![]() ![]() We combine large-scale, ab initio electronic structure calculations and the maximally-localised Wannier function (MLWF) approach in order to study the electronic properties of complex nanostructures. Maximally-localised Wannier functions as building blocks of electronic structure Finally, I will show an example of synergy between molecular-dynamics simulation and geometric simulation in the field of protein structure prediction. This in turn allows us to address flexible (slow, low-energy) motions in proteins using the technique of "geometric simulation". Rigidity analysis provides a natural coarse-graining for a simplified model of protein motion. So, we can apply rigidity analysis to protein structures (as obtained from X-ray or neutron crystallography) and identify rigid substructures. The "Molecular Framework Conjecture" states that the "pebble game" is valid for networks with nearest-neighbour and next-nearest-neighbour constraints, or equivalently, to frameworks with fixed bond lengths and angles and variable dihedral angles. ![]() The "pebble game" algorithm can rapidly identify the rigid and stressed regions of a two-dimensional framework. It has been known since Maxwell that a count of degrees of freedom and constraints can establish if a structure is, overall, floppy, rigid or stressed (overconstrained). Rigidity and flexible motion in biomolecules Swimming with a friend at low Reynolds number Interfacial properties of colloidal platelet dispersions Finally, if time allows, I will discuss how these same concepts can be used to answer the question of integrability in equilibrium and in non-equilibrium steady states.įrequency Splitting of Compressional Alfvén Waves Then I will show how these simple but slightly abstract concepts immediately give the full perturbative series (as multiple integrals), without using Feynmann diagrams or Keldysh time-ordering I will discuss the RG-improved results in the IRLM. I will explain how a non-equilibrium steady-state (Hershfield's) density matrix can be defined, why it is related the physical (Schwinger-Keldysh) construction of steady states, and how the dynamics can be encoded into conditions on the Hilbert space ("impurity conditions"). It is a new theoretical framework that I developed recently in the interacting resonant level model (IRLM). After reviewing the topic of quantum impurities with relevant experiments and theoretical ideas, I will present aspects of some recent progress I made. With the present experimental interest in quantum dots and other mesoscopic objects submitted to electric currents, an efficient theoretical framework for studying quantum impurities in non-equilibrium steady states is much needed. ![]() Quantum impurities in non-equilibrium steady states ![]()
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