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Statistical mechanics of impurity states I. General treatment
Author(s) -
Foglio M. E.
Publication year - 1978
Publication title -
physica status solidi (b)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.51
H-Index - 109
eISSN - 1521-3951
pISSN - 0370-1972
DOI - 10.1002/pssb.2220860203
Subject(s) - statistical mechanics , grand canonical ensemble , creation and annihilation operators , impurity , hamiltonian (control theory) , statistical ensemble , annihilation , canonical ensemble , statistical physics , physics , mathematics , quantum mechanics , statistics , mathematical optimization , quantum , monte carlo method
Creation and annihilation operators that replace one ion in a crystal by an impurity in one of a set of states are defined. To use statistical mechanics with these operators, an ensemble that is close to the grand canonical ensemble is introduced. From the model Hamiltonian (given at a fixed value of the volume per crystal site) and the empirical knowledge of the pressure, most of the thermodynamic quantities are derived. A simple example is worked out in detail.