Time evolution of the classical and quantum mechanical versions of diffusive anharmonic oscillator: an example of Lie algebraic techniques

José Geraldo Peixoto de Faria (1)

1 DADB - Departamento Acadêmico de Disciplinas Básicas

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 (Schr\"{o}dinger cat states) and revivals.

Mots clés: Decoherence; open systems; quantum statistical methods; Lie algebras of Lie groups

Domaines: Physique Quantique [quant-ph]

José Geraldo Peixoto de Faria. Time evolution of the classical and quantum mechanical versions of diffusive anharmonic oscillator: an example of Lie algebraic techniques. The European Physical Journal D : Atomic, molecular, optical and plasma physics, 2007, 42 (1), pp.153-162. ⟨10.1140/epjd/e2006-00278-8⟩. ⟨hal-00152895⟩