Intrinsic Inhomogeneity in strongly correlated systems: a possible playground for the cosmology in the lab

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``Intrinsic inhomogeneity'' by competing orders has attracted a keen interest in recent studies of strongly correlated systems. The superconducting gap is inhomogeneous at a nanoscale in high-temperature superconductors, the auto correlation function of which quite resembles that of the galaxy distribution. We have studied transport properties in strongly correlated systems, and have found a novel inhomogeneous state in a charge-ordered organic conductor. This particular material could be a good playground for self-gravitating systems, because (i) the Coulomb interaction is unscreened and thus long-ranged in the charge-ordered state. (ii) The system is close to the quantum critical point, where all the physical properties are scale invariant. (iii) The charge ordered domain accompanies lattice strain which works as a long-range attractive force.

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