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Statistics of quantum energy levels ...

Ma, Tao.

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Statistics of quantum energy levels of integrable systems and a stochastic network model with applications to natural and social sciences.

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Statistics of quantum energy levels of integrable systems and a stochastic network model with applications to natural and social sciences./
Author:	Ma, Tao.
Description:	252 p.
Notes:	Source: Dissertation Abstracts International, Volume: 75-02(E), Section: B.
Contained By:	Dissertation Abstracts International75-02B(E).
Subject:	Physics, General. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3601104
ISBN:	9781303516382

Statistics of quantum energy levels of integrable systems and a stochastic network model with applications to natural and social sciences.
Ma, Tao.

Statistics of quantum energy levels of integrable systems and a stochastic network model with applications to natural and social sciences. - 252 p.

Source: Dissertation Abstracts International, Volume: 75-02(E), Section: B.

Thesis (Ph.D.)--University of Cincinnati, 2013.

I have done two projects in my PhD period: first, the statistics of quantum energy levels of integrable systems and second, a stochastic network model with applications to natural and social sciences. Quantum chaos studies level statistics and wave-function characteristics in the semiclasscal regime where the system action is several orders of magnitude larger than Planck's constant. The level statistics of classically integrable systems and classically chaotic ones are different. The levels of classically chaotic systems repel each other while these of classically integrable ones seem to be uncorrelated. We have studied level statistics in semiclassical spectrum of classically integrable systems without extra degeneracies. Our new findings are as follows. We developed a parametric averaging method to achieve ensemble averaging. We found the interval level number variance displays persistent oscillations. Contrary to previous belief, the nearest-neighbor spacing distribution of integrable systems displays some repulsion. The theoretical explanations of level statistics are based on both semiclassical theory and quantum mechanical derivation. Distributions of mass of species in the field of biology, human response times in the field of psychology, personal wealth distribution in the field of economics, and stock return in finance, all display power-law tails. It is theoretically and practically meaningful to understand the characteristics and origin of these power-law tails. We study a stochastic network model that is able to generate generalized inverse gamma distribution with power-law tail. We apply this distribution to the field of psychology and find good fit of data of with human response times. At last, we extend the model to study the stock return.

ISBN: 9781303516382Subjects--Topical Terms:

1018488
Physics, General.

Statistics of quantum energy levels of integrable systems and a stochastic network model with applications to natural and social sciences.
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245 1 0 $a Statistics of quantum energy levels of integrable systems and a stochastic network model with applications to natural and social sciences.
300 $a 252 p.
500 $a Source: Dissertation Abstracts International, Volume: 75-02(E), Section: B.
500 $a Adviser: Rostislav Serota.
502 $a Thesis (Ph.D.)--University of Cincinnati, 2013.
520 $a I have done two projects in my PhD period: first, the statistics of quantum energy levels of integrable systems and second, a stochastic network model with applications to natural and social sciences. Quantum chaos studies level statistics and wave-function characteristics in the semiclasscal regime where the system action is several orders of magnitude larger than Planck's constant. The level statistics of classically integrable systems and classically chaotic ones are different. The levels of classically chaotic systems repel each other while these of classically integrable ones seem to be uncorrelated. We have studied level statistics in semiclassical spectrum of classically integrable systems without extra degeneracies. Our new findings are as follows. We developed a parametric averaging method to achieve ensemble averaging. We found the interval level number variance displays persistent oscillations. Contrary to previous belief, the nearest-neighbor spacing distribution of integrable systems displays some repulsion. The theoretical explanations of level statistics are based on both semiclassical theory and quantum mechanical derivation. Distributions of mass of species in the field of biology, human response times in the field of psychology, personal wealth distribution in the field of economics, and stock return in finance, all display power-law tails. It is theoretically and practically meaningful to understand the characteristics and origin of these power-law tails. We study a stochastic network model that is able to generate generalized inverse gamma distribution with power-law tail. We apply this distribution to the field of psychology and find good fit of data of with human response times. At last, we extend the model to study the stock return.
590 $a School code: 0045.
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650 4 $a Psychology, General. $3 1018034
650 4 $a Physics, Quantum. $3 1671062
650 4 $a Psychology, Cognitive. $3 1017810
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710 2 $a University of Cincinnati. $b Physics. $3 2102081
773 0 $t Dissertation Abstracts International $g 75-02B(E).
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