# What is quantum fluctuation in the Bose-Einstein condensates theory?

I would like to understand what quantum fluctuation really means. I think it's the particles that are not in the ground state. Am I right? But then, what are the differences between quantum fluctuations and thermal fluctuations?

Another question. How do these quantum fluctuations stabilize the BEC against the mean-field collapse? I've read something about soft and hard excitations, but I do not know how these stabilize the BEC.

• Quantum fluctuations are not from a system being out of the ground state. "Quantum fluctuations" refers to the fact that, for example, $\langle 0 | \hat{x}^2 | 0 \rangle \neq 0$, i.e. the mean square value of an operator in the ground state may not be zero. – DanielSank Oct 19 '18 at 19:48