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We study spin imbalance effects on the Larkin-Ovchinikov-Fulde-Ferrel (LOFF)state relevant for superconductors under a strong magnetic field and spinpolarized ultracold Fermi gas. We obtain the exact solution for the condensateswith arbitrary spin imbalance and the fermion spectrum perturbatively in thepresence of small spin imbalance. We also obtain fermion zero mode exactlywithout perturbation.

Spin imbalance effect on Larkin-Ovchinnikov-Fulde-Ferrel state