Journal ArticleDOI
Surface Specific Heat of an Isotropic Solid at Low Temperatures
TLDR
In this paper, the effect of realistic boundary conditions on the computation of the specific heat of an isotropic solid at low temperatures is investigated, and two cases are considered: the surface free of stress and the surface rigidly clamped.Abstract:
The effect of realistic boundary conditions on the computation of the specific heat of an isotropic solid at low temperatures is investigated. Two cases are considered: the surface free of stress and the surface rigidly clamped. The first of these is the one of physical interest. For both cases a term in the specific heat arises which is proportional to the surface area and to T2 and appreciably higher than Montroll's result in the case of the free solid. The effect of approximations introduced during the computation is estimated. Available experimental data are not adequate for a critical test of the theory.read more
Citations
More filters
Journal ArticleDOI
Random-matrix theories in quantum physics : common concepts
TL;DR: A review of the development of random-matrix theory (RMT) during the last fifteen years is given in this paper, with a brief historical survey of the developments of RMT and of localization theory since their inception.
Journal ArticleDOI
Random Matrix Theories in Quantum Physics: Common Concepts
TL;DR: It is suggested that the current development of random-matrix theory signals the emergence of a new “statistical mechanics”: Stochasticity and general symmetry requirements lead to universal laws not based on dynamical principles.
Journal ArticleDOI
Anderson localization of ultrasound
TL;DR: In this article, the authors studied the incoherent transport of ultrasound in two dimensions in the sub-MegaHertz range in an inhomogeneous 30 centimeter square aluminum plate.
Book ChapterDOI
Theoretical and Experimental Aspects of the Effects of Point Defects and Disorder on the Vibrations of Crystals*—2†
TL;DR: In this article, the authors show that more sophisticated models of the impurity atom than that which represents it simply as a particle whose mass differs from that of the atom it replaces seem to be required in many cases.
Journal ArticleDOI
Wave chaos in acoustics and elasticity
Gregor Tanner,Niels Søndergaard +1 more
TL;DR: In this paper, the authors provide an overview over basic concepts in this emerging field of wave chaos, which ranges from ray approximations of the Green function to periodic orbit trace formulae and random matrix theory and summarizes the state of the art in applying these ideas in acoustics.
References
More filters
Journal ArticleDOI
Das asymptotische Verteilungsgesetz der Eigenwerte linearer partieller Differentialgleichungen (mit einer Anwendung auf die Theorie der Hohlraumstrahlung)
Journal ArticleDOI
The Temperature Variation of the Elastic Moduli of NaCl, KCl and MgO
Abstract: The principal adiabatic and isothermal elastic moduli and elastic constants of NaCl, KCl and MgO have been measured over the temperature ranges 80\ifmmode^\circ\else\textdegree\fi{}K to 270\ifmmode^\circ\else\textdegree\fi{}K (Balamuth and Rose) and 270\ifmmode^\circ\else\textdegree\fi{}K to 480\ifmmode^\circ\else\textdegree\fi{}K for NaCl; 80\ifmmode^\circ\else\textdegree\fi{}K to 280\ifmmode^\circ\else\textdegree\fi{}K for KCl; and 80\ifmmode^\circ\else\textdegree\fi{}K to 560\ifmmode^\circ\else\textdegree\fi{}K for MgO. The Debye characteristic temperatures of these substances at 80\ifmmode^\circ\else\textdegree\fi{}K, calculated from the adiabatic elastic constants, are 320\ifmmode^\circ\else\textdegree\fi{}K, 246\ifmmode^\circ\else\textdegree\fi{}K and 946\ifmmode^\circ\else\textdegree\fi{}K, respectively. The variation of the isothermal ${c}_{11}$ and ${c}_{44}$ with temperature is described very accurately by the formula: ${({c}_{\mathrm{ii}})}_{u}={({c}_{\mathrm{ii}})}_{0}\mathrm{exp}(\ensuremath{-}{A}_{\mathrm{ii}}{F}_{\mathrm{ii}}(u))$, where $u=(\frac{T}{\ensuremath{\theta}})$, $T$ is the absolute temperature and $\ensuremath{\theta}$ the characteristic temperature, ${({c}_{\mathrm{ii}})}_{0}$ denotes the value at absolute zero, ${A}_{\mathrm{ii}}$ is a constant of the material, and ${F}_{\mathrm{ii}}(u)$ is a function of $u$ which assumes the value unity when $u=1$, and which is the same for all three substances. Experimental values of ${F}_{11}(u)$ and ${F}_{44}(u)$ are given for values of $u$ between 0.1 and 1.5. The isothermal ${c}_{12}$ does not vary with temperature, over the specified ranges, by more than the error of measurement.
Journal ArticleDOI
Über die Eigenwerte bei den Differentialgleichungen der mathematischen Physik
Journal ArticleDOI
On the heat capacity of crystalline magnesium oxide
TL;DR: The heat capacity of single crystals of magnesium oxide has been measured in the temperature range 3 to 270 $^{o}$K with estimated accuracies of $\pm $0$\cdot $5% for 10 20 $€ o}$k as mentioned in this paper.