The quantum geometric tensor(QGT)is a fundamental quantity for characterizing the geometric properties of quantum states and plays an essential role in elucidating various physical phenomena.The traditional QGT,defned...The quantum geometric tensor(QGT)is a fundamental quantity for characterizing the geometric properties of quantum states and plays an essential role in elucidating various physical phenomena.The traditional QGT,defned only for pure states,has limited applicability in realistic scenarios where mixed states are common.To address this limitation,we generalize the defnition of the QGT to mixed states using the purifcation bundle and the covariant derivative.Notably,our proposed defnition reduces to the traditional QGT when mixed states approach pure states.In our framework,the real and imaginary parts of this generalized QGT correspond to the Bures metric and the mean gauge curvature,respectively,endowing it with a broad range of potential applications.Additionally,using our proposed mixed-state QGT,we derive the geodesic equation applicable to mixed states.This work establishes a unifed framework for the geometric analysis of both pure and mixed states,thereby deepening our understanding of the geometric properties of quantum states.展开更多
以石灰石和工业氧化铝为原料研究了煅烧温度及配料组成对纯铝酸钙水泥性能的影响。结果表明,当 w Al2O 低于 376%时,随配料组成中 w Al2O 的增加, A 矿物的形成量增加,水泥的凝结时间延长且强度降低;...以石灰石和工业氧化铝为原料研究了煅烧温度及配料组成对纯铝酸钙水泥性能的影响。结果表明,当 w Al2O 低于 376%时,随配料组成中 w Al2O 的增加, A 矿物的形成量增加,水泥的凝结时间延长且强度降低;随煅烧温度提高,水泥的凝结 3 C 2时间延长但强度提高,尤其是 3d, 强度;掺少量 BaO , 7d ZnO 可缩短水泥的凝结时间但强度降低。展开更多
基金supported by the National Natural Science Foundation of China(Grant Nos.12347104,U24A2017,12461160276,and 12175075)the National Key Research and Development Program of China(Grant No.2023YFC2205802)+1 种基金the Natural Science Foundation of Jiangsu Province(Grant Nos.BK20243060 and BK20233001)in part by the State Key Laboratory of Advanced Optical Communication Systems and Networks,China。
文摘The quantum geometric tensor(QGT)is a fundamental quantity for characterizing the geometric properties of quantum states and plays an essential role in elucidating various physical phenomena.The traditional QGT,defned only for pure states,has limited applicability in realistic scenarios where mixed states are common.To address this limitation,we generalize the defnition of the QGT to mixed states using the purifcation bundle and the covariant derivative.Notably,our proposed defnition reduces to the traditional QGT when mixed states approach pure states.In our framework,the real and imaginary parts of this generalized QGT correspond to the Bures metric and the mean gauge curvature,respectively,endowing it with a broad range of potential applications.Additionally,using our proposed mixed-state QGT,we derive the geodesic equation applicable to mixed states.This work establishes a unifed framework for the geometric analysis of both pure and mixed states,thereby deepening our understanding of the geometric properties of quantum states.
文摘以石灰石和工业氧化铝为原料研究了煅烧温度及配料组成对纯铝酸钙水泥性能的影响。结果表明,当 w Al2O 低于 376%时,随配料组成中 w Al2O 的增加, A 矿物的形成量增加,水泥的凝结时间延长且强度降低;随煅烧温度提高,水泥的凝结 3 C 2时间延长但强度提高,尤其是 3d, 强度;掺少量 BaO , 7d ZnO 可缩短水泥的凝结时间但强度降低。
