IV. What is flow equilibrium?

 

The term thermal equilibrium means that all energy in a given system is statistical equally distributed. Let’s consider the biggest system we know, the whole universe.

The universe is NOT in thermal equilibrium! How do we know this? We just have to take a look at our solar system. In our solar system an outstanding amount of energy is concentrated in the sun, while the planets have much lower energy and are therefore much colder. So we can justify the statement that the energy in our solar system is NOT statistical equally distributed. Nevertheless we can label planets, or at least some regions on the planets, with a mean temperature, although it is strictly speaking ONLY defined in thermal equilibrium.

Why can we do this? The planets in our solar system are in so called flow equilibrium. They receive energy from the sun as a source and radiate it away into the universe. The gains and losses cancel each other out and we have a more or less stable temperature on the surface.

In the same manner we can keep the magnon gas in the YIG film in flow equilibrium by applying a constant microwave field. This microwave field will continuously create additional magnons. Due to the fact that dissipation of magnons into the lattice takes some time, the number of magnons in this “pumped” magnon gas will be higher than in thermal equilibrium. And due to the fact that interactions between magnons occur on a much shorter time scale than the interactions between magnons and crystalline lattice the energy distribution of this “pumped” magnon gas will be thermal.

Together with the increased magnon number we can conclude that the value of the chemical potential of a magnon gas in flow equilibrium will differ from that of a magnon gas in total thermal equilibrium.

With this section, all basic concepts concerning Magnon Bose Einstein Condensation should be well established. The next section will treat the question:

What are the signatures of a Magnon Bose Einstein Condensation?