Spectral form factor and semi-circle law in the time direction

Spectral form factor and semi-circle law in the time direction

Abstract We study the time derivative of the connected part of spectral form factor, which we call the slope of ramp, in Gaussian matrix model. We find a closed formula of the slope of ramp at finite N with non-zero inverse temperature. Using this exact result, we confirm numerically that the slope...

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Bibliographic Details
Main Author: Kazumi Okuyama
Format: Article
Language:English
Published: SpringerOpen 2019-02-01
Series:Journal of High Energy Physics
Subjects:
1/N Expansion
Matrix Models
Random Systems
Online Access:http://link.springer.com/article/10.1007/JHEP02(2019)161
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spelling doaj-a77956ca54b64671be2a15964f60bf722020-11-25T01:10:12ZengSpringerOpenJournal of High Energy Physics1029-84792019-02-012019211610.1007/JHEP02(2019)161Spectral form factor and semi-circle law in the time directionKazumi Okuyama0Department of Physics, Shinshu UniversityAbstract We study the time derivative of the connected part of spectral form factor, which we call the slope of ramp, in Gaussian matrix model. We find a closed formula of the slope of ramp at finite N with non-zero inverse temperature. Using this exact result, we confirm numerically that the slope of ramp exhibits a semi-circle law as a function of time.http://link.springer.com/article/10.1007/JHEP02(2019)1611/N ExpansionMatrix ModelsRandom Systems
collection DOAJ
language English
format Article
sources DOAJ
author Kazumi Okuyama
spellingShingle Kazumi Okuyama
Spectral form factor and semi-circle law in the time direction
Journal of High Energy Physics
1/N Expansion
Matrix Models
Random Systems
author_facet Kazumi Okuyama
author_sort Kazumi Okuyama
title Spectral form factor and semi-circle law in the time direction
title_short Spectral form factor and semi-circle law in the time direction
title_full Spectral form factor and semi-circle law in the time direction
title_fullStr Spectral form factor and semi-circle law in the time direction
title_full_unstemmed Spectral form factor and semi-circle law in the time direction
title_sort spectral form factor and semi-circle law in the time direction
publisher SpringerOpen
series Journal of High Energy Physics
issn 1029-8479
publishDate 2019-02-01
description Abstract We study the time derivative of the connected part of spectral form factor, which we call the slope of ramp, in Gaussian matrix model. We find a closed formula of the slope of ramp at finite N with non-zero inverse temperature. Using this exact result, we confirm numerically that the slope of ramp exhibits a semi-circle law as a function of time.
topic 1/N Expansion
Matrix Models
Random Systems
url http://link.springer.com/article/10.1007/JHEP02(2019)161
work_keys_str_mv AT kazumiokuyama spectralformfactorandsemicirclelawinthetimedirection
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