Related papers: Interatomic forces, phonons, the Foreman-Lomer The…
Phonons as bosons are different from electrons as fermions. Unlike interatomic electron hopping that can be either positive or negative and further tuned by spin-orbit coupling, interatomic spring constant is positive, or the structure of…
The out-of-plane fluctuations of carbon atoms in a graphene sheet have been studied by means of classical molecular dynamic simulations with an empirical force-field as a function of temperature. The Fourier analysis of the out-of-plane…
Phonon densities of states (DOS) of bcc $\alpha$-$^{57}$Fe were measured from room temperature through the 1044K Curie transition and the 1185K fcc $\gamma$-Fe phase transition using nuclear resonant inelastic x-ray scattering. At higher…
In [18] Fournier and Printems establish a methodology which allows to prove the absolute continuity of the law of the solution of some stochastic equations with H\"{o}lder continuous coefficients. This is of course out of reach by using…
The possibility of making precise predictions for the Casimir force is essential for the theoretical interpretation of current precision experiments on the thermal Casimir effect with metallic plates, especially for sub-micron separations.…
We review calculations and measurements of the phonon-dispersion relation of graphite. First-principles calculations using density-functional theory are generally in good agreement with the experimental data since the long-range character…
We present perturbation theory based on the inverse scattering transform method for solitons described by an equation with the inverse linear dispersion law $\omega\sim 1/k$, where $\omega$ is the frequency and $k$ is the wave number, and…
This article discusses quantum fluctuation properties of a crystal lattice, and in particular, phonon squeezed states. Squeezed states of phonons allow a reduction in the quantum fluctuations of the atomic displacements to below the…
The effect of pressure on the zone-center optical phonon modes of antimony in the A7 structure has been investigated by Raman spectroscopy. The A_g and E_g frequencies exhibit a pronounced softening with increasing pressure, the effect…
Riemann sums, a classical method for approximating the definite integral of a function, have been extensively studied in the past. However, their monotonic properties, while still of great importance, particularly in approximation theory…
We consider a simple quantum system subjected to a classical random force. Under certain conditions it is shown that the noise-averaged Wigner function of the system follows an integro-differential stochastic Liouville equation. In the…
Vibrational dynamics governs the fundamental properties of molecular crystals, shaping their thermodynamics, mechanics, spectroscopy, and transport phenomena. However desirable, the first-principles calculation of solid-state vibrations,…
We theoretically elucidate the boundary conditions for phonon distribution functions of long-wavelength acoustic phonons at smooth crystal interfaces. We first derive boundary conditions that fully incorporate reflection, transmission, and…
This work establishes the algebraic structure of the Kohn-Sham equations to be solved in a density formulation of electron and phonon dynamics, including the superconducting order parameter. A Bogoliubov transform is required to diagonalize…
We prove the murmuration phenomenon, which is a correlation between signs of functional equations and Fourier coefficients, in the case of modular forms in the weight aspect. We in particular improve the range of visibility of murmurations…
We first propose fundamental solutions of wave propagation in one-dimensional dispersive chain subject to a localized initial perturbation in the displacement. Analytical solutions are obtained for both second order nonlinear dispersive…
The breakdown of Hooke's law marks the onset of nonlinear behaviour: when displacements become large, restoring forces weaken and conventional proportionality fails. In quantum materials, intense optical excitation can drive the crystal…
Two different methods for establishing a space-like Coulomb sum rule for the relativistic Fermi gas are compared. Both of them divide the charge response by a normalizing factor such that the reduced response thus obtained fulfills the sum…
We describe a theoretical framework for the interpretation of time-resolved phonon absorption experiments carried out in the fractional quantum Hall regime of a magnetically quantized two-dimensional electron system (2des). The only phonons…
The spectral norm of a Boolean function $f:\{0,1\}^n \to \{-1,1\}$ is the sum of the absolute values of its Fourier coefficients. This quantity provides useful upper and lower bounds on the complexity of a function in areas such as learning…