E.H. Lieb: "The classical limit of quantum spin systems", Commun.Math.Phys. 62(1973) 327--340 Home/Search Document Not in Database Summary Related Articles Check |
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The Classical Limit of Quantum Theory - Werner (1995) (Correct)
....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 Hamiltonians the h wise action of the corresponding dynamics converges to the classical Hamiltonian dynamics. The connections with earlier approaches, based on the WKB method, or on Wigner distribution functions, or on the limits of coherent states are reviewed. Physics and Astronomy classification scheme PACS (1994) 03.65.Sq, 03.65.Db 1 FB Physik, Universitat Osnabruck, 49069 Osnabruck, Germany 2 Electronic mail: ....
....mathematical theory, whose applications are by no means confined to the classical limit. However, much of the rigorous work on the classical limit has been done under this heading. The symbol of a pseudodifferential operator is just its Wigner function, so much of what has been said under (B) applies. The main weakness is again the lack of control on operator norms, and hence of probability estimates, unless additional smoothness assumptions are introduced. Where such assumptions hold, the results fit well into the framework of the present paper, too. D) Feynman integrals. The basic ....
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E.H. Lieb: "The classical limit of quantum spin systems", Commun.Math.Phys. 62(1973) 327--340
Sharp Lieb-Thirring Inequalities In High Dimensions - Laptev, WEIDL (1999) (8 citations) (Correct)
....justified in [15] for certain domains of product structure by using the method of lifting with respect to the dimension d which is also one of the main ideas of this paper. If fl 1, then (0.6) is true for arbitrary Omega . This is a simple corollary of the Berezin Lieb inequality (see [2] x5; [20] and also [17] This approach has been extended in [15] to the Dirichlet boundary value problems for matrices of pseudodifferential operators in R d with constant coefficients. The Berezin Lieb inequality was also used in [16] in order to improve the Lieb constant [19] in the CLR inequality for ....
Lieb E.H.: The classical limit of quantum spin systems. Comm. Math. Phys. 31, 327340 (1973)
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