The lowenergy physics of systems coupled to their surroundings is understood by truncating to effective Hamiltonians; these tend to reduce to a few canonical forms, involving coupling to "baths" of oscillators or spins. The method for doing this is demonstrated using examples from magnetism, superconductivity, and measurement theory, as is the way one then solves for the lowenergy dynamics. Finally, detailed application is given to the exciting recent Quantum relaxation and tunneling work in naomagnets.
