Cell Model of Quantum Liquids and Solids. I. Crystalline State.
Abstract
A second quantized cell model Hamiltonian is derived to provide a model for quantum crystals and liquids. The Boson crystal is treated in this article. The cells are divided into two sublattices, regular which are usually occupied and interstitial which are usually empty. The particle hard cores are simulated by assuming Fermi commutation relations for operators referring to a single cell; this allows a discussion in terms of a spin analog Hamiltonian which is diagonalized in the spin wave approximation. Because the Hamiltonian includes a term which allows tunneling between regular and interstitial sites, the ground state includes a description of zero point motion and exchange via virtual intermediate interstitial occupation. Excited states include nonlocalized vacancies, interstitials and vacancy-interstitial pairs. Phonon states are not included in this analysis. The model exhibits a phase transition to the Bose condensed state which is examined briefly. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Nov 16, 1970
- Accession Number
- AD0714900
Entities
People
- William J. Mullin
Organizations
- University of Massachusetts Amherst