Statistical Mechanics and Thermodynamics: Boltzmann’s versus Planck’s State Definitions and Counting

During the physical foundation of his radiation formula in his December 1900 talk and subsequent 1901 article, Planck refers to Boltzmann’s 1877 combinatorial-probabilistic treatment and obtains his quantum distribution function, while Boltzmann did not. For this, Boltzmann’s memoirs are usually ascribed to classical statistical mechanics. Agreeing with Bach, it is shown that Boltzmann’s 1868 and 1877 calculations can lead to a Planckian distribution function, where those of 1868 are even closer to Planck than that of 1877. Boltzmann’s and Planck’s calculations are compared based on Bach’s three-level scheme ‘configuration–occupation–occupancy’. Special attention is paid to the concepts of interchangeability and the indistinguishability of particles and states. In contrast to Bach, the level of exposition is most elementary. I hope to make Boltzmann’s work better known in English and to remove misunderstandings in the literature.

Quantum Distribution-function Transport Equations in Non-normal Systems and in Ultra-fast Dynamics of Optically-excited Semiconductors

The derivation of the quantum distribution-function transport equations combines the Liouvillian super-Green's function technique and the lattice Weyl-Wigner formulation of the quantum theory of solids. A generating super-functional is constructed which allows an algebraic and straightforward application of quantum field-theoretical techniques in real time to derive coupled quantum-transport, condensate, and pairwavefunction equations. In optically-excited semiconductors, quantum distributionfunction transport equations are given for phonons, plasmons, photons, and electron-hole pairs and excitons by transforming the Bethe-Salpeter equation into a multi-time evolution equation. The virtue of quantum distribution function is that it allows easy application of ‘device-inflow’ subsidiary boundary conditions for simulating femtosecond device-switching phenomena.