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Local Lorentz Invariance violating (LLIV) and Einstein equivalence principleviolating (EEPV) effects in atomic experiments are discussed. The EEPV effectsare strongly enhanced in the narrow 7.8 eV transition in 229Th nucleus. NuclearLLIV momentum tensors describing anisotropy in the maximal attainable speed formassive particles (analog of Michelson-Morley experiment for light) areexpressed 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 improvethe limits on the proton LLIV constants by 4 orders of magnitude.

Enhanced violation of the Lorentz invariance and Einstein's equivalence principle in nuclei and atoms