Anomalous transport in classical one-dimensional systems
Prof. Antonio Politi - Institute for Complex Systems and Mathematical Biology, University of Aberdeen
Plenary Colloquium SIFS
Abstract: Transport properties of one-dimensional systems are reviewed, starting from the definition of heat flux, recently revisited to make it correct also over microscopic scales.
Various theoretical and numerical approaches are discussed in paradigmatic models to illustrate the conditions for the emergence of an anomalous (diverging) heat conductivity and to reconstruct the general scenario. Some finite-size effects are also reviewed, including the seemingly normal conductivity observed in nearly integrable systems.
In the second part of the colloquium, I turn the attention towards coupled transport processes in systems characterized by two conservation laws (such as energy and mass). The reference model will be the discrete nonlinear Schroedinger equation, often used in the study of DNA dynamics, cold atoms, and optical arrays. I mostly focus on anti-intuitive phenomena such non-monotonous temperature profiles, which can be accounted for by linear-response theory and the emergence of "negative" temperatures, associated with an intermittent transport of mass and energy.
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