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

页数：11

共 17 条

[11]

Kim M., IN PRESS

[12] WIGNER REPRESENTATION OF QUANTUM OPERATORS + ITS APPLICATIONS TO ELECTRONS IN MAGNETIC FIELD [J].

KUBO, R .

JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN, 1964, 19 (11) :2127-&

[13]

McCoy N H, 1932, Proc Natl Acad Sci U S A, V18, P674, DOI 10.1073/pnas.18.11.674

[14] QUANTUM MECHANICS AS A STATISTICAL THEORY [J].

MOYAL, JE .

PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY, 1949, 45 (01) :99-124

[15] WIGNER FUNCTION AS EXPECTATION VALUE OF A PARITY OPERATOR [J].

ROYER, A .

PHYSICAL REVIEW A, 1977, 15 (02) :449-450

[16]

Schleich W. P., 2001, QUANTUM OPTICS PHASE, P88

[17] On the quantum correction for thermodynamic equilibrium [J].

Wigner, E .

PHYSICAL REVIEW, 1932, 40 (05) :0749-0759

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