Pierangelo Marcati

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  Problems on Quantum Hydrodynamics
  Pierangelo Marcati

  The QHD system is used to describe models in superfluidity, in superconductivity, in Bose Einstein condensates and also to model carrier transport for semiconductor devices at nanoscale. Several mathematical questions need to be addressed to fully understand the various hydrodynamic quantities and their relationships with the Schroedinger and the Wigner pictures.

  
  

  The mathematics need to agree with the requirement from the physics on various issues. In particular the meaning of the velocity in presence of vacuum, the presence of quantum vortices, the presence of the collision terms in semiconductors modeling.

  
  

  Our approach is devised from an the analysis of the dispersive behavior of the solutions, on the factorization of the wave functions (polar decomposition) and stability of null forms.

  
  

  There will be sketched recent advances on Magneto Quantum Hydridynamics and on other dispersive models like Euler Korteweg systems. Weak Strong uniqueness via relative entropy methods will also be mentioned. Finally we discuss perspectives related to the study of quantum turbulence.