2005/12/31 by J. G. Peixoto de Faria, J.G. Peixoto de Faria · 1 citation
Physics and Astronomy · #Nonlinear Waves and Solitons #Quantum Mechanics and Non-Hermitian Physics #Quantum chaos and dynamical systems #quant-ph
paper · pdf · doi:10.1140/epjd/e2006-00278-8
published as European Physical Journal D 42, 153-162 (2007) · 21 pages, 6 figures, 2 tables
openalex publication_date 2006/12/21 · arxiv created 2007/06/07 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/29
We present the general solutions for the classical and quantum dynamics of the anharmonic oscillator coupled to a purely diffusive environment. In both cases, these solutions are obtained by the application of the Baker-Campbell-Hausdorff (BCH) formulas to expand the evolution operator in an ordered product of exponentials. Moreover, we obtain an expression for the Wigner function in the quantum version of the problem. We observe that the role played by diffusion is to reduce or to attenuate the the characteristic quantum effects yielded by the nonlinearity, as the appearance of coherent superpositions of quantum states (Schrödinger cat states) and revivals.