Related papers: Simple series solutions to specific heat-phonon sp…
In nonmetallic crystals, heat is transported by phonons of different frequencies, each contributing differently to the overall heat flux spectrum. In this study, we demonstrate a significant redistribution of heat flux among phonon…
Analytic solutions for cylindrical thermal waves in solid medium is given based on the nonlinear hyperbolic system of heat flux relaxation and energy conservation equations. The Fourier-Cattaneo phenomenological law is generalized where the…
In this work, we give the power series solutions around an ordinary point, in the case of variable coefficients, homogeneous sequential linear conformable fractional differential equations of order 2\alpha. Further, we introduce the…
A non-reciprocal phonon model for microwave or optical isolators is considered. It gives a simpler framework to further investigate the formerly argued possibility for a heat transfer between black bodies at common temperatures. While the…
Silicon is indispensable in semiconductor industry. Understanding its high-temperature thermodynamic properties is essential both for theory and applications. However, first-principle description of high-temperature thermodynamic properties…
The results on the heat kernel expansion for the electromagnetic field in the background of dielectric media are briefly reviewed. The common approaches to the calculation of the heat kernel coefficients are discussed from the viewpoint of…
The heat equation is considered in the complex medium consisting of many small bodies (particles) embedded in a given material. On the surfaces of the small bodies an impedance boundary condition is imposed. An equation for the limiting…
Precision spectroscopy of solid-state systems is challenging due to inhomogeneous broadening. We describe a technique -- coherent quantum beats -- that enables the measurement of small frequency shifts within an inhomogeneously broadened…
In this paper we consider the heat equation with a strongly singular potential and show that it has a very weak solution. Our analysis is devoted to general hypoelliptic operators and is developed in the setting of graded Lie groups. The…
A simple bulk model of electron-phonon coupling in metals has been surprisingly successful in explaining experiments on metal films that actually involve surface- or other low-dimensional phonons. However, by an exact application of this…
We investigate quantum heat transfer and thermal management in the nonequilibrium qubit-phonon hybrid system by applying the quantum master equation embedded with phononic coherent state. We obtain the steady state heat flow by tuning the…
I give a short guide into applications of the heat kernel technique to string/brane physics with an emphasis on the emerging boundary value problems.
An exactly solvable model in heat conduction is considered. The $C$-integrable (i.e., change-of-variables-integrable) equation for second sound (i.e., heat wave) propagation in a thin, rigid dielectric heat conductor uniformly heated on its…
The rotating linear dilatonic black hole is an asymptotically non-flat solution to Einstein-Maxwell-Dilaton-Axion gravity theory due to the existence of non-trivial matter fields. We have analytically studied the wave equation of scalar…
This paper introduces a new method for solving the planar heat equation based on the Lightning Method. The lightning method is a recent development in the numerical solution of linear PDEs which expresses solutions using sums of polynomials…
In previous works, we used a so-called deformation formula in order to study, in particular, the Borel summability of the heat kernel of some operators. A goal of this paper is to collect miscellaneous remarks related to these works. Here…
I develop here the microscopic quantum theory for description of creation of phonons and rotons in superfluid helium by a solid heater. Starting with correct transfer Hamiltonian describing a coupling between the solid and liquid $^4$He the…
Several past studies have described how absorption spectroscopy can be used to determine spatial temperature variations along the optical path by measuring the unique, nonlinear response to temperature of many molecular absorption…
An inverse source problem for the heat equation is considered. Extraction formulae for information about the time and location when and where the unknown source of the equation firstly appeared are given from a single lateral boundary…
Using a time-resolved phonon absorption technique, we have measured the specific heat of a two-dimensional electron system in the fractional quantum Hall effect regime. For filling factors $\nu = 5/3, 4/3, 2/3, 3/5, 4/7, 2/5$ and 1/3 the…