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A clock comparison experiment, analyzing the ratio of spin precession frequencies of stored ultracold neutrons and $^{199}$Hg atoms is reported. %57 No daily variation of this ratio could be found, from which is set an upper limit on the Lorentz invariance violating cosmic anisotropy field $b_{bot} < 2 times 10^{-20} {rm eV}$ (95% C.L.). This is the first limit for the free neutron. This result is also interpreted as a direct limit on the gravitational dipole moment of the neutron $|g_n| < 0.3 $eV/$c^2$ m from a spin-dependent interaction with the Sun. Analyzing the gravitational interaction with the Earth, based on previous data, yields a more stringent limit $|g_n| < 3 times 10^{-4} $eV/$c^2 $m.
A search for neutrino oscillations induced by Lorentz violation has been performed using 4,438 live-days of Super-Kamiokande atmospheric neutrino data. The Lorentz violation is included in addition to standard three-flavor oscillations using the non-
A test of parity-conserving, time-reversal non-invariance (PC TRNI) has been performed in 5.9 MeV polarized neutron transmission through nuclear spin aligned holmium. The experiment searches for the T-violating five-fold correlation via a double modu
A new test of Lorentz invariance in the weak interactions has been made by searching for variations in the decay rate of spin-polarized 20Na nuclei. This test is unique to Gamow-Teller transitions, as was shown in the framework of a recently develope
We search for a dependence of the lifetime of $^{20}text{Na}$ nuclei on the nuclear spin direction. Such a directional dependence would be evidence for Lorentz-invariance violation in weak interactions. A difference in lifetime between nuclei that ar
We analyze a dynamics of ultracold neutrons (UCNs) caused by interactions violating Lorentz invariance within the Standard Model Extension (SME) (Colladay and Kostelecky, Phys. Rev. D55, 6760 (1997) and Kostelecky, Phys. Rev. D69, 105009 (2004)). We