TY - JOUR
T1 - Cooperative surmounting of bottlenecks
AU - Hennig, D.
AU - Mulhern, C.
AU - Schimansky-Geier, L.
AU - Tsironis, G. P.
AU - Hänggi, P.
N1 - Funding Information:
The authors thank Sergej Flach and Anna Deluca Silberberg for constructive and insightful discussions. Further, the authors would like to give acknowledgement to former coauthors including S. Fugmann, S. Martens, T. Gross, A.D. Burbanks, and A.H. Osbaldestin. This research was supported by the Volkswagen-Foundation projects I/80425 (L.S.-G.) and I/80424 (P.H.) the DFG Sachbeihilfen HA1517/31-2, and HA1517/35 (P.H.). This work was partially supported by the European Union, Seventh Framework Programme (FP7-REGPOT-2012-2013-1) under grant agreement 316165 (G.T.). L.S-G would like to acknowledge DFG-IRT1740 for financial support.
PY - 2015/7/20
Y1 - 2015/7/20
N2 - The physics of activated escape of objects out of a metastable state plays a key role in diverse scientific areas involving chemical kinetics, diffusion and dislocation motion in solids, nucleation, electrical transport, motion of flux lines superconductors, charge density waves, and transport processes of macromolecules and astrophysics, to name but a few. The underlying activated processes present the multidimensional extension of the Kramers problem of a single Brownian particle. In comparison to the latter case, however, the dynamics ensuing from the interactions of many coupled units can lead to intriguing novel phenomena that are not present when only a single degree of freedom is involved. In this review we report on a variety of such phenomena that are exhibited by systems consisting of chains of interacting units in the presence of potential barriers.In the first part we consider recent developments in the case of a deterministic dynamics driving cooperative escape processes of coupled nonlinear units out of metastable states. The ability of chains of coupled units to undergo spontaneous conformational transitions can lead to a self-organised escape. The mechanism at work is that the energies of the units become re-arranged, while keeping the total energy conserved, in forming localised energy modes that in turn trigger the cooperative escape. We present scenarios of significantly enhanced noise-free escape rates if compared to the noise-assisted case.The second part of the review deals with the collective directed transport of systems of interacting particles overcoming energetic barriers in periodic potential landscapes. Escape processes in both time-homogeneous and time-dependent driven systems are considered for the emergence of directed motion. It is shown that ballistic channels immersed in the associated mixed high-dimensional phase space are at the source for the directed long-range transport. Open problems and future directions are discussed in order to invigorate readers to engage in their own research.
AB - The physics of activated escape of objects out of a metastable state plays a key role in diverse scientific areas involving chemical kinetics, diffusion and dislocation motion in solids, nucleation, electrical transport, motion of flux lines superconductors, charge density waves, and transport processes of macromolecules and astrophysics, to name but a few. The underlying activated processes present the multidimensional extension of the Kramers problem of a single Brownian particle. In comparison to the latter case, however, the dynamics ensuing from the interactions of many coupled units can lead to intriguing novel phenomena that are not present when only a single degree of freedom is involved. In this review we report on a variety of such phenomena that are exhibited by systems consisting of chains of interacting units in the presence of potential barriers.In the first part we consider recent developments in the case of a deterministic dynamics driving cooperative escape processes of coupled nonlinear units out of metastable states. The ability of chains of coupled units to undergo spontaneous conformational transitions can lead to a self-organised escape. The mechanism at work is that the energies of the units become re-arranged, while keeping the total energy conserved, in forming localised energy modes that in turn trigger the cooperative escape. We present scenarios of significantly enhanced noise-free escape rates if compared to the noise-assisted case.The second part of the review deals with the collective directed transport of systems of interacting particles overcoming energetic barriers in periodic potential landscapes. Escape processes in both time-homogeneous and time-dependent driven systems are considered for the emergence of directed motion. It is shown that ballistic channels immersed in the associated mixed high-dimensional phase space are at the source for the directed long-range transport. Open problems and future directions are discussed in order to invigorate readers to engage in their own research.
KW - Chaos
KW - Cooperative effects
KW - Deterministic escape
KW - First-passage phenomena
KW - Fluctuation phenomena
KW - Hamiltonian systems
KW - Negative mobility
KW - Nonlinear dynamics
KW - Stochastic dynamics
KW - Thermally activated escape
KW - Transport dynamics
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U2 - 10.1016/j.physrep.2015.05.003
DO - 10.1016/j.physrep.2015.05.003
M3 - Review article
AN - SCOPUS:84931563990
VL - 586
SP - 1
EP - 51
JO - Physics Reports
JF - Physics Reports
SN - 0370-1573
ER -