伪自伴量子系统的酉演化与绝热定理

删除或更新信息，请邮件至freekaoyan#163.com(#换成@)

本站小编 Free考研考试/2021-12-27

伪自伴量子系统的酉演化与绝热定理黄永峰^1,2, 曹怀信¹, 王文华³1 陕西师范大学数学与信息科学学院西安 710119;
2 昌吉学院数学系昌吉 831100;
3 陕西师范大学民族教育学院西安 710119 Unitary Evolution and Adiabatic Theorem of Pseudo Self-adjoint Quantum Systems Yong Feng HUANG^1,2, Huai Xin CAO¹, Wen Hua WANG³1 School of Mathematics and Information Science, Shaanxi Normal University, Xi'an 710119, P. R. China;
2 School of Mathematics, Changji University, Changji 831100, P. R. China;
3 School of Ethnic Education, Shaanxi Normal University, Xi'an 710119, P. R. China

摘要
图/表
参考文献
相关文章

全文: PDF(550 KB) HTML (1 KB)
输出: BibTeX | EndNote (RIS)

摘要经典量子系统的哈密尔顿是自伴算子.哈密尔顿算符的自伴性不仅确保了系统遵循酉演化，而且也保证了它自身具有实的能量本征值.但是，确实有一些物理系统，其哈密尔顿是非自伴的，但也具有实的能量本征值.这种具有非自伴哈密尔顿的系统就是非自伴量子系统.具有伪自伴哈密尔顿的系统是一类特殊的非自伴量子系统，其哈密尔顿相似于一个自伴算子.本文研究伪自伴量子系统的酉演化与绝热定理.首先，给出了伪自伴算子定义及其等价刻画；其次，对于伪自伴哈密尔顿系统，通过构造新内积，证明了伪自伴哈密尔顿在新内积下是自伴的，并给出了系统在新内积下为酉演化的充分必要条件.最后，建立了伪自伴量子系统的绝热演化定理及与绝热逼近定理.

服务

加入引用管理器

E-mail Alert

RSS

收稿日期: 2018-05-11

MR (2010):

O177.92

基金资助:国家自然科学基金（11871318，11771009，11601300，11571213）；中央高校基本科研业务费专项资金（GK20181020，GK201801011）及陕西省自然科学基础研究计划（2018JM1020）

通讯作者:曹怀信E-mail: caohx@snnu.edu.cn

作者简介: 黄永峰,E-mail:huangyongfeng@snnu.edu.cn;王文华,E-mail:wenhua@snnu.edu.cn

引用本文:

黄永峰, 曹怀信, 王文华. 伪自伴量子系统的酉演化与绝热定理[J]. 数学学报, 2019, 62(3): 469-478. Yong Feng HUANG, Huai Xin CAO, Wen Hua WANG. Unitary Evolution and Adiabatic Theorem of Pseudo Self-adjoint Quantum Systems. Acta Mathematica Sinica, Chinese Series, 2019, 62(3): 469-478.

链接本文:

http://www.actamath.com/Jwk_sxxb_cn/CN/或 http://www.actamath.com/Jwk_sxxb_cn/CN/Y2019/V62/I3/469

