Probabilistic aspects of the SU(2)-harmonic oscillator

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	Probabilistic aspects of the SU(2)-harmonic oscillator
	Luo, SL
	2000-03-01
发表期刊	JOURNAL OF APPLIED PROBABILITY
ISSN	0021-9002
卷号	37 期号:1 页码:306-314
摘要	In the framework of quantum probability, we present a simple geometrical mechanism which gives rise to binomial distributions, Gaussian distributions, Poisson distributions, and their interrelation. More specifically, by virtue of coherent states and a toy analogue of the Bargmann transform, we calculate the probability distributions of the position observable and the Hamiltonian arising in the representation of the classic group SU(2). This representation may be viewed as a constrained harmonic oscillator with a two-dimensional sphere as the phase space. It turns out that both the position observable and the Hamiltonian have binomial distributions, but with different asymptotic behaviours: with large radius and high spin limit, the former tends to the Gaussian while the latter tends to the Poisson.
关键词	harmonic oscillator SU(2) Bargmann transform binomial distributions Gaussian distributions Poisson distributions
语种	英语
WOS研究方向	Mathematics
WOS类目	Statistics & Probability
WOS记录号	WOS:000087186300026
出版者	APPLIED PROBABILITY TRUST
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/15296
专题	应用数学研究所
通讯作者	Luo, SL
作者单位	Acad Sinica, Acad Math & Syst Sci, Inst Appl Math, Beijing 100080, Peoples R China
推荐引用方式 GB/T 7714	Luo, SL. Probabilistic aspects of the SU(2)-harmonic oscillator[J]. JOURNAL OF APPLIED PROBABILITY,2000,37(1):306-314.
APA	Luo, SL.(2000).Probabilistic aspects of the SU(2)-harmonic oscillator.JOURNAL OF APPLIED PROBABILITY,37(1),306-314.
MLA	Luo, SL."Probabilistic aspects of the SU(2)-harmonic oscillator".JOURNAL OF APPLIED PROBABILITY 37.1(2000):306-314.