Fast Fourier-Chebyshev Approach to Real-Space Simulations of the Kubo Formula.

The Kubo formula is a cornerstone in our understanding of near-equilibrium transport phenomena. While conceptually elegant, the application of Kubo's linear-response theory to interesting problems is hindered by the need for algorithms that are accurate and scalable to large lattice sizes beyond one spatial dimension. Here, we propose a general framework to numerically study large systems, which combines the spectral accuracy of Chebyshev expansions with the efficiency of divide-and-conquer methods.

KITE: high-performance accurate modelling of electronic structure and response functions of large molecules, disordered crystals and heterostructures.

We present KITE, a general purpose open-source tight-binding software for accurate real-space simulations of electronic structure and quantum transport properties of large-scale molecular and condensed systems with tens of billions of atomic orbitals ( ∼ 10). KITE's core is written in C++, with a versatile Python-based interface, and is fully optimized for shared memory multi-node CPU architectures, thus scalable, efficient and fast. At the core of KITE is a seamless spectral expansion of lattice Green's functions, which enables large-scale calculations of generic target functions with uniform convergence and fine control over energy resolution.

Taming chaos to sample rare events: The effect of weak chaos.

Rare events in nonlinear dynamical systems are difficult to sample because of the sensitivity to perturbations of initial conditions and of complex landscapes in phase space. Here, we discuss strategies to control these difficulties and succeed in obtaining an efficient sampling within a Metropolis-Hastings Monte Carlo framework. After reviewing previous successes in the case of strongly chaotic systems, we discuss the case of weakly chaotic systems.