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Non-linear Response, Semi-Classical Percolation and Breakdown in the RRTN Model

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Book cover Quantum and Semi-classical Percolation and Breakdown in Disordered Solids

Part of the book series: Lecture Notes in Physics ((LNP,volume 762))

Abstract

In this chapter, we address the issue of non-linearity of response functions of disordered, granular composite materials and more specifically, an extension of the classical percolation (a classical insulator to metal phase transition; concisely reviewed by the author of the first chapter) problem to a situation where the contributions of nonclassical or non-diffusive processes cannot be neglected. In the paradigm of charge transport in electrical composites, this implies that the charge carriers travel not only inside metallic phases or grains but also outside of it; for example, in the microscopic gap between two such grains using some externally assisted hopping over the barrier potential due to the gap. The assistance may be due to the phonons (ambient thermal bath), impressed electrical and/or chemical potential differences, etc. As such, these processes are known to bring forth non-linearity in the response functions of the macroscopic system.

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    Sen, A. (2009). Non-linear Response, Semi-Classical Percolation and Breakdown in the RRTN Model. In: Chakrabarti, B., Bardhan, K., Sen, A. (eds) Quantum and Semi-classical Percolation and Breakdown in Disordered Solids. Lecture Notes in Physics, vol 762. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-85428-9_2

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