An article by Rossini, Benenti and Casati. They study two coupled qubits with a chaotic environment. The purpose is to determine if the chaotic environment gives enough complexity to mimic the effect of a many body real environment. The answer is yes, of course, but there are some points in the paper that make it less general than what it could be. In particular, the choice of coupling between system and environment is so that the environment ONLY couples to the states |00> and |11>, leaving in the end an effective spin 1/2 as the system. This is then obscured by the choice of initial state of the system, |phi>=|00>+|11>. With these choices, all the results can basically be described by a Loschmidt echo of the environment evolving with two kicking strengths. For instance, Fig 2 has only "Fermi golden rule" decay of the Loschmidt echo because of the initial state chosen for the environment, a random superposition. To get Lyapunov decay you would need a coherent state or something like that. The rest of the paper is nice, I like the analytical results they are able to obtain. 

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Posted by fercook to Science at 8/29/2006 09:38:25 AM

Labels: reviews, science