  Using numerical simulations we investigate dynamical quantum chaos in
isolated nuclear spin systems. We determine the structure of quantum states,
investigate the validity of the Curie law for magnetic susceptibility and find
the spectrum of magnetic noise. The spectrum is the same for positive and
negative temperatures. The study is motivated by recent interest in
condensed-matter experiments for searches of fundamental parity- and
time-reversal-invariance violations. In these experiments nuclear spins are
cooled down to microkelvin temperatures and are completely decoupled from their
surroundings. A limitation on statistical sensitivity of the experiments arises
from the magnetic noise.
