T. Brocker and R.F. Werner: "Mixed states with positive Wigner functions", J.Math.Phys. 36(1995) 62--75  Home/Search   Document Not in Database   Summary   Related Articles

....(W h ) 2=h) d Gamma ff h ( Pi) Delta ; 4:14) where ( Pi ) x) Gammax) is the parity operator [Gro] Here we have chosen the normalization such that formally, or with suitable regularization, 2) Gammad R dx dp (W h ) x; p) 1. Of course, W h is rarely positive [Hud,BW] and in general not even integrable. Ignoring such technical quibbles, however, as most of the literature on Wigner functions does, we get a simplified formulation of the classical limit, and also an interesting class of convergent states. The modified definition of the classical limit is ....

....) is positive for all h, or at least for a sequence h n along which we want to take the classical limit. In the terminology of Narcowich [Nar] this means that the Wigner spectrum of the Fourier transform of ae contains the sequence h n . This is a severe constraint on the classical densities ae [BW] 23 5. Proofs In this section we prove the results stated in Section 2 and Section 3, apart from the Theorems 3 and 4 about Poisson brackets and the dynamics [We5] We first state a Lemma that allows us to handle the maps j hh 0 with h; h 0 0 and their compositions more easily. The basic ....

[Article contains additional citation context not shown here]

T. Brocker and R.F. Werner: "Mixed states with positive Wigner functions", J.Math.Phys. 36(1995) 62--75

Online articles have much greater impact   More about CiteSeer.IST   Add search form to your site   Submit documents   Feedback  

CiteSeer.IST - Copyright Penn State and NEC