By an exact numerical calculation of the BCS pair wavefunction and the density correlation functions both between atoms in the same and in different spin states, we extract the spatial large distance behavior of the respective functions. After different initial transients, those distributions show an algebraic dependence accompanied with their own exponential decay and a well defined periodic oscillatory behavior. While in general, in the BCS side there are long-range correlations and in the BEC region the behavior is dominated by tight pairs formation, each distribution shows its own overall behavior. We derive analytic expressions for the mean pair size and the correlation lengths of the same and different density correlation functions. The whole analysis yields a quite complete description of the spatial structure of the superfluid along the crossover. arXiv:1910.10616v1 [cond-mat.quant-gas]

In this work, the effect of strain on the electronic structure of graphene modeled by several singleorbital third-nearest-neighbors tight-binding models is examined. The Hasegawa et al. conditions for gap opening in graphene under uniform tensile strain are revised to include up to third-nearest-neighbor interactions using parameters available in the literature. A comparison with ab initio density functional theory (DFT) calculations shows discrepancies. Based on the DFT calculations and through the projection of the Kohn−Sham wavefunctions into localized orbitals, the disagreement is explained by an angular dependence of the second-and third-nearest-neighbors tight-binding parameters.

No abstract

With the use of thermodynamics and general equilibrium conditions only, we study the entropy of a fluid in the vicinity of the critical point of the liquid–vapor phase transition. By assuming a general form for the coexistence curve in the vicinity of the critical point, we show that the functional dependence of the entropy as a function of energy and particle densities necessarily obeys the scaling form hypothesized by Widom. Our analysis allows for a discussion of the properties of the corresponding scaling function, with the interesting prediction that the critical isotherm has the same functional dependence, between the energy and the number of particles densities, as the coexistence curve. In addition to the derivation of the expected equalities of the critical exponents, the conditions that lead to scaling also imply that, while the specific heat at constant volume can diverge at the critical point, the isothermal compressibility must do so.