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تسجيل مستخدم جديدA Microscopic Field Theory for the Universal Shift of Sound Velocity and Dielectric Constant in Low-Temperature Glasses
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Di Zhou
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In low-temperature glasses, the sound velocity changes as the logarithmic function of temperature below $10$K: $[c(T) - c(T_0)]/c(T_0) = mathcal{C}ln(T/T_0)$. With increasing temperature starting from $T=0$K, the sound velocity does not increase monotonically, but reaches a maximum at a few Kelvin and decreases at higher temperatures. Tunneling-two-level-system (TTLS) model explained the $ln T$ dependence of sound velocity shift. In TTLS model the slope ratio of $ln T$ dependence of sound velocity shift between lower temperature increasing regime (resonance regime) and higher temperature decreasing regime (relaxation regime) is $mathcal{C}^{rm res }:mathcal{C}^{rm rel }=1:-frac{1}{2}$. In this paper we develop the generic coupled block model to prove the slope ratio of sound velocity shift between two regimes is $mathcal{C}^{rm res }:mathcal{C}^{rm rel }=1:-1$ rather than $1:-frac{1}{2}$, which agrees with the majority of the measurements. The dielectric constant shift in low-temperature glasses, $[epsilon_r(T)-epsilon_r(T_0)]/epsilon_r(T_0)$, has a similar logarithmic temperature dependence below $10$K: $[epsilon(T)-epsilon(T_0)]/epsilon(T_0) = mathcal{C}ln(T/T_0)$. In TTLS model the slope ratio of dielectric constant shift between resonance and relaxation regimes is $mathcal{C}^{rm res}:mathcal{C}^{rm rel}=-1:frac{1}{2}$. In this paper we apply the electric dipole-dipole interaction, to prove that the slope ratio between two regimes is $mathcal{C}^{rm res}:mathcal{C}^{rm rel} = -1:1$ rather than $-1:frac{1}{2}$. Our result agrees with the dielectric constant measurements. By developing a real space renormalization technique for glass non-elastic and dielectric susceptibilities, we show that these universal properties essentially come from the $1/r^3$ long range interactions, independent of the materials microscopic properties.
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The temperature dependence of the thermal conductivity of amorphous solids is markedly different from that of their crystalline counterparts, but exhibits universal behaviour. Sound attenuation is believed to be related to this universal behaviour. R
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Tunneling-two-level-system (TTLS) model has successfully explained several low-temperature glass universal properties which do not exist in their crystalline counterparts. The coupling constants between longitudinal and transverse phonon strain field
s and two-level-systems are denoted as $gamma_l$ and $gamma_t$. The ratio $gamma_l/gamma_t$ was observed to lie between $1.44$ and $1.84$ for 18 different kinds of glasses. Such universal property cannot be explained within TTLS model. In this paper by developing a microscopic generic coupled block model, we show that the ratio $gamma_l/gamma_t$ is proportinal to the ratio of sound velocity $c_l/c_t$. We prove that the universality of $gamma_l/gamma_t$ essentially comes from the mutual interaction between different glass blocks, independent of the microscopic structure and chemical compound of the amorphous materials. In the appendix we also give a detailed correction on the coefficient of non-elastic stress-stress interaction $Lambda_{ijkl}^{(ss)}$ which was obtained by Joffrin and Levelutcite{Joffrin1976}.
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