An “almost diagonal” reduced density matrix (in coordinate representation) is usually a result of environment induced decherence and is considered the sign of classical behavior. We show that the proton of a ground state hydrogen atom can indeed possess such a density matrix. This example demonstrates that the “almost diagonal” structure may be derived from an interaction with a low number of degrees of freedom which play the role of the environment. We also show that decoherence effects in our example can only be observed if the interaction with the measuring device is significantly faster than the interaction with the environment (the electron). In the opposite case, when the interaction with the environment is significant during the measurement process, coherence is maintained. Finally, we propose a neutron scattering experiment on cold He atoms to observe decoherence which shows up as an additional positive contribution to the differential scattering cross section. This contribution is inversely proportional to the bombarding energy.
We investigate light propagation in the Swiss-cheese model. On both sides of Swiss-cheese sphere surfaces, observers resting in the flat Friedmann-Robertson-Walker (FRW) space and the Schwarzschild space respectively, see the same light ray enclosing different angles with the normal. We examine light refraction at each crossing of the boundary surfaces, showing that the angle of refraction is larger than the angle of incidence for both directions of the light.
A classification of the time evolution of the two-soliton solutions of the Boussinesq equation is given, based on the number of extrema of the wave. For solitons moving in the same directions, three different scenarios are found, while it is shown that only one of these scenarios exists in case of oppositely moving solitons.
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