The quantum kicked rotor is investigated by field theoretical methods. It is shown that the effective theory describing the long wavelength physics of the system is precisely the supersymmetric nonlinear $\sigma$ model for quasi-one-dimensional metallic wires. This proves that the analogy between chaotic systems with dynamical localization and disordered metals can indeed be exact. The role of symmetries is discussed.

• Received 20 June 1996

DOI:https://doi.org/10.1103/PhysRevLett.77.4536