Related papers: Geometric Theory of Lattice Vibrations and Specifi…
The low-temperature properties of glasses present important differences with respect to crystalline matter. In particular, models such as the Debye model of solids, which assume the existence of an underlying regular lattice, predict that…
Finite temperature quantum field theory in the heat kernel method is used to study the heat capacity of condensed matter. The lattice heat is treated a la P. Debye as energy of the elastic (sound) waves. The dimensionless functional of free…
Realistic phenomena can be described more appropriately using generalized canonical ensemble, with proper parameter sets involved. We have generalized the Einstein's theory for specific heat of solid in Tsallis statistics, where the…
We construct a quantum mechanical model of perfectly isotropic amorphous solids as fuzzy crystals and establish an analytical theory of vibrations for glasses at low temperature. Our theoretical framework relies on the basic principle that…
The successful prediction of the specific heat of solids is a milestone in the kinetic theory of matter, due to Debye (1912). No such success, however, has ever been obtained for the specific heat of liquids, which has remained a mystery…
Self-consistent approach for interacting phonons description in lattice, which generalized Debye model, is proposed. Notion of "self-consistent" phonons is introduced, speed of which depends on temperature and is determined from non-linear…
Low-temperature specific-heat study has been performed on the insulating giant dielectric constant material CaCu3Ti4O12 and two related compounds, Bi2/3Cu3Ti4O12 and La0.5Na0.5Cu3Ti4O12, from 0.6 to 10 K. From analyzing the specific heat…
For a thermodynamic system obeying both the equipartition theorem in high temperature and the third law in low temperature, the curve showing relationship between the specific heat and the temperature has two common behaviors:\ it…
Low-temperature properties of crystalline solids can be understood using harmonic perturbations around a perfect lattice, as in Debye's theory. Low-temperature properties of amorphous solids, however, strongly depart from such descriptions,…
The theoretical model proposed by Einstein to describe the phononic specific heat of solids as a function of temperature consists the very first application of the concept of energy quantization to describe the physical properties of a real…
We extend recent \textit{ab initio} calculations of the electronic band structure and the phonon dispersion relations of rhombohedral GeTe to calculations of the density of phonon states and the temperature dependent specific heat. The…
The question here is whether the Debye model is suited to evaluate the specific heat of nanocrystals. For this, the simplest possible nanocrystal is considered: a basic cubic structure made of atoms that interact through a harmonic…
Using previous results and general thermodynamical formalism,an expression is obtained for the specific heat per particle under constant volume of a degenerate non-relativistic electron gas on a 1D lattice.The result is a non-linear…
In a recent paper (Phys. Rev. E {\bf 104}, 014103 (2021) ) M. Baggioli and A. Zaccone formulate a theoretical description of the specific heat of liquids by using Debye's expression for the specific heat of solids and inserting a density of…
We present the detailed study of the thermodynamics of vibrational modes in disordered elastic systems such as the Bragg glass phase of lattices pinned by quenched impurities. Our study and our results are valid within the (mean field)…
We have developed a new method for evaluating the specific heat of lattice spin systems. It is based on the knowledge of high-temperature series expansions, the total entropy of the system and the low-temperature expected behavior of the…
The field (geometrical) theory of specific heat is based on the universal thermal sum, a new mathematical tool derived from the evolution equation in the Euclidean four-dimensional spacetime, with the closed time coordinate. This theory…
Textbooks introduce the Debye temperature to simplify the integration of the heat capacity. This approach gives the impression that the Debye temperature is a parameter which makes the integration more convenient. The Debye frequency cut…
We study the thermodynamics of the vibrational modes of a lattice pinned by impurity disorder in the absence of topological defects (Bragg glass phase). Using a replica variational method we compute the specific heat $C_v$ in the quantum…
We point out that the repeatedly reported glass-like properties of crystalline materials are not necessarily associated with localized (or quasilocalized) excitations. In real crystals, optical and short-wavelength acoustical vibrations…