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P. D. Bogdanoff and B. Fultz, “The Role of Phonons in the Thermodynamics of the Martensitic Transformation in NiTi,” Philisophical Magazine B, Vol. 81, No. 3, 2001, pp. 299-311. doi:10.1080/13642810108221985

has been cited by the following article:

• TITLE: Hamiltonian of Acoustic Phonons in Inhomogeneous Solids

  AUTHORS: Stanislav Minarik, Vladimir Labas

  KEYWORDS: Phonons; Mass Density; Elastic Coefficient; Energy States; Inhomogeneities; 1D Ionic Chain; Hamiltonian

  JOURNAL NAME: Journal of Modern Physics, Vol.4 No.3, March 22, 2013

  ABSTRACT: Theoretical solid-state physicists formulate their models usually in the form of a Hamiltonian. In quantum mechanics, the Hamilton operator (Hamiltonian) is of fundamental importance in most formulations of quantum theory. Mentioned operator corresponds to the total energy of the system and its spectrum determines the set of possible outcomes when one measures the total energy. Interpretation of results obtained by the applying of models based on the Hamiltonian indicates very specific mechanisms of some observed phenomena that are not fully consistent with the experience. Such approach may occasionally lead to surprises when obtained results are confronted with expectations. The aim of this work is to find Hamilton operator of acoustic phonons in inhomogeneous solids. The transport of energy in the vibrating crystal consisting of ions whose properties differ over long distances is described in the work. We modeled crystal lattice by 1D “inhomogeneous” ionic chain vibrating by acoustic frequencies and found the Hamiltonian of such system in the second quantization. The influence of long-distance inhomogeneities on the acoustic phonons quantum states can be discussed on basis of our results.