Ground state energy of the low density Hubbard model. An upper bound

We derive an upper bound on the ground state energy of the three-dimensional (3D) repulsive Hubbard model on the cubic lattice agreeing in the low density limit with the known asymptotic expression of the ground state energy of the dilute Fermi gas in the continuum. As a corollary, we prove an old conjecture on the low density behavior of the 3D Hubbard model, i.e., that the total spin of the ground state vanishes as the density goes to zero.Comment: 13 pages; Version accepted for publication on the Journal of Mathematical Physics; minor change

Model-independent assessment of current direct searches for spin-dependent dark matter

I evaluate the current results of spin-dependent weakly interacting massive particle (WIMP) searches within a model-independent framework, showing the most restrictive limits to date derive from the combination of xenon and sodium iodide experiments. The extension of this analysis to the case of positive signal experiments is elaborated.Comment: 4 pages, 4 figures, revised and accepted for publication on Phys. Rev. Let

Effect of model selection on combustor performance and stability predictions using ROCCID

The ROCket Combustor Interactive Design (ROCCID) methodology is an interactive computer program that combines previously developed combustion analysis models to calculate the combustion performance and stability of liquid rocket engines. Test data from 213 kN (48,000 lbf) Liquid Oxygen (LOX)/RP-1 combustor with an O-F-O (oxidizer-fuel-oxidizer) triplet injector were used to characterize the predictive capabilities of the ROCCID analysis models for this injector/propellant configuration. Thirteen combustion performance and stability models were incorporated into ROCCID, and ten of them, which have options for triplet injectors, were examined. Calculations using different combinations of analysis models, with little or no anchoring, were carried out on a test matrix of operating combinations matching those of the test program. Results of the computer analyses were compared to test data, and the ability of the model combinations to correctly predict combustion stability or instability was determined. For the best model combination(s), sensitivity of the calculations to fuel drop size and mixing efficiency was examined. Error in the stability calculations due to uncertainty in the pressure interaction index (N) was examined. The recommended model combinations for this O-F-O triplet LOX/RP-1 configuration are proposed

Non-adiabatic electron dynamics in time-dependent density-functional theory

Time-dependent density-functional theory (TDDFT) treats dynamical exchange and correlation (xc) via a single-particle potential, Vxc(r,t), defined as a nonlocal functional of the density n(r',t'). The popular adiabatic local-density approximation (ALDA) for Vxc(r,t) uses only densities at the same space-time point (r,t). To go beyond the ALDA, two local approximations have been proposed based on quantum hydrodynamics and elasticity theory: (a) using the current as basic variable (C-TDDFT) [G. Vignale, C. A. Ullrich, and S. Conti, Phys. Rev. Lett. 79, 4878 (1997)], (b) working in a co-moving Lagrangian reference frame (L-TDDFT) [I. V. Tokatly, Phys. Rev. B 71, 165105 (2005)]. This paper illustrates, compares, and analyzes both non-adiabatic theories for simple time-dependent model densities in the linear and nonlinear regime, for a broad range of time and frequency scales. C- and L-TDDFT are identical in certain limits, but in general exhibit qualitative and quantitative differences in their respective treatment of elastic and dissipative electron dynamics. In situations where the electronic density rapidly undergoes large deformations, it is found that non-adiabatic effects can become significant, causing the ALDA to break down.Comment: 15 pages, 15 figure

To what extent can dynamical models describe statistical features of turbulent flows?

Statistical features of "bursty" behaviour in charged and neutral fluid turbulence, are compared to statistics of intermittent events in a GOY shell model, and avalanches in different models of Self Organized Criticality (SOC). It is found that inter-burst times show a power law distribution for turbulent samples and for the shell model, a property which is shared only in a particular case of the running sandpile model. The breakdown of self-similarity generated by isolated events observed in the turbulent samples, is well reproduced by the shell model, while it is absent in all SOC models considered. On this base, we conclude that SOC models are not adequate to mimic fluid turbulence, while the GOY shell model constitutes a better candidate to describe the gross features of turbulence.Comment: 14 pages, 4 figures, in press on Europhys. Lett. (may 2002

On the "Causality Paradox" of Time-Dependent Density Functional Theory

I show that the so-called causality paradox of time-dependent density functional theory arises from an incorrect formulation of the variational principle for the time evolution of the density. The correct formulation not only resolves the paradox in real time, but also leads to a new expression for the causal exchange-correlation kernel in terms of Berry curvature. Furthermore, I show that all the results that were previously derived from symmetries of the action functional remain valid in the present formulation. Finally, I develop a model functional theory which explicitly demonstrates the workings of the new formulation.Comment: 21 page

Universal conductivity and dimensional crossover in multi-layer graphene

We show, by exact Renormalization Group methods, that in multi-layer graphene the dimensional crossover energy scale is decreased by the intra-layer interaction, and that for temperatures and frequencies greater than such scale the conductivity is close to the one of a stack of independent layers up to small corrections

Striped periodic minimizers of a two-dimensional model for martensitic phase transitions

In this paper we consider a simplified two-dimensional scalar model for the formation of mesoscopic domain patterns in martensitic shape-memory alloys at the interface between a region occupied by the parent (austenite) phase and a region occupied by the product (martensite) phase, which can occur in two variants (twins). The model, first proposed by Kohn and Mueller, is defined by the following functional: $${\cal E}(u)=\beta||u(0,\cdot)||^2_{H^{1/2}([0,h])}+ \int_{0}^{L} dx \int_0^h dy \big(|u_x|^2 + \epsilon |u_{yy}| \big)$$ where $u:[0,L]\times[0,h]\to R$ is periodic in $y$ and $u_y=\pm 1$ almost everywhere. Conti proved that if $\beta\gtrsim\epsilon L/h^2$ then the minimal specific energy scales like $\sim \min\{(\epsilon\beta/L)^{1/2}, (\epsilon/L)^{2/3}\}$, as $(\epsilon/L)\to 0$. In the regime $(\epsilon\beta/L)^{1/2}\ll (\epsilon/L)^{2/3}$, we improve Conti's results, by computing exactly the minimal energy and by proving that minimizers are periodic one-dimensional sawtooth functions.Comment: 29 pages, 3 figure