Non local screening in a vortex line liquid

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We show that the recent experiments \cite{safar} reporting the onset of the non-local conductivity in the vortex state of $YBaCuO$ single crystals indicate the presence of a new liquid phase of vortices. This phase is intermediate between the normal metal and the Abrikosov lattice. We use the mapping of the vortex problem to the problem of bose liquid to determine theoretically the properties of the proposed vortex liquid phase and compare them with the data.
This is a more detailed ``Letter'' version of the paper which was originally a very short ``Comment''; 3 pages, LATEX file with 1 figure

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