Quantum and Semi-classical Percolation and Breakdown in Disordered Solids

1. Front Matter

   Pages 1-12

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2. Classical Percolation

   • D. Stauffer

   Pages 1-19

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

   • A.K. Sen

   Pages 1-62

4. Quantum Transmittance Through Random Media

   • A. Mookerjee, T. Saha-Dasgupta, I. Dasgupta

   Pages 1-25

5. Quantum Percolation in Two Dimensions

   • H. Nakanishi, Md. Fhokrul Islam

   Pages 1-26

6. Quantum Percolation in Disordered Structures

   • G. Schubert, H. Fehske

   Pages 1-28

7. Quantum Percolation in the Quantum Hall Regime

   • C. Sohrmann, J. Oswald, R.A.R ömer

   Pages 1-31

8. Percolative Quantum Transport in Manganites

   • P. Majumdar

   Pages 1-32

9. Classical and quantum breakdown in disordered

   • D. Samanta, B.K. Chakrabarti, P. Ray

   Pages 1-24

10. Nonequilibrium Quantum Breakdown in a Strongly Correlated Electron System

    • T. Oka, H. Aoki

    Pages 1-35

11. Percolation in quantum computation and

    • K. Kieling, J. Eisert

    Pages 1-33

12. Back Matter

    Pages 1-6

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This lecture notes in physics volume mainly focuses on the semi classical and qu- tum aspects of percolation and breakdown in disordered, composite or granular s- tems. The main reason for this undertaking has been the fact that, of late, there have been a lot of (theoretical) work on quantum percolation, but there is not even a (single) published review on the topic (and, of course, no book). Also, there are many theoretical and experimental studies on the nonlinear current-voltage characteristics both away from, as well as one approaches, an electrical breakdown in composite materials. Some of the results are quite intriguing and may broadly be explained utilising a semi classical (if not, fully quantum mechanical) tunnelling between - cron or nano-sized metallic islands dispersed separated by thin insulating layers, or in other words, between the dangling ends of small percolation clusters. There have also been several (theoretical) studies of Zener breakdown in Mott or Anderson in- lators. Again, there is no review available, connecting them in any coherent fashion. A compendium volume connecting these experimental and theoretical studies should be unique and very timely, and hence this volume. The book is organised as follows. For completeness, we have started with a short and concise introduction on classical percolation. In the ?rst chapter, D. Stauffer reviews the scaling theory of classical percolation emphasizing (biased) diffusion, without any quantum effects. The next chapter by A. K.

• breakdown phenomena
• composite material
• disordered materials
• granular material
• quantum computing
• quantum percolation
• random media

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