---------------------------- Interaction with a heat bath ---------------------------- Quantum mechanics in the presence of a heat bath requires the use of density matrices. Instead of the usual von-Neumann equation rhodot = rho \lp H (for \lp see the section on 'Quantum-classical correspondence'), the dynamics of the density matrix is given by a dissipative version of it, rhodot = rho \lp H + L(rho) usually associated with the name of Lindblad. Here L(rho) is a linear operator responsible for dissipation of energy to the heat bath; it is not a simple commutator but can have a rather complex form. To get the Lindblad dynamics from a Hamiltonian description of system plus bath, one uses the projection operator formalism. The clearest treatment I know of is in H Grabert, Projection Operator Techniques in Nonequilibrium Statistical Mechanics, Springer Tracts in Modern Physics, 1982. The final equations for the Lindblad dynamics are (5.4.48/49) in Grabert's book.