Andreev levels as a quantum dissipative environment

We argue that at subgap energies quantum behavior of superconducting weak links can be exactly accounted for by an effective Hamiltonian for a Josephson particle in a quantum dissipative environment formed by Andreev levels. This environment can constitute an important source for intrinsic inelastic relaxation and dephasing in highly transparent weak links. We investigate the problem of macroscopic quantum tunneling in such weak links demonstrating that---depending on the barrier transmission---the supercurrent decay can be described by three different regimes: (i) weak intrinsic dissipation, (ii) strong intrinsic dissipation, and (iii) strong capacitance renormalization. Crossover between quantum and thermally assisted supercurrent decay regimes can also be strongly affected by the Andreev level environment.