# Quantum Critical Paraelectrics and the Casimir Effect in Time

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Quantum Critical Paraelectrics and the Casimir Effect in Time**

We study the quantum paraelectric-ferroelectric transition near a quantum critical point, emphasizing the role of temperature as a -finite size effect- in time. The influence of temperature near quantum criticality may thus be likened to a temporal Casimir effect. The resulting finite-size scaling approach yields $\frac{1}{T^2}$ behavior of the paraelectric susceptibility $\chi$ and the scaling form $\chi\omega,T = \frac{1}{\omega^2} F\frac{\omega}{T}$, recovering results previously found by more technical methods. We use a Gaussian theory to illustrate how these temperature-dependences emerge from a microscopic approach; we characterize the classical-quantum crossover in $\chi$, and the resulting phase diagram is presented. We also show that coupling to an acoustic phonon at low temperatures $T$ is relevant and influences the transition line, possibly resulting in a reentrant quantum ferroelectric phase. Observable consequences of our approach for measurements on specific paraelectric materials at low temperatures are discussed.

Author: **L. Palova; P. Chandra; P. Coleman**

Source: https://archive.org/