Participating group members: |
David Speer, Peter Reimann |

Main cooperation partners: |
Ralf Eichhorn, NORDITA (Stockholm);
Dieter Koelle and Reinhold Kleiner (Solid State Physics, Tübingen) |

A first main issue are unusual transport properties of an underdamped
Brownian particle in a periodic potential, e.g. particle current
v and static force F of opposite signs.
Their origin is a subtle interplay between the stability of coexisting attractors,
noise-induced metastability, and transient chaos.
The theoretically predicted unusual transport against force has been verified experimentally by measuring a a negative resistance of about -1 Ohm in a Josephson junction. The correspondence between the electrical properties of a Josephson junction and the transport properties of a Brownian particle in a periodic potential is established by the Stewart-McCumber model for Josephson junctions. |

Left: Generalized potential, describing the exponentially leading behavior of the invariant probability density for weak noise at the onset of chaos along the Feigenbaum route. Right: Pre-exponential part of the invariant density. |

A second main topic is the influence of weak noise on systems with chaotic deterministic dynamics in discrete time (deterministic diffusion, Feigenbaum-scenario, crises, fully developed chaos) and on anomalous transport properties of Hamiltonian chaotic systems and their possible regularization through weak random fluctuations by means of renormalization methods (stochastic Markov-chain- and Markov-tree-models).

One cornerstone of this research is the general mathematical formalism
for describing the
decay of complex metastable states,
in particular the concept of generalized (non-equilibrium) potentials (see figure).

Main publications:

P. Reimann and C. Van den Broeck

*Intermittent Diffusion in the Presence of Noise*

Physica D **75**, 509 (1994)

P. Reimann

*Suppression of Deterministic Diffusion by Noise*

Phys. Rev. E **50**, 727 (1994)

P. Reimann

*Noisy One-Dimensional Maps near a Crisis*

J. Stat. Phys. **82**, 1467 (1996); **85**, 403 (1996)

D. Speer, R. Eichhorn, and P. Reimann

*Brownian motion: Anomalous response due to noisy chaos*

Europhys. Lett. **79**, 10005 (2007)

D. Speer, R. Eichhorn, and P. Reimann

* Transient chaos induces anomalous transport properties of an underdamped Brownian particle*

Phys. Rev. E **76**, 051110 (2007)

J. Nagel, D. Speer, T. Gaber, A. Sterck, R. Eichhorn, P. Reimann, K. Ilin, M. Siegel, D. Koelle, and R. Kleiner

* Observation of Negative Absolute Resistance in a Josephson Junction*

Phys. Rev. Lett. **100**, 217001 (2008)

D. Speer, R. Eichhorn, and P. Reimann

* Directing Brownian Motion on a Periodic Surface*

Phys. Rev. Lett. **102**, 124101 (2009)

D. Speer, R. Eichhorn, and P. Reimann

* Exploiting Lattice Potentials for Sorting Chiral Particles*

Phys. Rev. Lett. **105**, 090602 (2010)

D. Speer, R. Eichhorn, and P. Reimann

*Anisotropic diffusion in square lattice potentials: giant enhancement and control*

EPL **97**, 60004 (2012)

*Last modified on 2012-03-14*