  Local Lorentz Invariance violating (LLIV) and Einstein equivalence principle
violating (EEPV) effects in atomic experiments are discussed. The EEPV effects
are strongly enhanced in the narrow 7.8 eV transition in 229Th nucleus. Nuclear
LLIV momentum tensors describing anisotropy in the maximal attainable speed for
massive particles (analog of Michelson-Morley experiment for light) are
expressed in terms of the experimental values of nuclear quadrupole moments.
Calculations for nuclei of experimental interest 133Cs, 85Rb, 87Rb, 201Hg,
131Xe and 21Ne have been performed. The results for 21Ne are used to improve
the limits on the proton LLIV constants by 4 orders of magnitude.
