Particle-Time Duality in the Kicked Ising Chain I: The Dual Operator
  We demonstrate that the dynamics of kicked spin chains possess a remarkable duality property. The trace of the unitary evolution operator for $N$ spins at time $T$ is related to one of a non-unitary evolution operator for $T$ spins at time $N$. We investigate the spectrum of this dual operator with a focus on the different parameter regimes (chaotic, regular) of the spin chain. We present applications of this duality relation to spectral statistics in an accompanying paper. 
M. Akila, D. Waltner, B. Gutkin, T. Guhr
nlin.CD quant-ph