Time reversal of Bose-Einstein condensates
  Using Gross-Pitaevskii equation, we study the time reversibility of Bose-Einstein condensates (BEC) in kicked optical lattices, showing that inside the regime of quantum chaos the dynamics can be inverted from explosion to collapse. The accuracy of time reversal decreases with the increase of atom interactions inside BEC, until it is completely lost. Surprisingly, quantum chaos helps to restore time reversibility. These predictions can be tested with existing experimental setups. 
J. Martin, B. Georgeot and D. L. Shepelyansky