# Thermalization and possible signatures of quantum chaos in complex crystalline materials

## Abstract

Analyses of thermal diffusivity data on complex insulators and on strongly correlated electron systems hosted in similar complex crystal structures suggest that quantum chaos is a good description for thermalization processes in these systems, particularly in the high-temperature regime where the many phonon bands and their interactions dominate the thermal transport. Here we observe that for these systems diffusive thermal transport is controlled by a universal Planckian timescale $\tau \sim \hslash /{k}_{B}T$ and a unique velocity ${v}_{E}$ . Specifically, ${v}_{E}\approx {v}_{ph}$ for complex insulators, and ${v}_{ph}\lesssim {v}_{E}\ll {v}_{F}$ in the presence of strongly correlated itinerant electrons ( ${v}_{ph}$ and ${v}_{F}$ are the phonon and electron velocities, respectively). For the complex correlated electron systems we further show that charge diffusivity, while also reaching the Planckian relaxation bound, is largely dominated by the Fermi velocity of the electrons, hence suggesting that it is only the thermal (energy) diffusivity that describes chaos diffusivity.

- Authors:

- Publication Date:

- Research Org.:
- Stanford University, CA (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC), Basic Energy Sciences (BES)

- OSTI Identifier:
- 1561414

- Alternate Identifier(s):
- OSTI ID: 1564086

- Grant/Contract Number:
- AC02-76SF00515

- Resource Type:
- Published Article

- Journal Name:
- Proceedings of the National Academy of Sciences of the United States of America

- Additional Journal Information:
- Journal Name: Proceedings of the National Academy of Sciences of the United States of America Journal Volume: 116 Journal Issue: 40; Journal ID: ISSN 0027-8424

- Publisher:
- Proceedings of the National Academy of Sciences

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; quantum chaos; thermalization; thermal diffusivity; phonons

### Citation Formats

```
Zhang, Jiecheng, Kountz, Erik D., Behnia, Kamran, and Kapitulnik, Aharon. Thermalization and possible signatures of quantum chaos in complex crystalline materials. United States: N. p., 2019.
Web. doi:10.1073/pnas.1910131116.
```

```
Zhang, Jiecheng, Kountz, Erik D., Behnia, Kamran, & Kapitulnik, Aharon. Thermalization and possible signatures of quantum chaos in complex crystalline materials. United States. doi:10.1073/pnas.1910131116.
```

```
Zhang, Jiecheng, Kountz, Erik D., Behnia, Kamran, and Kapitulnik, Aharon. Thu .
"Thermalization and possible signatures of quantum chaos in complex crystalline materials". United States. doi:10.1073/pnas.1910131116.
```

```
@article{osti_1561414,
```

title = {Thermalization and possible signatures of quantum chaos in complex crystalline materials},

author = {Zhang, Jiecheng and Kountz, Erik D. and Behnia, Kamran and Kapitulnik, Aharon},

abstractNote = {Analyses of thermal diffusivity data on complex insulators and on strongly correlated electron systems hosted in similar complex crystal structures suggest that quantum chaos is a good description for thermalization processes in these systems, particularly in the high-temperature regime where the many phonon bands and their interactions dominate the thermal transport. Here we observe that for these systems diffusive thermal transport is controlled by a universal Planckian timescale τ ∼ ℏ / k B T and a unique velocity v E . Specifically, v E ≈ v p h for complex insulators, and v p h ≲ v E ≪ v F in the presence of strongly correlated itinerant electrons ( v p h and v F are the phonon and electron velocities, respectively). For the complex correlated electron systems we further show that charge diffusivity, while also reaching the Planckian relaxation bound, is largely dominated by the Fermi velocity of the electrons, hence suggesting that it is only the thermal (energy) diffusivity that describes chaos diffusivity.},

doi = {10.1073/pnas.1910131116},

journal = {Proceedings of the National Academy of Sciences of the United States of America},

number = 40,

volume = 116,

place = {United States},

year = {2019},

month = {9}

}

DOI: 10.1073/pnas.1910131116

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