Ballistic transport in classical and quantum integrable systems

Details Ballistic transport in classical and quantum integrable systems Ballistic transport in classical and quantum integrable systems

2001-09-13

arxiv.org/abs/cond-mat/0109233v1

Journal of Low Temperature Physics, v.126, p.1185 (2002)

Physics

Condensed Matter

Strongly Correlated Electrons

10 pages, 2 Postscript figures

Scientific paper

In this essay, we first sketch the development of ideas on the extraordinary dynamics of integrable classical nonlinear and quantum many body Hamiltonians. In particular, we comment on the state of mathematical techniques available for analyzing their thermodynamic and dynamic properties. Then, we discuss the unconventional finite temperature transport of integrable systems using as example the classical Toda chain and the toy model of a quantum particle interacting with a fermionic bath in one dimension; we focus on the singular long time asymptotic of current-current correlations, we introduce the notion of the Drude weight and we emphasize the role played by conservation laws in establishing the ballistic character of transport in these systems.

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