NON-HERMITIAN TUNNELING OF OPEN QUANTUM-SYSTEMS

We discuss some aspects of the time picture of tunneling for open quan tum systems described by non-Hermitian (NH) Hamiltonians. The concept of sojourn time for such systems is introduced in the framework of the biorthonormal formalism. Due to the various definitions of probabilit y density in the non-Hermitian case, we get three different sojourn ti mes, two real and one complex. We consider as model of a dissipative N H system the complex, generalized parametric oscillator, for which we derive the exact expressions of the three sojourn times in terms of th e Wei-Norman characteristic functions entering the non-unitary evoluti on operators. The special case of the inverted Caldirola-Kanai oscilla tor with complex friction parameter is investigated for an initial ext ended wavepacket. We also discuss the Landau-Zener-like transitions of the NH parametric oscillator, i.e. the dissipative tunneling through a dynamical barrier due to the perturbative effect of the damping.