Moscow International School of Physics 2022

One of conventional measures of chaotic behavior in classical Hamiltonian systems is the Lyapunov exponent. This quantity has a nonunique generalization to quantum case. Comparison of such a different generalization has a difficulty, namely, chaotic systems are nonintegrable, so that rare system can be analyzed analytically. We compute classical Lyapunov exponent numerically in the particular model of nonlinear vector mechanics and compare it to it's quantum counterpart, calculated analytically in the limit of a large number of particles $N$. Then, using this example, we discuss the difficulties of the definitions of both classical and quantum exponent, namely the dependence on initial conditions and the choice of an ensemble.