Loschmidt echoes in two-body random matrix ensembles

Details Loschmidt echoes in two-body random matrix ensembles Loschmidt echoes in two-body random matrix ensembles

2007-02-05

arxiv.org/abs/cond-mat/0702079v2

Phys. Rev. B 76, 035122 (2007)

Physics

Condensed Matter

Other Condensed Matter

9 pages, 5 figures (6 eps files), RevTex; v2: slight modifications following referees' suggestions

Scientific paper

10.1103/PhysRevB.76.035122

Fidelity decay is studied for quantum many-body systems with a dominant independent particle Hamiltonian resulting e.g. from a mean field theory with a weak two-body interaction. The diagonal terms of the interaction are included in the unperturbed Hamiltonian, while the off-diagonal terms constitute the perturbation that distorts the echo. We give the linear response solution for this problem in a random matrix framework. While the ensemble average shows no surprising behavior, we find that the typical ensemble member as represented by the median displays a very slow fidelity decay known as ``freeze''. Numerical calculations confirm this result and show, that the ground state even on average displays the freeze. This may contribute to explanation of the ``unreasonable'' success of mean field theories.

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