Faster than Hermitian quantum mechanics.

@article{Bender2007FasterTH,
  title={Faster than Hermitian quantum mechanics.},
  author={Carl M. Bender and Dorje C. Brody and H W Francis Jones and Bernhard K. Meister},
  journal={Physical review letters},
  year={2007},
  volume={98 4},
  pages={040403}
}
Given an initial quantum state |psi(I)> and a final quantum state |psi(F)>, there exist Hamiltonians H under which |psi(I)> evolves into |psi(F)>. Consider the following quantum brachistochrone problem: subject to the constraint that the difference between the largest and smallest eigenvalues of H is held fixed, which H achieves this transformation in the least time tau? For Hermitian Hamiltonians tau has a nonzero lower bound. However, among non-Hermitian PT-symmetric Hamiltonians satisfying… CONTINUE READING

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