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The calculation of the density matrix for fermions and bosons in the GrandCanonical Ensemble allows an efficient way for the inclusion of fermionic andbosonic statistics at all temperatures. It is shown that in a Path IntegralFormulation fermionic density matrix can be expressed via an integration over anovel representation of the universal temperature dependent functional. Whileseveral representations for the universal functional have already beendeveloped, they are usually presented in a form inconvenient for computercalculations. In this work we discuss a new representation for the universalfunctional in terms of Hankel functions which is advantageous for computationalapplications. Temperature scaling for the universal functional and itsderivatives are also introduced thus allowing an efficient rescaling ratherthen recalculation of the functional at different temperatures. A simpleillustration of the method of calculation of density profiles in GrandCanonical ensemble is presented using a system of noninteracting electrons in afinite confining potential.Comment: 13 pages 3 figure

Nonzero-temperature path-integral method for fermions and bosons: A grand canonical approach