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Fuchs, P., Jüngel, A., & Von Renesse, M. (2013). On the Lagrangian structure of quantum fluid models. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 34(4), 1375–1396. http://hdl.handle.net/20.500.12708/155473
Quantum hydrodynamics; quantum Navier-Stokes systems
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Abstract:
Siehe englisches Abstract.
de
Some quantum
uid models are written as the Lagrangian
ow of
mass distributions and their geometric properties are explored. The rst model
includes magnetic e ects and leads, via the Madelung transform, to the electromagnetic
Schr odinger equation in the Madelung representation. It is shown
that the Madelung transform is a symplectic map between Hamiltonian systems.
The second model is obt...
Some quantum
uid models are written as the Lagrangian
ow of
mass distributions and their geometric properties are explored. The rst model
includes magnetic e ects and leads, via the Madelung transform, to the electromagnetic
Schr odinger equation in the Madelung representation. It is shown
that the Madelung transform is a symplectic map between Hamiltonian systems.
The second model is obtained from the Euler-Lagrange equations with
friction induced from a quadratic dissipative potential. This model corresponds
to the quantum Navier-Stokes equations with density-dependent viscosity. The
fact that this model possesses two di erent energy-dissipation identities is explained
by the de nition of the Noether currents.
en
Research Areas:
Quantum Modelling and Simulation: 30% Mathematical and Algorithmic Foundations: 70%
