# Dresden 2017 – wissenschaftliches Programm

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# HL: Fachverband Halbleiterphysik

## HL 19: Transport: Graphene and Carbon Nanostructures (jointly with DY, DS, HL, MA, O)

### HL 19.8: Vortrag

### Montag, 20. März 2017, 17:00–17:15, HSZ 204

**Quantum chaos and out-of-time order correlation functions in graphene** — •Markus Klug, Mathias Scheurer, and Jörg Schmalian — Institute for Theoretical Condensed Matter Physics, Karlsruhe Institute of Technology, 76131 Karlsruhe, Deutschland

Out-of-time order correlation functions of type *C*=⟨ *A*(*t*)*B*(0)*A*(*t*)*B*(0) ⟩_{β} are believed to be a reasonable measure of quantum chaos which manifests in an exponential growth of C with a certain Lyapunov exponent determined by the microscopic model under considerations. Recently, it was conjectured hat this Lyapunov exponent is be bounded by λ ≤ 2π *k*_{B} *T*/ℏ [1].

In this work we investigate the out-of-time order correlation functions in graphene subject to the long range Coulomb interaction. To this end we develop a formalism to capture the relevant effects which determines the dominant time dependence of C. We demonstrate that the critical Dirac fluid graphene is a good candidate for saturating the bound mentioned above.

[1] J. Maldacena, S.H. Shenker and D. J. Stanford, High Energ. Phys. (2016) 2016: 106.