Reduced density matrix and internal dynamics for multicomponent regions Casini, H; Huerta, M [Centro Atomico Bariloche, 8400-S.C. de Bariloche, Rio Negro (Argentina)] 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; DECOMPOSITION; DENSITY MATRIX; ENTROPY; EVOLUTION; MASS; QUANTUM ENTANGLEMENT; QUANTUM TELEPORTATION; SPACE; TRAJECTORIES; VACUUM STATES; CHEMICAL REACTIONS; MATRICES; PHYSICAL PROPERTIES; THERMODYNAMIC PROPERTIES CHEMICAL REACTIONS; MATRICES; PHYSICAL PROPERTIES; THERMODYNAMIC PROPERTIES We find the density matrix corresponding to the vacuum state of a massless Dirac field in two dimensions reduced to a region of the space formed by several disjoint intervals. We calculate explicitly its spectral decomposition. The imaginary power of the density matrix is a unitary operator implementing an internal time flow (the modular flow). We show that in the case of more than one interval, this evolution is non-local, producing both advance in the causal structure and 'teleportation' between the disjoint intervals. However, it only mixes the fields on a finite number of trajectories, one for each interval. As an application of these results we compute the entanglement entropy for the massive multi-interval case in the small mass limit. Available from http://dx.doi.org/10.1088/0264-9381/26/18/185005 United Kingdom 2009-09-21 English Journal Article Journal Name: Classical and Quantum Gravity; Journal Volume: 26; Journal Issue: 18; Other Information: DOI: 10.1088/0264-9381/26/18/185005; PII: S0264-9381(09)17120-4 Medium: X; Size: 15 pages https://doi.org/10.1088/0264-9381/26/18/185005 [] 18 26 Journal ID: ISSN 0264-9381; CQGRDG; TRN: GB10P2734106647 GBN 2012-12-21 21376193