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Artificial interface conditions parametrized by a complex number $\theta_{0}$are introduced for 1D-Schr\"odinger operators. When this complex parameterequals the parameter $\theta\in i\R$ of the complex deformation which unveilsthe shape resonances, the Hamiltonian becomes dissipative. This makes possiblean adiabatic theory for the time evolution of resonant states for arbitrarilylarge time scales. The effect of the artificial interface conditions on theimportant stationary quantities involved in quantum transport models is alsochecked to be as small as wanted, in the polynomial scale $(h^N)_{N\in \N}$ as$h\to 0$, according to $\theta_{0}$.

Adiabatic evolution of 1D shape resonances: an artificial interface conditions approach