Boris Fine — Skolkovo Institute of Science and Technology #
Reversing Chaos #

One of the ways to manipulate artificially created quantum systems is to reverse their dynamics. Our 
ability to do this is limited by the phenomenon of chaos. In classical systems, chaos implies exponential 
sensitivity to small perturbations. It is to be shown in this presentation that nonintegrable lattices of 
spins 1/2, which are often considered to be chaotic, are not exponentially sensitive to small 
perturbations [1]. This result is obtained by comparing the responses of chaotic lattices of classical 
spins and nonintegrable lattices of spins 1/2 to imperfect reversal of spin dynamics known as Loschmidt 
echo. In the classical case, Loschmidt echoes exhibit exponential sensitivity to small perturbations 
characterized by twice the value of the largest Lyapunov exponent of the system. In the case of spins 1/2, 
Loschmidt echoes are only power-law sensitive to small perturbations. Our findings imply that it is 
impossible to define Lyapunov exponents for lattices of spins 1/2 even in the macroscopic limit. At the 
same time, the above absence of exponential sensitivity to small perturbations is an encouraging news for 
the efforts to create quantum simulators. The power-law sensitivity of spin 1/2 lattices to small 
perturbations is predicted to measurable in nuclear magnetic resonance experiments.
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[1] B. V. Fine, T. A. Elsayed, C. M. Kropf and A. S. de Wijn, Phys. Rev. E 89, 012923 (2014).