Two approaches for the efficient rational approximation of the Fermi-Dirac function are discussed: one uses the contour integral representation and conformal mapping and the other is based on a version of the multipole representation of the Fermi-Dirac function that uses only simple poles. Both representations have logarithmic computational complexity. They are of great interest for electronic ...

Two approaches for the efficient rational approximation of the Fermi-Dirac function are discussed: one uses the contour integral representation and conformal mapping, and the other is based on a version of the multipole representation of the Fermi-Dirac function that uses only simple poles. Both representations have logarithmic computational complexity. They are of great interest for electronic...

We propose a promising extension of the path integral molecular dynamics method to Bose-Einstein and Fermi-Dirac statistics. The partition function for the quantum statistics was re-written in a form amenable to the molecular dynamics method with the aid of an idea of pseudopotential for the permutation of particles. Our pseudopotential is a rigorous one describing the whole effect of Bose-Eins...

Fermi-Dirac and Bose-Einstein functions arise as quantum statistical distributions. The Riemann zeta function and its extension, the polylogarithm function, arise in the theory of numbers. Though it might not have been expected, these two sets of functions belong to a wider class of functions whose members have operator representations. In particular, we show that the Fermi-Dirac and Bose-Einst...

• Fermi-Dirac integrals appear in problems nuclear astrophysics, solid state physics or the fundamental theory of semiconductor modeling, among others areas application. In this paper, we give new and complete asymptotic expansions for relativistic integral. These could be useful to obtain a correct qualitative understanding Fermi systems. The performance is illustrated with numerical examples.

In this paper, we study the properties of integral functionals induced on LE(S, μ) by closed convex functions on a Euclidean space E. We give sufficient conditions for such integral functions to be strongly rotund (well-posed). We show that in this generality functions such as the Boltzmann-Shannon entropy and the Fermi-Dirac entropy are strongly rotund. We also study convergence in measure and...

We present a coherent picture of the spin-statistics theorem in path integral formulation. The local path integral measure and Lorentz invariant local Lagrangian, when combined with Green’s functions defined in terms of time ordered products, ensure causality regardless of statistics. The Feynman’s m−iǫ prescription ensures the positive energy condition regardless of statistics, and the abnorma...

Based on quantum hydrodynamics theory (QHD), the propagation of nonlinear quantum dust-ion acoustic (QDIA) solitary waves in a ‎collision-less, unmagnetized four component quantum plasma consisting of electrons, positrons, ions and stationary negatively charged ‎dust grains with dust charge variation is investigated using reductive perturbation method. The charging current to the dust grains ca...