Adiabatic Measurements on Metastable Systems

In several situations, most notably when describing metastable states, a system can evolve according to an effective non hermitian Hamiltonian. To each eigenvalue of a non hermitian Hamiltonian is associated an eigenstate $\vert\phi\rangle$ which evolves forward in time and an eigenstate $\langle{\psi}\vert$ which evolves backward in time. Quantum measurements on such systems are analyzed in detail with particular emphasis on adiabatic measurements in which the measuring device is coupled weakly to the system. It is shown that in this case the outcome of the measurement of an observable $A$ is the weak value $\langle{\psi}\vert A\vert\phi\rangle / \langle{\psi}\vert{\phi}\rangle$ associated to the two-state vector $\langle{\psi}\vert$ $\vert\phi\rangle$ corresponding to one of the eigenvalues of the non hermitian Hamiltonian. The possibility of performing such measurements in a laboratory is discussed.