Ballistic transport in classical and quantum integrable systems
arXiv:cond-mat/0109233
Abstract
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.
10 pages, 2 Postscript figures
Cited by in corpus (5)
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- Transport in perturbed classical integrable systems: the pinned Toda chain
- Thermal conductivity of the Toda lattice with conservative noise
- Revisiting the Mazur bound and the Suzuki equality
- Nonequilibrium phenomena in nonlinear lattices: from slow relaxation to anomalous transport