Energy dissipation in unitary dynamics

Question

In the context of quantum mechanics it is often (e.g. in several Wikipedia pages, like on Quantum dissipation) stated, that:

"If the time evolution of a system is unitary (e.g. always in the Hamiltonian formalism), then we have no dissipation of energy. To include such energy dissipation, we need something like a Lindblad equation."

As far as I understand the subject, that is wrong. One can have energy dissipation in a unitary time evolution, e.g. if the Hamiltonian is explicitely time dependent. My assumption at the moment is, that a non-unitary time evolution (like with a Lindblad equation) was introduced to describe something like dephasing. Maybe dephasing is related to information/entropy dissipation and the authors had a wrong definition of "dissipation" in this context?

I do not find any references wich explain the subject the way I see it, just the other way round. Is there an expert on the subject who can comment on this?

Answer 1

I do not know much about the Lindblad equation, but I think you are correct, a time dependent Hamiltonian can describe dissipative process where the system loses energy. In classical mechanics it is possible to understand this time dependent Hamiltonian as a result of evaluating some bigger Hamiltonian where the terms depending on environments variables are replaced by their time dependent values.

However, for systems that manifest dissipation due to interaction with environment, it is difficult to find the time dependent functions necessary, because that requires solving the equations of motion with very large number of degrees of freedom.

So simplified view on the environment is more popular, there are some plausible assumptions which restrict the possible effects of environment on density matrix of the system, and these then lead to Lindblad like equations.