Exploring Options Beyond Eigenstate Thermalization

Have you ever wondered what happens to a small group of particles when they're left alone in a quantum world? According to the eigenstate thermalization hypothesis (ETH), these particles should eventually reach a state of thermal equilibrium. But what if they don't? Let's take a look at some interesting alternatives to ETH. First, let's chat about von Neumann's quantum ergodic theorem. This theorem basically assumes that the particles will spread out evenly, covering all possible states. Sounds a bit like ETH, right? Now, what if we suddenly change the rules of the game, a process called a "sudden quench"? Can special types of initial states still lead to thermal behavior, even in systems that don't follow ETH, like integrable systems? We found that it's possible, but only if the initial states played by ETH's rules before the sudden change. It's like when you're playing a game with strict rules, and then someone suddenly changes the rules. If you were playing by the old rules, you might still see some familiar patterns. But if you were doing something completely different, it might be a whole new ball game.