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We study the quantum-mechanical problem of scattering caused by a localizedobstacle that breaks spatial and temporal reversibility. Accordingly, we followMaxwell's prescription to achieve a violation of the second law ofthermodynamics by means of a momentum-dependent interaction in the Hamiltonian,resulting in what is known as Maxwell's demon. We obtain the energy-dependentGreen's function analytically, as well as its meromorphic structure. The poleslead directly to the solution of the evolution problem, in the spirit of M.Moshinsky's work in the 1950s. Symmetric initial conditions are evolved in thisway, showing important differences between classical and wave-likeirreversibility in terms of collapses and revivals of wave packets. Our settingcan be generalized to other wave operators, e.g. electromagnetic cavities in aclassical regime.

Exact Green's functions for localized irreversible potentials