Scale invariant distribution functions in quantum systems with few degrees of freedom

Understand

Scale invariance usually occurs in extended systems where correlation functions decay algebraically in space and/or time.

• Here we introduce a new type of scale invariance, occurring in the distribution functions of physical observables.
• At equilibrium these functions decay over a typical scale set by the temperature, but they can become scale invariant in a sudden quantum quench.
• We exemplify this effect through the analysis of linear and non-linear quantum oscillators.