2015/09/25 by Dima Bolmatov, D. V. Zav’yalov, Dmitry Zav’yalov +4 · 60 citations
Engineering · Materials Science · Physics and Astronomy · #Acoustic Wave Phenomena Research #Advanced Thermodynamics and Statistical Mechanics #Condensed matter physics #Debye #Hamiltonian (control theory) #Ideal gas #Material Dynamics and Properties #Phonon #Physics #Quantum mechanics #Statistical physics #Thermodynamic limit #cond-mat.mtrl-sci #cond-mat.soft #cond-mat.stat-mech
paper · pdf · doi:10.1016/j.aop.2015.09.018
published in Annals of Physics 363, 221-242 (Elsevier BV) · 21 pages, 7 figures, 3 tables
openalex publication_date 2015/09/25 · arxiv created 2015/12/22 · arxiv updated 2015/12/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We introduce a unified approach to states of matter (solid, liquid and gas) and describe the thermodynamics of the pressure-temperature phase diagram in terms of phonon excitations. We derive the effective Hamiltonian with low-energy cutoff in two transverse phonon polarizations (phononic band gaps) by breaking the symmetry in phonon interactions. Further, we construct the statistical mechanics of states of aggregation employing the Debye approximation. The introduced formalism covers the Debye theory of solids, the phonon theory of liquids, and thermodynamic limits such as the Dulong-Petit thermodynamic limit, the ideal gas limit and the new thermodynamic limit, dubbed here the Frenkel line thermodynamic limit. We discuss the phonon propagation and localization effects in liquids above and below the Frenkel line, and explain the "fast sound" phenomenon. As a test for our theory we calculate velocity-velocity autocorrelation and pair distribution functions within the Green-Kubo formalism. We show the consistency between dynamics of phonons and pair correlations in the framework of the unified approach. New directions towards advancements in phononic band gaps engineering, hypersound manipulation technologies and exploration of exotic behaviour of fluids relevant to geo- and planetary sciences are discussed. The presented results are equally important both for practical implications and for fundamental research.