Practical DFT-BEC Connections Within Thomas-Fermi Approximation

3 Practical DFT-BEC Connections Within Thomas-Fermi Approximation 

The practical implementation of BEC and of its mean-field approximation usually makes use of thermodynamic limit constraint, namely for systems with many-to-infinite number of particles N oo). The so-called Thomas-Fermi approximation [46, 47] may be used such that the potential and the interaction energies are larger than the kinetic energy, which can be therefore neglected in the stationary Gross-Pitaevsky equation, reducing it to the algebraic form [41, 42]  

The answer is fortunately given by a series of pioneering papers in physics philosophically questioning the significant difference in systems with more or infinitely more components [48-50] the conclusion is simply that 

These may be seen as nothing more than a re-definition of Fermi and Bose statistics, respectively. In other words, when more than one but a finite number of particles are present in a system, the statistical behavior is different than that of single-particle systems, while when an infinite number of particles comes into play, they all tend to behave as in a (the) single-particle case. Moreover, the Anderson assertion may be translated for chemical systems as 

Returning to the Thomas-Fermi approximation, the approximation is indeed in agreement with the thermodynamic limit for bosonic condensation and can also be used for chemical systems, for chemical bonds are present down to the limiting case of single-chemical-bond systems (as in the paradigmatic homopolar bindings of molecular hydrogen and helium, H2 and He2). 

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