Superconductivity close to the Mott state: From condensed-matter systems to superfluidity in optical lattices

Since the discovery of high-temperature superconductivity in 1986 by Bednorz and Mueller, great efforts have been devoted to finding out how and why it works. From the d-wave symmetry of the order parameter, the importance of antiferromagnetic fluctuations, and the presence of a mysterious pseudogap phase close to the Mott state, one can conclude that high-Tc superconductors are clearly distinguishable from the well-understood BCS superconductors. The d-wave superconducting state can be understood through a Gutzwiller-type projected BCS wave-function. In this review article, we revisit the Hubbard model at half-filling and focus on the emergence of exotic superconductivity with d-wave symmetry in the vicinity of the Mott state, starting from ladder systems and then studying the dimensional crossovers to higher dimensions. This allows to confirm that short-range antiferromagnetic fluctuations can mediate superconductivity with d-wave symmetry. Ladders are also nice prototype systems allowing to demonstrate the truncation of the Fermi surface and the emergence of a Resonating Valence Bond (RVB) state with preformed pairs in the vicinity of the Mott state. In two dimensions, a similar scenario emerges from renormalization group arguments. We also discuss theoretical predictions for the d-wave superconducting phase as well as the pseudogap phase, and address the crossover to the overdoped regime. Finally, cold atomic systems with tunable parameters also provide a complementary insight into this outstanding problem.Comment: 98 pages and 18 figures; Final version (references added and misprints corrected

Data from: Timing of head movements is consistent with energy minimization in walking ungulates

Many ungulates show a conspicuous nodding motion of the head when walking. Until now, the functional significance of this behaviour remained unclear. Combining in vivo kinematics of quadrupedal mammals with a computer model, we show that the timing of vertical displacements of the head and neck is consistent with minimizing energy expenditure for carrying these body parts in an inverted pendulum walking gait. Varying the timing of head movements in the model resulted in increased metabolic cost estimate for carrying the head and neck of up to 63%. Oscillations of the head–neck unit result in weight force oscillations transmitted to the forelimbs. Advantageous timing increases the load in single support phases, in which redirecting the trajectory of the centre of mass (COM) is thought to be energetically inexpensive. During double support, in which—according to collision mechanics—directional changes of the impulse of the COM are expensive, the observed timing decreases the load. Because the head and neck comprise approximately 10% of body mass, the effect shown here should also affect the animals' overall energy expenditure. This mechanism, working analogously in high-tech backpacks for energy-saving load carriage, is widespread in ungulates, and provides insight into how animals economize locomotion

Maple worksheet

The .zip folder contains the Maple worksheet used for the publication "Timing of head movements is consistent with energy minimization in walking ungulates"

Loscher et al Matlab Code

The .zip folder contains all Matlab code used for the publication "Timing of head movements is consistent with energy minimization in walking ungulates". SEE README FILE FOR FURTHER EXPLANATIO

Loscher et al_ESM_text and figures from Timing of head movements is consistent with energy minimization in walking ungulates

ESM text describing methods in detail including two figure