# Defects&TLSs and glass transition



## theory

- 2022 [Theory of melting of glasses](https://arxiv.org/pdf/2208.11648.pdf) Chandra M. Varma

motivation - specific heat peak at melting temperature is closely connected with the density of LEEs see also as linear-in-temperature specific heat at VERY low temperatures. Therefore LEAKING (with or without tunneling). Both phenomena, peak at $T_g$ and $\gamma*T$ of specific heat at glass temperature and low tempreatures correspondingly, occur concurrently

- 2019 [Nussinov-Weingarter](https://arxiv.org/pdf/1902.06593.pdf)
⏎
already topological-KT transition⏎
⏎

- [2017 - Chandra Varma](https://www.condmatjclub.org/uploads/2017/10/JCCM_October_2017_03.pdf)

Third, the measured $T^3$ specific heat is **larger than that given by the elastic constants - the original TLM has nothing to say about this**.
The change in the so called excess $T^3$  specific heat **with density is identical to that** of the linear in T heat capacity

**HUGE peak for crystal but noticeable peak for glass - features of the specific heat**

- [2006 Wolynes-Lyubchenko](https://knowen-production.s3.amazonaws.com/uploads/attachment/file/5430/lyubchenko.pdf)

## open questions


 - a) since $T_G \sim 100-1000K$, **for defect-freezing-out transition the defect size needs to be** $\xi_G \sim 10A=10^{-7}cm$
 
 1-order of magnitude ---BPeak energy scale of defect is (30k), but glass temperature (300k)


crossover temparature $T_Q \sim 10K$ is by KT relation $T_Q \approx \frac{1}{2} \rho_s \sim \frac{\gamma^2}{\rho c_t^2 \xi^3}$

$10K \sim 10^{-15} erg \sim 10^{-3} eV \sim \frac{\hbar c}{R_0}$
$10^{-15} erg = \frac{10^{-27} erg*s *4*10^5 cm/s}{50 A}$, so $R_0 \sim 50A$

IF $\gamma \sim 6.3eV$ and $\rho c_t^2 \xi^3 \approx 2(g/cm^3) 4^2 10^{10} (cm/s)^2 125*10^{-21} cm^3 \approx 4*10^{-8} erg=40,000eV$,
so $T_Q \sim 10^{-3} eV \sim 10K$


- b) **RG equations to be checked/reproduced?**

2022 [Anomalous Elasticity and **Emergent Dipole Screening** in Three-Dimensional Amorphous Solids](https://arxiv.org/pdf/2209.05311.pdf)



## experimental links - forcing out of "universal"/natural regime

- 2015 [Two-Level Systems in Evaporated Amorphous Silicon](https://arxiv.org/abs/1506.04284)
D.R. Queen, X. Liu, J. Karel, H.C. Jacks, T.H. Metcalf, F. Hellman

2021 [Decoupling between propagating acoustic waves and two-level systems in hydrogenated amorphous silicon](https://arxiv.org/pdf/2105.02513.pdf)

- 2014 [Suppression of tunneling two-level systems in ultrastable glasses of indomethacin](https://www.pnas.org/doi/full/10.1073/pnas.1405545111)
Tomás Pérez-Castañeda, Cristian Rodríguez-Tinoco, Javier Rodríguez-Viejo, and Miguel A. Ramos

## experiments around "universal regime"

[How Universal are the Low Temperature Acoustic Properties of Glasses? - 1988 - Berret-Meissner](https://knowen-production.s3.amazonaws.com/uploads/attachment/file/5375/Berret-Meiner1988_Article_HowUniversalAreTheLowTemperatu.pdf)






# Parents

* Elastic point defects
* Glass transition - theories