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Railway switch transport model

Martin Horvat^* and Tomaž Prosen^†

Giuliano Benenti^‡ and Giulio Casati^§

Faculty of Mathematics and Physics, Department of Physics, University of Ljubljana, Ljubljana, Slovenia

CNISM and Center for Nonlinear and Complex Systems, Università degli Studi dell'Insubria, via Valleggio 11, 22100 Como, Italy and Istituto Nazionale di Fisica Nucleare, Sezione di Milano, via Celoria 16, 20133 Milano, Italy

^*martin.horvat@fmf.uni-lj.si
^†tomaz.prosen@fmf.uni-lj.si
^‡giuliano.benenti@uninsubria.it
^§giulio.casati@uninsubria.it

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Phys. Rev. E 86, 052102 – Published 26 November, 2012

DOI: https://doi.org/10.1103/PhysRevE.86.052102

Abstract

We propose a simple model of coupled heat and particle transport based on zero-dimensional classical deterministic dynamics, which is reminiscent of a railway switch whose action is a function only of the particle's energy. It is shown that already in the minimal three-terminal model, where the second terminal is considered as a probe with zero net particle and heat currents, one can find extremely asymmetric Onsager matrices as a consequence of time-reversal symmetry breaking of the model. This minimalistic transport model provides a better understanding of thermoelectric heat engines in the presence of time-reversal symmetry breaking.

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References (24)

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An alternative measure of asymmetry can be defined as
$\begin{matrix} z = \frac{l_{21} - l_{12}}{l_{12} + l_{21}} = \frac{\int d μ Δ f}{Q_{11} D - \int d μ \bar{f}}, \end{matrix}$ (29)
which is related to $x$ (20) via $x = (1 + z) / (1 - z)$ . In the time-reversal symmetric case $l_{12} = l_{21}$ and therefore $z = 0$ . In this Brief Report we prefer to focus on parameter $x$ rather than $z$ , as it directly appears in formula (21) for maximum thermoelectric efficiency.
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Symmetries (22) imply that, if the realization $(π, ε)$ of the railway switch model leads to large asymmetry $x$ and large thermoelectric efficiency, then $(\hat{T} π, ε)$ corresponds to small asymmetry $1 / x$ and large refrigeration efficiency [15,22]
$\begin{matrix} η_{\max}^{(r)} = η_{C} \frac{1}{x} \frac{\sqrt{1 + y} - 1}{\sqrt{1 + y} + 1} . \end{matrix}$ (30)
D. Sánchez and M. Büttiker, Phys. Rev. Lett. 93, 106802 (2004).

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Railway switch transport model

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