The Quantum-Statistical Canonical and Grand Canonical Ensembles

Yu. R. Dashyan

Diego R. Alcoba, Roberto C. Bochicchio, G. E. Massacessi +2 more

We deal with many-electron systems having a noninteger number of electrons, which cannot be described properly by means of pure states or by canonical statistical ensemble states. The study of the one-electron reduced density matrix for these systems raises the problem of its representability in statistical ensembles of grand canonical type. We derive the necessary and sufficient conditions for the representability of the one-electron reduced density matrix of grand-canonical statistical ensembles.

Second Quantization

In this chapter we introduce the many-body Hamiltonian for the N -electron system and rewrite it in terms of annihilation and creation operators. This rewriting is called second quantization. We introduce the canonical and the grand canonical ensemble which is the framework in which quantum statistical mechanics has to be formulated. By considering the ideal Fermi gas, we try to motivate that the grand canonical ensemble may be more practical for computations than the canonical ensemble.

Gregor Skačej, P. Ziherl

Alfredo M. Ozorio de Almeida, Gert‐Ludwig Ingold, Olivier Brodier