  Spectral quasi correlations are small sums of lattice points lying on the
same circle; we show that, for generic integers representable as the sum of two
squares, there are no spectral quasi-correlations. Moreover, we apply our
result to study the nodal length of Arithmetic Random Waves at small scales: we
show that there exists a phase-transition for the distribution of the nodal
length at a logarithmic power above Planck-scale. Furthermore, we give strong
evidence for the existence of an intermediate phase between Arithmetic and
Berry's random waves.
