Stochastic linear scaling for metals and non metals

Total energy electronic structure calculations, based on density functional theory or on the more empirical tight binding approach, are generally believed to scale as the cube of the number of electrons. By using the localisaton property of the high temperature density matrix we present exact deterministic algorithms that scale linearly in one dimension and quadratically in all others. We also introduce a stochastic algorithm that scales linearly with system size. These results hold for metallic and non metallic systems and are substantiated by numerical calculations on model systems.Comment: 9 pages, 2 figure

Non-linear sigma-models in noncommutative geometry: fields with values in finite spaces

We study sigma-models on noncommutative spaces, notably on noncommutative tori. We construct instanton solutions carrying a nontrivial topological charge q and satisfying a Belavin-Polyakov bound. The moduli space of these instantons is conjectured to consists of an ordinary torus endowed with a complex structure times a projective space $CP^{q-1}$.Comment: Latex, 10 page

Quantum field theory on projective modules

We propose a general formulation of perturbative quantum field theory on (finitely generated) projective modules over noncommutative algebras. This is the analogue of scalar field theories with non-trivial topology in the noncommutative realm. We treat in detail the case of Heisenberg modules over noncommutative tori and show how these models can be understood as large rectangular pxq matrix models, in the limit p/q->theta, where theta is a possibly irrational number. We find out that the modele is highly sensitive to the number-theoretical aspect of theta and suffers from an UV/IR-mixing. We give a way to cure the entanglement and prove one-loop renormalizability.Comment: 52 pages, uses feynm

Linear scaling electronic structure calculations and accurate sampling with noisy forces

Numerical simulations based on electronic structure calculations are finding ever growing applications in many areas of physics. A major limiting factor is however the cubic scaling of the algorithms used. Building on previous work [F. R. Krajewski and M. Parrinello, Phys.Rev. B71, 233105 (2005)] we introduce a novel statistical method for evaluating the inter-atomic forces which scales linearly with system size and is applicable also to metals. The method is based on exact decomposition of the fermionic determinant and on a mapping onto a field theoretical expression. We solve exactly the problem of sampling the Boltzmann distribution with noisy forces. This novel approach can be used in such diverse fields as quantum chromodynamics, quantum Monte Carlo or colloidal physics.Comment: 5 pages, 2 figure

Extracellular signal-regulated kinases mediate the enhancing effects of inflammatory mediators on resurgent currents in dorsal root ganglion neurons

Previously we reported that a group of inflammatory mediators significantly enhanced resurgent currents in dorsal root ganglion neurons. To understand the underlying intracellular signaling mechanism, we investigated the effects of inhibition of extracellular signal-regulated kinases and protein kinase C on the enhancing effects of inflammatory mediators on resurgent currents in rat dorsal root ganglion neurons. We found that the extracellular signal-regulated kinases inhibitor U0126 completely prevented the enhancing effects of the inflammatory mediators on both Tetrodotoxin-sensitive and Tetrodotoxin-resistant resurgent currents in both small and medium dorsal root ganglion neurons. U0126 substantially reduced repetitive firing in small dorsal root ganglion neurons exposed to inflammatory mediators, consistent with prevention of resurgent current amplitude increases. The protein kinase C inhibitor Bisindolylmaleimide I also showed attenuating effects on resurgent currents, although to a lesser extent compared to extracellular signal-regulated kinases inhibition. These results indicate a critical role of extracellular signal-regulated kinases signaling in modulating resurgent currents and membrane excitability in dorsal root ganglion neurons treated with inflammatory mediators. It is also suggested that targeting extracellular signal-regulated kinases-resurgent currents might be a useful strategy to reduce inflammatory pain