Mappings of open quantum systems onto chain representations and Markovian embeddings
Abstract
We derive a sequence of measures whose corresponding Jacobi matrices have special properties and a general mapping of an open quantum system onto 1D semi infinite chains with only nearest neighbour interactions. Then we proceed to use the sequence of measures and the properties of the Jacobi matrices to derive an expression for the spectral density describing the open quantum system when an increasing number of degrees of freedom in the environment have been embedded into the system. Finally, we derive convergence theorems for these residual spectral densities.
 Publication:

arXiv eprints
 Pub Date:
 November 2011
 DOI:
 10.48550/arXiv.1111.5262
 arXiv:
 arXiv:1111.5262
 Bibcode:
 2011arXiv1111.5262W
 Keywords:

 Quantum Physics;
 Mathematical Physics
 EPrint:
 44 pages, 1 figure. V2, small changes