# Field theory of quantum chaos

Prof. Fritz Haake accepted the invitation on 30 May 2011

for deadline see the agreement by Alexander Altland

Prof. Fritz Haake, Physics, University of Duisburg-Essen, Germany, was invited on 28 April 2011.

**Short note and Related References
added by Scholarpedia Editor D.Shepelyansky in May 2020 **

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. This note is taken from [1].

Certain conter examples are discussed in [2]. Also an example of the kicked Harper model shows that, even if in the classical limit this system is characterized by chaos and global diffusion, in the quantum case it may be diffusive, localized or ballistic (see [3] and Refs. therein). This shows that the validity of the field theoretical methods described in [1] requires certain additional conditions for their validity.

## Related References

- A.Altland, M.R.Zirnbauer, "Field theory of the quantum kicked rotor", Phys. Rev. Lett. 77: 4536 (1996); "Reply" Phys. Rev. Lett. 80: 641 (1998)
- G.Casati, F.M.Izrailev, V.V.Sokolov, "Comment on “dynamical theory of quantum chaos or a hidden random matrix ensemble?", Phys. Rev. Lett. 80: 640 (1998)
- R.Artuso, "Kicked Harper model", Scholarpedia 6(10):10462 (2011)

## See also internal links

Chirikov standard map, Anderson localization and quantum chaos maps, Random matrix theory