Working in phase-space with Wigner and Weyl

被引:8
作者
Ben-Benjamin, Jonathan S. [1 ,2 ,3 ]
Kim, Moochan B. [1 ,2 ]
Schleich, Wolfgang P. [1 ,2 ,4 ,5 ,6 ]
Case, William B. [7 ]
Cohen, Leon [8 ,9 ]
机构
[1] Texas A&M Univ, IQSE, College Stn, TX 77843 USA
[2] Texas A&M Univ, Dept Phys & Astron, College Stn, TX 77843 USA
[3] Baylor Univ, Dept Phys, Waco, TX 76798 USA
[4] Univ Ulm, Inst Quantenphys, Albert Einstein Allee 11, D-89069 Ulm, Germany
[5] Univ Ulm, Ctr Integrated Quantum Sci & Technol IQST, Albert Einstein Allee 11, D-89069 Ulm, Germany
[6] Texas A&M Univ, Texas A&M Univ Inst Adv Study TIAS, College Stn, TX 77843 USA
[7] Grinnell Coll, Dept Phys, POB 805, Grinnell, IA 50112 USA
[8] CUNY Hunter Coll, Dept Phys & Astron, New York, NY 10065 USA
[9] CUNY, Grad Ctr, New York, NY 10065 USA
来源
FORTSCHRITTE DER PHYSIK-PROGRESS OF PHYSICS | 2017年 / 65卷 / 6-8期
基金
美国国家科学基金会;
关键词
Phase space quantum mechanics; Wigner Weyl distribution; Wigner Weyl symmetric ordering; Weyl and its inverse transform; operator symbol correspondence;
D O I
10.1002/prop.201600092
中图分类号
O4 [物理学];
学科分类号
0702 ;
摘要
Quantum phase-space distributions offer a royal road into the fascinating quantum-classical interface; the Wigner function being the first and best example. However, the subject is frequent with subtleties and textbook-level misinformation; e.g. The Wigner distribution can give wrong answers for some operator expectation values . Since the Wigner distribution is just another representation of the density matrix, it must yield correct answers. To that end, Marlan Scully has asked at several international conferences (the 2015 Prague conference being one of them) the following question: Starting with the density matrix (not the Moyal characteristic function), could you give me a simple direct derivation of the Wigner distribution? Section contains his answer. In Appendix D, we give a related treatment and make contact with other approaches. We hope that as a result of our studies, the Wigner distribution will become more deeply appreciated.
引用
收藏
页数:11
相关论文
共 17 条
[1]  
[Anonymous], 1973, Quantum Statistical Properties of Radiation
[2]  
[Anonymous], 1931, THEORY GROUPS QUANTU
[3]  
Bopp F., 1961, HEISENBERG PHYS UNSE
[4]   DENSITY OPERATORS AND QUASIPROBABILITY DISTRIBUTIONS [J].
CAHILL, KE ;
GLAUBER, RJ .
PHYSICAL REVIEW, 1969, 177 (5P1) :1882-+
[5]   Wigner functions and Weyl transforms for pedestrians [J].
Case, William B. .
AMERICAN JOURNAL OF PHYSICS, 2008, 76 (10) :937-946
[6]   GENERALIZED PHASE-SPACE DISTRIBUTION FUNCTIONS [J].
COHEN, L .
JOURNAL OF MATHEMATICAL PHYSICS, 1966, 7 (05) :781-&
[7]  
Cohen L., 2013, The Weyl Operator and Its Generalization, DOI DOI 10.1007/978-3-0348-0294-9
[8]   ON THE OPERATOR BASES UNDERLYING WIGNER, KIRKWOOD AND GLAUBER PHASE-SPACE FUNCTIONS [J].
ENGLERT, BG .
JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 1989, 22 (06) :625-640
[9]  
Giese E., 2014, P INT SCH PHYS E FER
[10]   DISTRIBUTION-FUNCTIONS IN PHYSICS - FUNDAMENTALS [J].
HILLERY, M ;
OCONNELL, RF ;
SCULLY, MO ;
WIGNER, EP .
PHYSICS REPORTS-REVIEW SECTION OF PHYSICS LETTERS, 1984, 106 (03) :121-167