  Violation of fundamental symmetries in atoms is the subject of intense
experimental and theoretical interest. P-odd, T-even transitions have been
observed and are in excellent agreement with electroweak theory. Searches for
permanent electric dipole moments have placed bounds on T-odd, P-odd
interactions, constraining proposed extensions to the Standard Model of
elementary particles. Here we propose a new search for T-odd, P-even (TOPE)
interactions in atoms. We consider open-shell atoms, such as the rare-earth
atoms, which have dense, chaotic excitation spectra with strong level
repulsion. The strength of the level repulsion depends on the underlying
symmetries of the atomic Hamiltonian. TOPE interactions lead to enhanced level
repulsion. We demonstrate how a statistical analysis of many chaotic spectra
can determine the strength of level repulsion; in particular, the variance of
the number of levels in an energy range has been shown to be a useful measure.
We estimate that, using frequency comb spectroscopy, a sufficient number of
chaotic levels could be measured to match or exceed the current experimental
bounds on TOPE interactions.
