Mott transition in one dimension: Benchmarking dynamical cluster approaches

The variational cluster approach (VCA) is applied to the one-dimensional Hubbard model at zero temperature using clusters (chains) of up to ten sites with full diagonalization and the Lanczos method as cluster solver. Within the framework of the self-energy-functional theory (SFT), different cluster reference systems with and without bath degrees of freedom, in different topologies and with different sets of variational parameters are considered. Static and one-particle dynamical quantities are calculated for half-filling as a function of U as well as for fixed U as a function of the chemical potential to study the interaction- and filling-dependent metal-insulator (Mott) transition. The recently developed Q-matrix technique is used to compute the SFT grand potential. For benchmarking purposes we compare the VCA results with exact results available from the Bethe ansatz, with essentially exact dynamical DMRG data, with (cellular) dynamical mean-field theory and full diagonalization of isolated Hubbard chains. Several issues are discussed including convergence of the results with cluster size, the ability of cluster approaches to access the critical regime of the Mott transition, efficiency in the optimization of correlated-site vs. bath-site parameters and of multi-dimensional parameter optimization. We also study the role of bath sites for the description of excitation properties and as charge reservoirs for the description of filling dependencies. The VCA turns out to be a computationally cheap method which is competitive with established cluster approaches.Comment: 19 pages, 19 figures, v3 with minor corrections, extended discussio

In-field fuel use and load states of agricultural field machinery

The ability to define in-field tractor load states offers the potential to better specify and characterize fuel consumption rate for various field operations. For the same field operation, the tractor experiences diverse load demands and corresponding fuel use rates as it maneuvers through straight passes, turns, suspended operation for adjustments, repair and maintenance, and biomass or other material transfer operations. It is challenging to determine the actual fuel rate and load states of agricultural machinery using force prediction models, and hence, some form of in-field data acquisition capability is required. Controller Area Networks (CAN) available on the current model tractors provide engine performance data which can be used to determine tractor load states in field conditions. In this study, CAN message data containing fuel rate, engine speed and percent torque were logged from the tractor’s diagnostic port during anhydrous NH3 application, field cultivation and planting operations. Time series and frequency plots of fuel rate and percent torque were generated to evaluate tractor load states. Based on the percent torque, engine speed and rated engine power, actual load on the tractor was calculated in each tractor load state. Anhydrous NH3 application and field cultivation were characterized by three distinct tractor load states (TS-I, TS-II and TS-III) corresponding to idle states, parallel and headland passes, and turns, whereas corn planting was characterized by two load states (TS-I and TS-II): idle, and a combined state with parallel, headland passes and turns. For anhydrous NH3 application and field cultivation at ground speeds of 7.64 km h–1 and 8.68 km h–1, average tractor load per tool and fuel use rate per tool of the implement were found to be 7.21 kW tool–1, 3.28 L h–1 tool–1, and 1.31 kW tool–1, 0.64 L h–1 tool–1, respectively. For planting, average tractor load per row and fuel use rate per row were found to be 4.65 kW row–1 and 1.70 L h–1 row–1 at a ground speed of 7.04 km h–1

Strange Particle Production at RHIC

We report STAR measurements of mid-rapidity yields for the $\Lambda$, $\bar{\Lambda}$, $K^{0}_{S}$, $\Xi^{-}$, $\bar{\Xi}^{+}$, $\Omega^{-}$, and $\bar{\Omega}^{+}$ particles in Cu+Cu and Au+Au $\sqrt{s_{NN}} = 200$ GeV collisions. We show that at a given number of participating nucleons, bulk strangeness production is higher in Cu+Cu collisions compared to Au+Au collisions at the same center of mass energy, counter to predictions from the Canonical formalism. We compare both the Cu+Cu and Au+Au yields to AMPT and EPOS predictions, and find they reproduce key qualitative aspects of the data. Finally, we investigate other scaling parameters and find bulk strangeness production for both the measured data and theoretical predictions, scales better with the number participants that undergo more than one collision.Comment: Conference proceedings for Hot Quarks 2008, 5 pages and 4 figure

