One-dimensional pseudoharmonic oscillator: classical remarks and quantum-information theory

IF 1.1 Q3 PHYSICS, MULTIDISCIPLINARY
O. Olendski
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引用次数: 1

Abstract

Motion along semi-infinite straight line in a potential that is a combination of positive quadratic and inverse quadratic functions of the position is considered with the emphasis on the analysis of its quantum-information properties. Classical measure of symmetry of the potential is proposed and its dependence on the particle energy and the factor a describing a relative strength of its constituents is described; in particular, it is shown that a variation of the parameter a alters the shape from the half-harmonic oscillator (HHO) at a=0 to the perfectly symmetric one of the double frequency oscillator (DFO) in the limit of huge a . Quantum consideration focuses on the analysis of information-theoretical measures, such as standard deviations, Shannon, Rényi and Tsallis entropies together with Fisher information, Onicescu energy and non–Gaussianity. For doing this, among others, a method of calculating momentum waveforms is proposed that results in their analytic expressions in form of the confluent hypergeometric functions. Increasing parameter a modifies the measures in such a way that they gradually transform into those corresponding to the DFO what, in particular, means that the lowest orbital saturates Heisenberg, Shannon, Rényi and Tsallis uncertainty relations with the corresponding position and momentum non–Gaussianities turning to zero. A simple expression is derived of the orbital-independent lower threshold of the semi-infinite range of the dimensionless Rényi/Tsallis coefficient where momentum components of these one-parameter entropies exist which shows that it varies between 1/4 at HHO and zero when a tends to infinity. Physical interpretation of obtained mathematical results is provided.
一维伪谐振子:经典评述与量子信息论
考虑了由位置的正二次函数和反二次函数组合而成的势中沿半无限直线的运动,重点分析了其量子信息性质。提出了电势对称性的经典度量,并描述了它对粒子能量和描述其成分相对强度的因子a的依赖性;特别地,参数a的变化改变了从a=0的半谐振荡器(HHO)到在巨大a的极限下的双频振荡器(DFO)的完全对称振荡器的形状。量子考虑侧重于分析信息理论度量,如标准差、Shannon、Rényi和Tsallis熵,以及Fisher信息、Onicescu能量和非高斯性。为了做到这一点,除其他外,提出了一种计算动量波形的方法,该方法得到了它们以合流超几何函数形式的解析表达式。增加参数a以这样一种方式修改度量,即它们逐渐转变为与DFO相对应的度量,特别是,这意味着最低轨道饱和了海森堡、香农、雷尼和Tsallis的不确定性关系,相应的位置和动量非高斯变为零。导出了无量纲Rényi/Tsallis系数半无限范围的轨道无关下阈值的一个简单表达式,其中存在这些单参数熵的动量分量,这表明当A趋于无穷大时,它在HHO的1/4和0之间变化。提供了对所获得的数学结果的物理解释。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
Journal of Physics Communications
Journal of Physics Communications PHYSICS, MULTIDISCIPLINARY-
CiteScore
2.60
自引率
0.00%
发文量
114
审稿时长
10 weeks
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