Proca equation for laser pulses interaction with matter
  In this paper the interaction of ultrashort laser pulses with matter is investigated. The scattering and potential motion of heat carriers, as well as the external force are considered. It is shown that the heat transport is described by the Proca equation. For thermal Heisenberg type relation V\tau ~ \hbar, (\tau is the relaxation time and V is the potential) the solution of the Proca equation (PR) are the distortionless damped wave equation.   Key words: Ultrashort laser pulses; Quantum heat transport equation; Proca thermal equation. 
J. Marciak-Kozlowska, M. Kozlowski