Low temperature quantum bounds on simple models
In the past few years, there has been considerable activity around a set of quantum bounds on transport coefficients (viscosity) and chaos (Lyapunov exponent), relevant at low temperatures. The interest comes from the fact that Black-Hole models seem to saturate all of them. The goal of this work...
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| Format: | Article |
| Language: | English |
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SciPost
2022-07-01
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| Series: | SciPost Physics |
| Online Access: | https://scipost.org/SciPostPhys.13.1.006 |
| _version_ | 1818190778123419648 |
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| author | Silvia Pappalardi, Jorge Kurchan |
| author_facet | Silvia Pappalardi, Jorge Kurchan |
| author_sort | Silvia Pappalardi, Jorge Kurchan |
| collection | DOAJ |
| description | In the past few years, there has been considerable activity around a set of
quantum bounds on transport coefficients (viscosity) and chaos (Lyapunov
exponent), relevant at low temperatures. The interest comes from the fact that
Black-Hole models seem to saturate all of them. The goal of this work is to
gain physical intuition about the quantum mechanisms that enforce these bounds
on simple models. To this aim, we consider classical and quantum free dynamics
on curved manifolds. These systems exhibit chaos up to the lowest temperatures
and - as we discuss - they violate the bounds in the classical limit. First of
all, we show that the quantum dimensionless viscosity and the Lyapunov exponent
only depend on the de Broglie length and a geometric length-scale, thus
establishing the scale at which quantum effects become relevant. Then, we focus
on the bound on the Lyapunov exponent and identify three different ways in
which quantum effects arise in practice. We illustrate our findings on a toy
model given by the surface of constant negative curvature - a paradigmatic
model of quantum chaos - glued to a cylinder. By exact solution and numerical
investigations, we show how the chaotic behaviour is limited by the quantum
effects of the curvature itself. Interestingly, we find that at the lowest
energies the bound to chaos is dominated by the longest length scales, and it
is therefore a collective effect. |
| first_indexed | 2024-12-12T00:04:07Z |
| format | Article |
| id | doaj.art-82e9d11cf5a1481bbc73ffbaec6f4930 |
| institution | Directory Open Access Journal |
| issn | 2542-4653 |
| language | English |
| last_indexed | 2024-12-12T00:04:07Z |
| publishDate | 2022-07-01 |
| publisher | SciPost |
| record_format | Article |
| series | SciPost Physics |
| spelling | doaj.art-82e9d11cf5a1481bbc73ffbaec6f49302022-12-22T00:45:10ZengSciPostSciPost Physics2542-46532022-07-0113100610.21468/SciPostPhys.13.1.006Low temperature quantum bounds on simple modelsSilvia Pappalardi, Jorge KurchanIn the past few years, there has been considerable activity around a set of quantum bounds on transport coefficients (viscosity) and chaos (Lyapunov exponent), relevant at low temperatures. The interest comes from the fact that Black-Hole models seem to saturate all of them. The goal of this work is to gain physical intuition about the quantum mechanisms that enforce these bounds on simple models. To this aim, we consider classical and quantum free dynamics on curved manifolds. These systems exhibit chaos up to the lowest temperatures and - as we discuss - they violate the bounds in the classical limit. First of all, we show that the quantum dimensionless viscosity and the Lyapunov exponent only depend on the de Broglie length and a geometric length-scale, thus establishing the scale at which quantum effects become relevant. Then, we focus on the bound on the Lyapunov exponent and identify three different ways in which quantum effects arise in practice. We illustrate our findings on a toy model given by the surface of constant negative curvature - a paradigmatic model of quantum chaos - glued to a cylinder. By exact solution and numerical investigations, we show how the chaotic behaviour is limited by the quantum effects of the curvature itself. Interestingly, we find that at the lowest energies the bound to chaos is dominated by the longest length scales, and it is therefore a collective effect.https://scipost.org/SciPostPhys.13.1.006 |
| spellingShingle | Silvia Pappalardi, Jorge Kurchan Low temperature quantum bounds on simple models SciPost Physics |
| title | Low temperature quantum bounds on simple models |
| title_full | Low temperature quantum bounds on simple models |
| title_fullStr | Low temperature quantum bounds on simple models |
| title_full_unstemmed | Low temperature quantum bounds on simple models |
| title_short | Low temperature quantum bounds on simple models |
| title_sort | low temperature quantum bounds on simple models |
| url | https://scipost.org/SciPostPhys.13.1.006 |
| work_keys_str_mv | AT silviapappalardijorgekurchan lowtemperaturequantumboundsonsimplemodels |