[1] Ashok D., Pseudo-Hermitian quantum mechanics, J. Phys. Conf. Ser., 2011, 287(1):012002.
[2] Bender C. M., Boettcher S., Real spectra in non-Hermitian Hamiltonians having P T -symmetry, Phys. Rev. Lett., 1998, 80(24):5243-5246.
[3] Bender C. M., Berry M. V., Mandilara A., Generalized P T -symmetry and real spectra, J. Phys. A:Math. Gen., 2002, 35(31):L467-L471.
[4] Bender C. M., Brody D. C., Jones H. F., Must a Hamiltonian be Hermitian? Amer. J. Phys., 2003, 71(11):1095-1102.
[5] Bender C. M., Making sense of non-Hermitian Hamiltonians, Rep. Prog. Phys., 2007, 70:947-1018.
[6] Born M., Fock V., Beweis des adiabatensatzes, Z. Phys., 1928, 51:165-180.
[7] Cao H. X., Guo Z. H., Foundation of Wavelet Analysis, Science Press, Beijing, 2016.
[8] Cao H. X., Guo Z. H., Chen Z. L., et al., Quantitative sufficient condition for adiabatic approximation, Sci. China-Phys. Mech. Astron., 2013, 56(7):1401-1407.
[9] Chen L., Cao H. X., Meng H. X., Generalized duality quantum computers acting on mixed states, Quantum Inf. Process., 2015, 14(11):4351-4360.
[10] Guo Z. H., Cao H. X., Lu L., Adiabatic approximation in P T -symmetric quantum mechanics, Sci. ChinaPhys. Mech. Astron., 2014, 57(10):1835-1839.
[11] Kato T., On the adiabatic theorem of quantum mechanics, J. Phys. Soc. Jpn., 1950, 5:435-439.
[12] Long G. L., General quantum interference principle and duality computer, Commun. Theor. Phys., 2006, 45(5):825-844.
[13] Long G. L., Duality quantum computing and duality quantum information processing, Int. J. Theor. Phys., 2011, 50(4):1305-1318.
[14] Longhi S., Fisica D. D., Time reversal of a discrete system coupled to a continuum based on non-Hermitian flip, Sci. Bull., 2017, 62(12):869-874.
[15] Marzlin K. P., Sanders B. C., Inconsistency in the application of the adiabatic theorem, Phys. Rev. Lett., 2004, 93(16):160408.
[16] Mostafazadeh A., Pseudo-Hermiticity versus P T -symmetry:The necessary condition for the reality of the spectrum of a non-Hermitian Hamiltonian, J. Math. Phys., 2001, 43(1):205-214.
[17] Mostafazadeh A., Pseudo-Hermiticity versus P T -Symmetry Ⅱ:A complete characterization of non-Hermitian Hamiltonians with a real spectrum, J. Math. Phys., 2002, 43(5):2814-2816.
[18] Mostafazadeh A., Pseudo-Hermiticity versus P T -symmetry Ⅲ:Equivalence of pseudo-Hermiticity and the presence of antilinear symmetries, J. Math. Phys., 2002, 43(8):3944-3951.
[19] Mostafazadeh A., Pseudo-Hermitian representation of quantum mechanics, Int. J. Geom. Methods Mod. Phys., 2010, 7(7):1191-1306.
[20] Nenciu G., On the adiabatic theorem of quantum mechanics, J. Phys. A:Math. Gen., 1980, 13(2):L15-L18.
[21] Qiang X. G., Zhou X. Q., Aungskunsiri K., et al., Quantum processing by remote quantum control, Quantum Sci. Technol., 2017, 2:045002.
[22] Tong D. M., Singh K., Kwek L. C., et al., Sufficiency criterion for the validity of the adiabatic approximation, Phys. Rev. Lett., 2007, 98(15):150402.
[23] Wang W. H., Cao H. X., Chen Z. L., Adiabatic approximation theorem for the evolution by an A-uniformly pseudo-Hermitian Hamiltonian, Theor. Math. Phys., 2017, 192(3):1219-1233.
[24] Yu B. M., Cao H. X., Guo Z. H., et al., Computable upper bounds for the adiabatic approximation errors, Sci. China-Phys. Mech. Astron., 2014, 57(11):2031-2038.
[25] Zheng C., Hao L., Long G. L., Observation of a fast evolution in a parity-time-symmetric system, Philos. Trans. A Math. Phys. Eng. Sci., 2013, 371(1989):20120053.

[1]	周仙耕, 张敏. 两类统计收敛的表示定理[J]. Acta Mathematica Sinica, English Series, 2010, 53(2): 251-256.
[2]	关伟波, 宋文. Banach空间中的弱凸集和W-太阳集[J]. Acta Mathematica Sinica, English Series, 2010, 53(1): 45-50.
[3]	施慧华, 王波. 理想收敛的若干研究及推广[J]. 数学学报, 2016, 59(3): 335-342.

PDF全文下载地址:

http://www.actamath.com/Jwk_sxxb_cn/CN/article/downloadArticleFile.do?attachType=PDF&id=23405