Is Classical Statistical Mechanics Self-Consistent? (A paper in honour of C. F. von Weizsacker, 1912-2007)

Б. И. Садовников, M. Kh. Kharrasov

Giovanni Ciccotti, S. Caprara, Federica Agostini

P. Enders

In addition to his outstanding achievements in physics and activities in policy,C.-F. von Weizsacker is famous for his talks, given as a member of the Academy¨Leopoldina. Due to the latter, I could learn quite a lot from his methodologicalwritings. In particular, he is the only modern thinker I’m aware of who has pointedto the difference between Newton’s and Laplace’s notions of state. But this differenceis essential for the relationship between classical and quantum physics. Moreover it isthe clue to overcoming Gibbs’ paradox within classical statistical mechanics itself.

Brandon P. van Zyl, Aaron Farrell, E. Zaremba +3 more

The average-density approximation is used to construct a nonlocal kinetic energy functional for an inhomogeneous two-dimensional Fermi gas. This functional is then used to formulate a Thomas-Fermi-von Weizs\"acker-like theory for the description of the ground-state properties of the system. The quality of the kinetic energy functional is tested by performing a fully self-consistent calculation for an ideal, harmonically confined, two-dimensional system. Good agreement with exact results are found, with the number and kinetic energy densities exhibiting oscillatory structure associated with the nonlocality of the energy functional. Most importantly, this functional shows a marked improvement over the two-dimensional Thomas-Fermi von Weizs\"acker theory, particularly in the vicinity of the classically forbidden region.

Walter Felipe Wreszinski, G. Scharf

Brandon P. van Zyl, E. Zaremba, P. Pisarski

We systematically develop a density functional description for the equilibrium properties of a two-dimensional, harmonically trapped, spin-polarized dipolar Fermi gas based on the Thomas--Fermi--von Weizs\"acker approximation. We pay particular attention to the construction of the two-dimensional kinetic energy functional, where corrections beyond the local density approximation must be motivated with care. We also present an intuitive derivation of the interaction energy functional associated with the dipolar interactions and provide physical insight into why it can be represented as a local functional. Finally, a simple and highly efficient self-consistent numerical procedure is developed to determine the equilibrium density of the system for a range of dipole interaction strengths.