity structure, which provide insight into the clustering and regularity of network connections. While many existing network characterizations rely on constructing benchmark networks for comparison or fail to describe the structural properties of relatively densely connected networks, our classification relies only on the intrinsic network structure and is quite robust with respect to changes in connection density, producing stable results across network realizations. Using this framework, we analyze several real-world networks and reveal new structural properties, which are often indiscernible by previously established characterizations of network connectivity

Single hadron response measurement and calorimeter jet energy scale uncertainty with the ATLAS detector at the LHC

The uncertainty on the calorimeter energy response to jets of particles is derived for the ATLAS experiment at the Large Hadron Collider (LHC). First, the calorimeter response to single isolated charged hadrons is measured and compared to the Monte Carlo simulation using proton-proton collisions at centre-of-mass energies of sqrt(s) = 900 GeV and 7 TeV collected during 2009 and 2010. Then, using the decay of K_s and Lambda particles, the calorimeter response to specific types of particles (positively and negatively charged pions, protons, and anti-protons) is measured and compared to the Monte Carlo predictions. Finally, the jet energy scale uncertainty is determined by propagating the response uncertainty for single charged and neutral particles to jets. The response uncertainty is 2-5% for central isolated hadrons and 1-3% for the final calorimeter jet energy scale.Comment: 24 pages plus author list (36 pages total), 23 figures, 1 table, submitted to European Physical Journal

Standalone vertex finding in the ATLAS muon spectrometer

A dedicated reconstruction algorithm to find decay vertices in the ATLAS muon spectrometer is presented. The algorithm searches the region just upstream of or inside the muon spectrometer volume for multi-particle vertices that originate from the decay of particles with long decay paths. The performance of the algorithm is evaluated using both a sample of simulated Higgs boson events, in which the Higgs boson decays to long-lived neutral particles that in turn decay to bbar b final states, and pp collision data at √s = 7 TeV collected with the ATLAS detector at the LHC during 2011