科研之友
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摘要
We construct a Madelung fluid model with time variable parameters as a dissipative quantum fluid and linearize it in terms of Schrodinger equation with time-dependent parameters. It allows us to find exact solutions of the nonlinear Madelung system in terms of solutions of the Schrodinger equation and the corresponding classical linear ordinary differential equation with variable frequency and damping. For the complex velocity field, the Madelung system takes the form of a nonlinear complex Schrodinger-Burgers equation, for which we obtain exact solutions using complex Cole-Hopf transformation. In particular, we give exact results for nonlinear Madelung systems related with Caldirola-Kanai-type dissipative harmonic oscillator. Collapse of the wave function in dissipative models and possible implications for the quantum cosmology are discussed.
- 出版日期2010-12