Energy and centrality dependences of charged multiplicity density in relativistic nuclear collisions

Using a hadron and string cascade model, JPCIAE, the energy and centrality dependences of charged particle pseudorapidity density in relativistic nuclear collisions were studied. Within the framework of this model, both the relativistic $p+\bar p$ experimental data and the PHOBOS and PHENIX $Au+Au$ data at $\sqrt s_{nn}$=130 GeV could be reproduced fairly well without retuning the model parameters. The predictions for full RHIC energy $Au+Au$ collisions and for $Pb+Pb$ collisions at the ALICE energy were given. Participant nucleon distributions were calculated based on different methods. It was found that the number of participant nucleons, $$, is not a well defined variable both experimentally and theoretically. Therefore, it is inappropriate to use charged particle pseudorapidity density per participant pair as a function of$$ for distinguishing various theoretical models.Comment: 10 pages, 4 figures, submitted to Phy. Lett.

Werner states and the two-spinors Heisenberg anti-ferromagnet

We ascertain, following ideas of Arnesen, Bose, and Vedral concerning thermal entanglement [Phys. Rev. Lett. {\bf 87} (2001) 017901] and using the statistical tool called {\it entropic non-triviality} [Lamberti, Martin, Plastino, and Rosso, Physica A {\bf 334} (2004) 119], that there is a one to one correspondence between (i) the mixing coefficient $x$ of a Werner state, on the one hand, and (ii) the temperature $T$ of the one-dimensional Heisenberg two-spin chain with a magnetic field $B$ along the $z-$axis, on the other one. This is true for each value of $B$ below a certain critical value $B_c$. The pertinent mapping depends on the particular $B-$value one selects within such a range

Competition of crystal field splitting and Hund's rule coupling in two-orbital magnetic metal-insulator transitions

Competition of crystal field splitting and Hund's rule coupling in magnetic metal-insulator transitions of half-filled two-orbital Hubbard model is investigated by multi-orbital slave-boson mean field theory. We show that with the increase of Coulomb correlation, the system firstly transits from a paramagnetic (PM) metal to a {\it N\'{e}el} antiferromagnetic (AFM) Mott insulator, or a nonmagnetic orbital insulator, depending on the competition of crystal field splitting and the Hund's rule coupling. The different AFM Mott insulator, PM metal and orbital insulating phase are none, partially and fully orbital polarized, respectively. For a small $J_{H}$ and a finite crystal field, the orbital insulator is robust. Although the system is nonmagnetic, the phase boundary of the orbital insulator transition obviously shifts to the small $U$ regime after the magnetic correlations is taken into account. These results demonstrate that large crystal field splitting favors the formation of the orbital insulating phase, while large Hund's rule coupling tends to destroy it, driving the low-spin to high-spin transition.Comment: 4 pages, 4 figure

New determination of structure parameters in strong field tunneling ionization theory of molecules

In the strong field molecular tunneling ionization theory of Tong et al. [Phys. Rev. A 66, 033402 (2002)], the ionization rate depends on the asymptotic wavefunction of the molecular orbital from which the electron is removed. The orbital wavefunctions obtained from standard quantum chemistry packages in general are not good enough in the asymptotic region. Here we construct a one-electron model potential for several linear molecules using density functional theory (DFT). We show that the asymptotic wavefunction can be improved with an iteration method and after one iteration accurate asymptotic wavefunctions and structure parameters are determined. With the new parameters we examine the alignment-dependent tunneling ionization probabilities for several molecules and compare with other calculations and with recent measurements, including ionization from inner molecular orbitals

Valence bond solid formalism for d-level one-way quantum computation

The d-level or qudit one-way quantum computer (d1WQC) is described using the valence bond solid formalism and the generalised Pauli group. This formalism provides a transparent means of deriving measurement patterns for the implementation of quantum gates in the computational model. We introduce a new universal set of qudit gates and use it to give a constructive proof of the universality of d1WQC. We characterise the set of gates that can be performed in one parallel time step in this model.Comment: 26 pages, 9 figures. Published in Journal of Physics A: Mathematical and Genera