Connes distance of 2D harmonic oscillators in quantum phase space

作     者：林冰生 衡太骅 Bing-Sheng Lin;Tai-Hua Heng

作者机构：School of MathematicsSouth China University of TechnologyGuangzhou 510641China Laboratory of Quantum Science and EngineeringSouth China University of TechnologyGuangzhou 510641China School of Physics and Material ScienceAnhui UniversityHefei 230601China 

出 版 物：《Chinese Physics B》 (中国物理B（英文版）)

年 卷 期：2021年第30卷第11期

页      面：170-179页

核心收录：

学科分类：07[理学] 070201[理学-理论物理] 0702[理学-物理学] 

基　　金：Project supported by the Key Research and Development Project of Guangdong Province,China(Grant No.2020B0303300001) the National Natural Science Foundation of China(Grant No.11911530750) the Guangdong Basic and Applied Basic Research Foundation,China(Grant No.2019A1515011703) the Fundamental Research Funds for the Central Universities,China(Grant No.2019MS109) the Natural Science Foundation of Anhui Province,China(Grant No.1908085MA16) 

主　　题：Connes distance noncommutative geometry harmonic oscillator 

摘      要：We study the Connes distance of quantum states of two-dimensional(2D)harmonic oscillators in phase *** the Hilbert–Schmidt operatorial formulation,we construct a boson Fock space and a quantum Hilbert space,and obtain the Dirac operator and a spectral triple corresponding to a four-dimensional(4D)quantum phase *** on the ball condition,we obtain some constraint relations about the optimal *** construct the corresponding optimal elements and then derive the Connes distance between two arbitrary Fock states of 2D quantum harmonic *** prove that these two-dimensional distances satisfy the Pythagoras *** results are significant for the study of geometric structures of noncommutative spaces,and it can also help us to study the physical properties of quantum systems in some kinds of noncommutative spaces.