Exploring Quantum Systems: Steady States and Eigenstate Behavior

In the world of quantum physics, understanding how systems behave is crucial. One key idea is the Eigenstate Thermalization Hypothesis (ETH). It suggests that individual quantum states can represent the thermal properties of a system. But what about systems that are always changing, not in balance? This is where the Gorini-Kossakowski-Lindblad-Sudarshan (GKLS) Master Equation comes into play. It helps describe these open quantum systems. Researchers have found that the eigenstates of non-equilibrium steady state (NESS) density matrices also follow a version of ETH. This is similar to how eigenstates of Gibbs density matrices behave in systems at equilibrium. The new version, called NESS-ETH, can help find pure states that show the same properties as the NESS. These pure states can be seen as solutions to the GKLS Master Equation. But does NESS-ETH always work? Not necessarily. It can break down when there are symmetries, integrability, or many-body localization in the system. This means the behavior of quantum systems can be quite complex and depends on various factors. Understanding these concepts can help in developing new technologies and improving our knowledge of quantum mechanics. It's a fascinating area of study that continues to evolve.