# Glimmers of a Quantum KAM Theorem: Insights from Quantum Quenches in One-Dimensional Bose Gases

## Abstract

Real-time dynamics in a quantum many-body system are inherently complicated and hence difficult to predict. There are, however, a special set of systems where these dynamics are theoretically tractable: integrable models. Such models possess non-trivial conserved quantities beyond energy and momentum. These quantities are believed to control dynamics and thermalization in low dimensional atomic gases as well as in quantum spin chains. But what happens when the special symmetries leading to the existence of the extra conserved quantities are broken? Is there any memory of the quantities if the breaking is weak? Here, in the presence of weak integrability breaking, we show that it is possible to construct residual quasi-conserved quantities, so providing a quantum analog to the KAM theorem and its attendant Nekhoreshev estimates. We demonstrate this construction explicitly in the context of quantum quenches in one-dimensional Bose gases and argue that these quasi-conserved quantities can be probed experimentally.

- Authors:

- Univ. of Amsterdam (Netherlands)
- Brookhaven National Lab. (BNL), Upton, NY (United States)

- Publication Date:

- Research Org.:
- Brookhaven National Laboratory (BNL), Upton, NY (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22)

- OSTI Identifier:
- 1234072

- Alternate Identifier(s):
- OSTI ID: 1412757

- Report Number(s):
- BNL-114730-2017-JA

Journal ID: ISSN 2160-3308; PRXHAE; R&D Project: PO015; KC0202030; TRN: US1800349

- Grant/Contract Number:
- SC0012704; AC02-98CH10886

- Resource Type:
- Journal Article: Published Article

- Journal Name:
- Physical Review. X

- Additional Journal Information:
- Journal Volume: 5; Journal Issue: 4; Journal ID: ISSN 2160-3308

- Publisher:
- American Physical Society

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY

### Citation Formats

```
Brandino, G. P., Caux, J. -S., and Konik, R. M..
```*Glimmers of a Quantum KAM Theorem: Insights from Quantum Quenches in One-Dimensional Bose Gases*. United States: N. p., 2015.
Web. doi:10.1103/PhysRevX.5.041043.

```
Brandino, G. P., Caux, J. -S., & Konik, R. M..
```*Glimmers of a Quantum KAM Theorem: Insights from Quantum Quenches in One-Dimensional Bose Gases*. United States. doi:10.1103/PhysRevX.5.041043.

```
Brandino, G. P., Caux, J. -S., and Konik, R. M.. Wed .
"Glimmers of a Quantum KAM Theorem: Insights from Quantum Quenches in One-Dimensional Bose Gases". United States. doi:10.1103/PhysRevX.5.041043.
```

```
@article{osti_1234072,
```

title = {Glimmers of a Quantum KAM Theorem: Insights from Quantum Quenches in One-Dimensional Bose Gases},

author = {Brandino, G. P. and Caux, J. -S. and Konik, R. M.},

abstractNote = {Real-time dynamics in a quantum many-body system are inherently complicated and hence difficult to predict. There are, however, a special set of systems where these dynamics are theoretically tractable: integrable models. Such models possess non-trivial conserved quantities beyond energy and momentum. These quantities are believed to control dynamics and thermalization in low dimensional atomic gases as well as in quantum spin chains. But what happens when the special symmetries leading to the existence of the extra conserved quantities are broken? Is there any memory of the quantities if the breaking is weak? Here, in the presence of weak integrability breaking, we show that it is possible to construct residual quasi-conserved quantities, so providing a quantum analog to the KAM theorem and its attendant Nekhoreshev estimates. We demonstrate this construction explicitly in the context of quantum quenches in one-dimensional Bose gases and argue that these quasi-conserved quantities can be probed experimentally.},

doi = {10.1103/PhysRevX.5.041043},

journal = {Physical Review. X},

issn = {2160-3308},

number = 4,

volume = 5,

place = {United States},

year = {2015},

month = {12}

}

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