Please use this identifier to cite or link to this item: https://hdl.handle.net/11147/2591
Title: Madelung representation of damped parametric quantum oscillator and exactly solvable Schrödinger-Burgers equations
Authors: Atılgan Büyükaşık, Şirin
Pashaev, Oktay
Keywords: Schrödinger equation
Fluid equations
Hydrodynamics
Exact solutions
Issue Date: 1-Dec-2010
Publisher: American Institute of Physics
Source: Atılgan Büyükaşık, Ş., and Pashaev, O. (2010). Madelung representation of damped parametric quantum oscillator and exactly solvable Schrödinger-Burgers equations. Journal of Mathematical Physics, 51(12). doi:10.1063/1.3524505
Abstract: We construct a Madelung fluid model with time variable parameters as a dissipative quantum fluid and linearize it in terms of Schrödinger equation with time-dependent parameters. It allows us to find exact solutions of the nonlinear Madelung system in terms of solutions of the Schrödinger 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 Schrödinger-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. © 2010 American Institute of Physics.
URI: http://doi.org/10.1063/1.3524505
http://hdl.handle.net/11147/2591
ISSN: 0022-2488
0022-2488
Appears in Collections:Mathematics / Matematik
Scopus İndeksli Yayınlar Koleksiyonu / Scopus Indexed Publications Collection
WoS İndeksli Yayınlar Koleksiyonu / WoS Indexed Publications Collection

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