2007/09/21 by L. Kaplan, L Kaplan, F. Leyvraz +5 · 1 citation
Mathematics · Physics and Astronomy · #Quantum chaos and dynamical systems #Random Matrices and Applications #Spectral Theory in Mathematical Physics #quant-ph
paper · pdf · doi:10.1088/1751-8113/40/49/f04
published as J. Phys. A: Math. Theor. 40 F1063-F1068 (2007) · 7 pages 3 figures
arxiv created 2007/09/21 · openalex publication_date 2007/11/21 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
It is commonly thought that a state-dependent quantity, after being averaged over a classical ensemble of random Hamiltonians, will always become independent of the state. We point out that this is in general incorrect: if the ensemble of Hamiltonians is time reversal invariant, and the quantity involves the state in higher than bilinear order, then we show that the quantity is only a constant over the orbits of the invariance group on the Hilbert space. Examples include fidelity and decoherence in appropriate models.