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We revisit the quantum phase transition from a paraelectric state to a ferroelectric one and in particular the widespread distinction between a longitudinal modes to transverse one. In contrast to transitions at finite temperature, for a quantum phase transition breaking a discrete symmetry the splitting between the modes is irrelevant. We show that an anisotropy in the context of a quantum phase transition leads to a different behavior, compared to a classical transition, and suggest an experiment to observe it. The result is essential for explaining the pairing mechanism in strontium titanate.
Accurately determining the crystallographic structure of a material, organic or inorganic, is a critical primary step in material development and analysis. The most common practices involve analysis of diffraction patterns produced in laboratory XRD,
The lattice dynamics of the $rm YMnO_3$ magneto-electric compound has been investigated using density functional calculations, both in the ferroelectric and the paraelectric phases. The coherence between the computed and experimental data is very goo
Motivated by recent experimental findings, we study the contribution of a quantum critical optical phonon branch to the thermal conductivity of a paraelectric system. We consider the proximity of the optical phonon branch to transverse acoustic phono
We demonstrate how the quantum paraelectric ground state of SrTiO$_3$ can be accessed via a microscopic $ab~initio$ approach based on density functional theory. At low temperature the quantum fluctuations are strong enough to stabilize the paraelectr
Analysis of the spheroidal modes of vibration of a free elastic sphere show that they can be qualitatively grouped into two categories: primarily longitudinal and primarily transverse. This is not a sharp distinction. However, there is a relatively s