Mappings of open quantum systems onto chain representations and Markovian embeddings

Details Mappings of open quantum systems onto chain representations and Markovian embeddings Mappings of open quantum systems onto chain representations and Markovian embeddings

2011-11-22

arxiv.org/abs/1111.5262v1

Physics

Quantum Physics

44 pages, 1 figure

Scientific paper

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.

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