Journal of Physics A Mathematical and Theoretical

Emergent randomness in the Jaynes–Cummings model

B. M. Garraway, Stig Stenholm

Published Feb 5, 2008• 1 citation

Abstract

We consider the well-known JaynesCummings model and ask if it can display randomness. As a solvable Hamiltonian system, it does not display chaotic behaviour in the ordinary sense. Here, however, we look at the distribution of values taken up during the total time evolution. This evolution is determined by the eigenvalues distributed as the square roots of integers and leads to a seemingly erratic behaviour. That this may display a random Gaussian value distribution is suggested by an exactly provable result by Kac. In order to reach our conclusion we use the Kac model to develop tests for the emergence of a Gaussian. Even if the consequent double limits are difficult to evaluate numerically, we find definite indications that the JaynesCummings case also produces a randomness in its value distributions. Numerical methods do not establish such a result beyond doubt, but our conclusions are definite enough to suggest strongly an unexpected randomness emerging in a dynamic time evolution.

DOI: 10.1088/1751-8113/41/7/075304

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