# Physicists have figured out why some quantum systems never reach equilibrium

Some quantum systems never show equilibrium. Physicists have tried for years to understand

the cause of this instability. However, now scientists have proposed a theory that puts everything in its place. The research article was published in the journal Proceedings of the National Academy of Sciences.

If you extract a cold drink fromrefrigerator and place the container with it on the table, then after a while the liquid will acquire room temperature. That is, thermal equilibrium will be established between the liquid and the room. At the macro level, this rule is always respected, but when quantum laws come into play, sometimes something strange begins to happen.

### Research text

In turn, unstable quantum systems do not come to equilibrium. It's like a glass of water from the refrigerator at room temperature starts to cool down.

Nicolo Defenou, a scientist at the Zurich Institute for Theoretical Physics, has now found a way to elegantly explain this behavior.

He considered a one-dimensional system in which there isthe only quantum particle that can only be in strictly limited positions along the line. This is similar to a game in which the figure moves along a straight line for as many cells as indicated by the die roll. For example, that there is a dice, all sides of which are marked as "one" or "minus one", and suppose the player rolls it once, second, third. The figurine will move to the adjacent square, and from there it will either go back or go to the next one. Etc.

However, the question is:what happens if the player rolls the die an infinite number of times? If there are only a few squares in the game, then from time to time it will return to its starting point. But it is completely impossible to predict exactly where he will be at any given time - after all, the die rolls are unknown. A similar situation develops with particles that obey the laws of quantum mechanics: it is impossible to know exactly where they are at a given moment in time. Yet their location can be determined using probability distributions.

Every distribution is the resultdifferent superposition of probabilities for individual places and corresponds to a certain energy state of the particle. As a result, the number of stable energy states coincides with the number of degrees of freedom of the system and, therefore, exactly corresponds to the number of admissible positions. It is worth noting that all stable probability distributions at the starting point are not at all equal to zero. As a result, at some point, the cube returns to its original location.

For a quantum particle, this means thatthere are an immeasurable number of ways in which the probabilities of individual locations can be combined to form distributions. As a result, they can occupy not only certain discrete energy states, but also all possible ones in the continuous spectrum. The new theory put forward by Nicolo Defenu explains what scientists have already observed in experiments many times: systems in which long-range interactions take place do not reach a stable equilibrium, but rather a metastable state in which they always return to their original position.