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Title: Integrable matrix theory: Level statistics

Authors:
; ;
Publication Date:
Sponsoring Org.:
USDOE
OSTI Identifier:
1315855
Grant/Contract Number:
FG02-06ER46319
Resource Type:
Journal Article: Publisher's Accepted Manuscript
Journal Name:
Physical Review E
Additional Journal Information:
Journal Volume: 94; Journal Issue: 3; Related Information: CHORUS Timestamp: 2016-09-02 18:09:59; Journal ID: ISSN 2470-0045
Publisher:
American Physical Society
Country of Publication:
United States
Language:
English

Citation Formats

Scaramazza, Jasen A., Shastry, B. Sriram, and Yuzbashyan, Emil A. Integrable matrix theory: Level statistics. United States: N. p., 2016. Web. doi:10.1103/PhysRevE.94.032106.
Scaramazza, Jasen A., Shastry, B. Sriram, & Yuzbashyan, Emil A. Integrable matrix theory: Level statistics. United States. doi:10.1103/PhysRevE.94.032106.
Scaramazza, Jasen A., Shastry, B. Sriram, and Yuzbashyan, Emil A. Fri . "Integrable matrix theory: Level statistics". United States. doi:10.1103/PhysRevE.94.032106.
@article{osti_1315855,
title = {Integrable matrix theory: Level statistics},
author = {Scaramazza, Jasen A. and Shastry, B. Sriram and Yuzbashyan, Emil A.},
abstractNote = {},
doi = {10.1103/PhysRevE.94.032106},
journal = {Physical Review E},
number = 3,
volume = 94,
place = {United States},
year = {Fri Sep 02 00:00:00 EDT 2016},
month = {Fri Sep 02 00:00:00 EDT 2016}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record at 10.1103/PhysRevE.94.032106

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  • The number of levels with energy less than [ital E] of an integrable quantum system with two degrees of freedom is equal to [lambda][ital E]+[ital sE][sup 1/4], where [lambda] is a constant and [ital s] a fluctuating quantity with a non-Gaussian distribution. The probability distribution of [ital s] decreases roughly like exp([minus][ital s][sup 4]) when [ital s] is large. The number of levels between [ital E] and [ital E]+[ital z] [radical][ital E] is equal to [lambda][ital z] [radical][ital E] +[ital rE][sup 1/4] where [ital r] is another fluctuating quantity. The distribution of [ital r] tends to a Gaussian distribution asmore » [ital z][r arrow]0 and oscillates around some limiting non-Gaussian distribution as [ital z][r arrow][infinity].« less
  • The CPT theorem (G. Luders, Kgl. Danske Videnskab. Selskab Mat.-fys. Medd., 28: No. 5(1954)) and the normal connection between spin and statistics are consequences of postulates of the S-matrix approach to elementary particle physics. These are weaker than those of field theory. Neither local fields nor any reference to space-time points are used. Quantum commutation relations and properties of the vacuum play no role. Completeness of the asymptotic states and positive definiteness or the metric are not required, though certain weaker asymptotic conditions prevail. The proofs depend on unitarity, macroscopic relativistic invariance, and a very weak analyticity requirement on themore » mass- shell scattering functions. The proofs are in the framework of the new S-matrix approach to elementary particle physics, which is established on a formal basis. (auth)« less