Dissipative squeezed vacuum in non-equilibrium thermo field dynamics

Degenerate parametric amplification accompanied by dissipation is analyzed within the canonical operator formalism for quantum dissipative systems named non-equilibrium thermo field dynamics. The vacuum of the system is subject to both dissipation and breaking of phase symmetry due to squeezing. The annihilation-creation operators for the vacuum are derived and the structure of the vacuum is examined. The effects of dissipation on squeezing and uncertainty relation are estimated.