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Abstract: . For a quantum observable A h depending on a parameter h we define the notion "A h converges in the classical limit". The limit is a function on phase space. Convergence is in norm in the sense that A h ! 0 is equivalent with kA h k ! 0. The h-wise product of convergent observables converges to the product of the limiting phase space functions. h \Gamma1 times the commutator of suitable observables converges to the Poisson bracket of the limits. For a large class of convergent... (Update)
Context of citations to this paper: More
.... An approach to the classical limit emphasizing the limit of observables and their algebraic structure has recently been developed in [We2] (compare also [Rie, Em1] This approach makes rigorous the intuitive criterion for deciding which observables in quantum theory may...
...R.F. Werner 1;2 Abstract. We construct the unique optimal quantum device for turning a finite number of d level quantum systems in the same unknown pure state oe into M systems of the same kind, in an approximation of the M fold tensor product of the state oe. 1 Inst. f....
Cited by: More
Optimal Cloning of Pure States - Werner (1998) (Correct)
Classical Mechanics as Quantum Mechanics with Infinitesimal h - Werner, Wolff (1995) (Correct)
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0.9: On the Concentration of Quantum States in Phase Space - Werner (1993) (Correct)
0.6: Mixed States with Positive Wigner Functions - Bröcker, Werner (1994) (Correct)
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BibTeX entry: (Update)
R.F. Werner:"The classical limit of quantum theory", Preprint, Osnabr uck 1994 http://citeseer.ist.psu.edu/article/werner95classical.html More
@misc{ werner94classical,
author = "R. Werner",
title = "The classical limit of quantum theory",
text = "R.F. Werner:The classical limit of quantum theory, Preprint, Osnabr uck
1994",
year = "1994",
url = "citeseer.ist.psu.edu/article/werner95classical.html" }
Citations (may not include all citations):50 the quantum correction for thermodynamic equilibrium (context) - Wigner - 1932
13 Classical limit of the quantized hyperbolic toral automorphi.. - Esposti, Graffi et al. - 1995
12 Ground states of the infinite q-deformed Heisenberg ferromag.. - Gottstein, Werner - 1994
12 Deformation quantization of Heisenberg manifolds (context) - Rieffel - 1989
11 New York (context) - Katznelson, to et al. - 1968
9 Evolution of semiclassical quantum states in phase space (context) - Berry, Balazs - 1979
8 The classical limit of quantum partition of functions (context) - Simon - 1980
5 The classical limit for quantum mechanical correlation funct.. (context) - Hepp - 1974
4 Fedoriuk: Semi-classical approximation in quantum mechanics (context) - Maslov - 1981
4 When is the Wigner quasi-probability density nonnegative (context) - Hudson - 1974
4 Quantum harmonic analysis on phase space (context) - Werner - 1984
4 New York (context) - Kato, for et al. - 1984
4 North Holland (context) - Holevo, statistical et al. - 1982
4 Deformations of algebras of observables and the classical li.. - Landsman - 1993
3 Wigner and Husimi functions in quantum mechanics (context) - Takahashi - 1986
3 An algebra of pseudodifferential operators and the asymptoti.. (context) - Voros - 1978
3 Local dynamics of mean-field quantum systems - Duffield, Werner - 1992
2 The Gibbs variational principle for inhomogeneous mean field.. (context) - Raggio, Werner - 1991
2 Classical mechanics as quantum mechanics with infinitesimal .. - Werner, Wolff - 1994
2 Oscillatory integrals and the method of stationary phase in .. (context) - Albeverio, Hegh-Krohn - 1977
2 Lindstrm: Nonstandard methods in stochastic analysis and mat.. (context) - Albeverio, Fenstad et al. - 1986
2 A non-negative Wigner-type distribution (context) - Cartwright - 1976
2 Heisenberg's picture and non commutative geometry of the sem.. (context) - Bellissard, Vittot - 1990
2 the semiclassical localization of quantum probability (context) - Duclos, Hogreve - 1993
2 The classical limit of quantum spin systems (context) - Lieb - 1973
2 the validity of the WKB approximation (context) - Burdick, Schmidt - 1994
2 Quantum coherent operators: a generalization of coherent sta.. (context) - Lieb, Solovej - 1991
2 Geometric dequantization and the correspondence problem (context) - Emch - 1983
1 McGraw-Hill Kogakusha (context) - Schiff, mechanics - 1955
1 The classical limit of quantum theory (context) - Bruer - 1982
1 Estimates of quantum deviations from classical mechanics usi.. (context) - Blanchard, Combe et al. - 1985
1 Classical and thermodynamic limits for generalised quantum s.. (context) - Duffield - 1990
1 La m'echanique quantique est-elle une m'echanique statistiqu.. (context) - Bopp - 1956
1 Lectures in the Mark Kac Seminar, Summer 1993; Written versi.. (context) - quantum, large - 1993
1 volumes Springer (context) - Hormander, of et al. - 1985
1 Feynman path integrals and quantum mechanics as h ! 0 (context) - Truman - 1976
1 Mixed states with positive Wigner functions (context) - Brocker, Werner - 1995
1 Some extensions of the semiclassical limit h ! 0 for Wigner .. (context) - Arai - 1995
1 Springer Lect (context) - Helffer, for et al. - 1988
1 Dynamics by white noise Hamiltonians (context) - Fischer, Leschke et al. - 1994
1 Parity operator and quantization of delta-functions (context) - Grossmann - 1976
1 the relation between classical and quantum statistical mecha.. (context) - Wreszinski, Scharf - 1987
1 Froman: JWKB Approximation; Contributions to the theory (context) - Froman - 1965
1 The classical limit of dynamics for spaces quantized by an a.. (context) - Rieffel - 1995
Documents on the same site (http://www.imaph.tu-bs.de/qi/papers.html): More
On Some Additivity Problems in Quantum Information Theory - Amosov Holevo And (Correct)
All Teleportation and Dense Coding Schemes - Werner (2000) (Correct)
Quantum Information Theory - an Invitation - Werner (2001) (Correct)
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