The Hubbard model on a complete graph: Exact Analytical results

We derive the analytical expression of the ground state of the Hubbard model with unconstrained hopping at half filling and for arbitrary lattice sites.Comment: Email:[email protected]

Landau-Zener Tunneling of Bose-Einstein Condensates in an Optical Lattice

A theory of the non-symmetric Landau-Zener tunneling of Bose-Einstein condensates in deep optical lattices is presented. It is shown that periodic exchange of matter between the bands is described by a set of linearly coupled nonlinear Schr\"{o}dinger equations. The key role of the modulational instability in rendering the inter-band transitions irreversible is highlighted.Comment: 4 pages, 3 figure

Hierarchy of boundary driven phase transitions in multi-species particle systems

Interacting systems with $K$ driven particle species on a open chain or chains which are coupled at the ends to boundary reservoirs with fixed particle densities are considered. We classify discontinuous and continuous phase transitions which are driven by adiabatic change of boundary conditions. We build minimal paths along which any given boundary driven phase transition (BDPT) is observed and reveal kinetic mechanisms governing these transitions. Combining minimal paths, we can drive the system from a stationary state with all positive characteristic speeds to a state with all negative characteristic speeds, by means of adiabatic changes of the boundary conditions. We show that along such composite paths one generically encounters $Z$ discontinuous and $2(K-Z)$ continuous BDPTs with $Z$ taking values $0\leq Z\leq K$ depending on the path. As model examples we consider solvable exclusion processes with product measure states and $K=1,2,3$ particle species and a non-solvable two-way traffic model. Our findings are confirmed by numerical integration of hydrodynamic limit equations and by Monte Carlo simulations. Results extend straightforwardly to a wide class of driven diffusive systems with several conserved particle species.Comment: 12 pages, 11 figure

Thermal conductance measurements of pressed OFHC copper contacts at liquid helium temperatures

The thermal conductance of oxygen-free high conductivity (OFHC) copper sample pairs with surface finishes ranging from 0.1 to 1.6-micrometers rms roughness was investigated over the range of 1.6 to 6.0-K under applied contact forces up to 670 N. The thermal conductance increases with increasing contact force; however, no correlation can be drawn with respect to surface finish

Thermal conductance of pressed contacts at liquid helium temperatures

The thermal contact conductance of a 0.4 micrometer surface finish OFHC copper sample pair has been investigated from 1.6 to 3.8 K for a range of applied contact forces up to 670 N. Experimental data have been fitted to the relation Q = the integral alpha T to the nth power dt by assuming that the thermal contact conductance is a simple power function of the sample temperature. It has been found that the conductance is proportional to T squared and that conductance increases with an increase in applied contact force. These results confirm earlier work

A comparison of the biodegradation of nitrobenzene, 1-butanol, and 2,4-dichlorphenoxyacetic acid using a municipal mixed liquor and three commercial bacterial preparations

The biological degradation of nitrobenzene, 1-butanol, and 2,4-dichlorophenoxyacetic acid (2,4-D) was studied in aerated 6 liter batch reactors using activated sludge from the Livingston, NJ wastewater treatment plant-- by itself and in a 10:1 by volume mixture with each of three commercial bacterial preparations: Hydrobac, BI-CHEM DC-1006/7, and Liquid Live Microorganisms (LLMO). Air stripping and adsorption were determined to be insignificant removal mechanisms for the three compounds studied. None of the bacterial mixtures were able to degrade 10 ppm nitrobenzene to any significant extent. A small but noticeable improvement in degradation rates occurred when the Livingston sludge was mixed with the commercial preparations in a 10:1 volume ratio. However, such a ratio would be economically impractical. At the manufacturer\u27s recommended ratio of 106:1, the mixture would behave like the Livingston sludge alone

Synthesis of Curcumin Derivatives and Analysis of Their Antitumor Effects in Triple Negative Breast Cancer (TNBC) Cell Lines

We analyzed antitumor effects of a series of curcumin analogues. Some of them were obtained by reaction of substitution involving the two phenolic OH groups of curcumin while the analogues with a substituent at C-4 was prepared following an original procedure that regards the condensation of benzenesulfenic acid onto the nucleophilic central carbon of the curcumin skeleton. We analyzed cytotoxic effects of such derivatives on two TNBC (triple negative breast cancer) cell lines, SUM 149 and MDA-MB-231, but only three of them showed an IC50 in a lower micromolar range with respect to curcumin. We also focused on these three derivatives that in both cell lines exhibited a higher or at least equivalent pro-apoptotic effect than curcumin. The analysis of molecular mechanisms of action of the curcumin derivatives under study has highlighted that they decreased NF-κB transcriptional factor activity, and consequently the expression of some NF-κB targets. Our data confirmed once again that curcumin may represent a very good lead compound to design analogues with higher antitumor capacities and able to overcome drug resistance with respect to conventional ones, even in tumors difficult to treat as TNBC

Thermal conductance of pressed aluminum and stainless steel contacts at liquid helium temperatures

The thermal conductance of aluminum and stainless steel 304 sample pairs with surface finishes ranging from 0.1 to 1.6 microns rms roughness was investigated over a temperature range from 1.6 to 6.0 k. The thermal conductance follows a simple power law function of temperature, with the exponent ranging from 0.5 to 2.25, increases asymptotically with increasing applied force, and exhibits an anomaly for surface finishes in the 0.4 micron region

Soliton ratchets induced by ac forces with harmonic mixing

The ratchet dynamics of a kink (topological soliton) of a dissipative sine-Gordon equation in the presence of ac forces with harmonic mixing (at least bi-harmonic) of zero mean is studied. The dependence of the kink mean velocity on system parameters is investigated numerically and the results are compared with a perturbation analysis based on a point particle representation of the soliton. We find that first order perturbative calculations lead to incomplete descriptions, due to the important role played by the soliton-phonon interaction in establishing the phenomenon. The role played by the temporal symmetry of the system in establishing soliton ratchets is also emphasized. In particular, we show the existence of an asymmetric internal mode on the kink profile which couples to the kink translational mode through the damping in the system. Effective soliton transport is achieved when the internal mode and the external force get phase locked. We find that for kinks driven by bi-harmonic drivers consisting of the superposition of a fundamental driver with its first odd harmonic, the transport arises only due to this {\it internal mode} mechanism, while for bi-harmonic drivers with even harmonic superposition, also a point-particle contribution to the drift velocity is present. The phenomenon is robust enough to survive the presence of thermal noise in the system and can lead to several interesting physical applications.Comment: 9 pages, 13 figure

Compactons in Nonlinear Schr\"odinger Lattices with Strong Nonlinearity Management

The existence of compactons in the discrete nonlinear Schr\"odinger equation in the presence of fast periodic time modulations of the nonlinearity is demonstrated. In the averaged DNLS equation the resulting effective inter-well tunneling depends on modulation parameters {\it and} on the field amplitude. This introduces nonlinear dispersion in the system and can lead to a prototypical realization of single- or multi-site stable discrete compactons in nonlinear optical waveguide and BEC arrays. These structures can dynamically arise out of Gaussian or compactly supported initial data.Comment: 4 pages, 4 figure