Quantum dynamical semigroup

Imagine you have a ball that you can bounce as hard as you want. But every time you bounce it, it starts losing a little bit of its energy until eventually, it becomes too tired to bounce anymore. This is kind of like what happens with quantum dynamical semigroups.

For a quantum system, like an atom or a molecule, it can exist in different states, kind of like how you can be standing up or sitting down. But when the quantum system interacts with something else, like light or another particle, it can lose a little bit of its energy and transition to a different state. If this happens over and over again, the quantum system can lose all of its energy and become stuck in a specific state.

Now, a quantum dynamical semigroup is just a fancy way of describing a situation where a quantum system is constantly interacting with something else and losing energy, causing it to eventually settle into a specific state. This can happen in many different quantum systems, from atoms to molecules to even larger structures like biological systems.

But don't worry, sometimes when the quantum system interacts with something else, it can actually gain energy instead of losing it, keeping it from settling into a specific state. This is what is known as a non-Markovian system, which is like our ball bouncing higher and higher with each bounce instead of getting tired.

So, in short, a quantum dynamical semigroup describes a situation where a quantum system is constantly losing energy and settling into a specific state, but not all interactions with the outside world are like this and sometimes a quantum system can gain energy instead.