*Tero T. Heikkilä*

- Published in print:
- 2013
- Published Online:
- December 2013
- ISBN:
- 9780199592449
- eISBN:
- 9780191747618
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199592449.003.0004
- Subject:
- Physics, Condensed Matter Physics / Materials

This chapter describes the main quantum interference effects on electron transport besides the resonant tunnelling and quantized conductance described in Chapter 3. These are the Aharonov-Bohm ...
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This chapter describes the main quantum interference effects on electron transport besides the resonant tunnelling and quantized conductance described in Chapter 3. These are the Aharonov-Bohm effect, weak and strong localization, universal conductance fluctuations, and persistent currents. The first three are described with the phenomenological Feynman path approach, which is a simplified version of the semiclassical path integral descriptions developed in the 1980s. It connects the phenomena to the present day by briefly discussing the observation of interference effects in graphene. Persistent currents are described starting from the Schrödinger equation for a ring and developing theory for wave functions satisfying periodic boundary conditions. The chapter also discusses recent experiments of persistent currents in light of the model developed for them.Less

This chapter describes the main quantum interference effects on electron transport besides the resonant tunnelling and quantized conductance described in Chapter 3. These are the Aharonov-Bohm effect, weak and strong localization, universal conductance fluctuations, and persistent currents. The first three are described with the phenomenological Feynman path approach, which is a simplified version of the semiclassical path integral descriptions developed in the 1980s. It connects the phenomena to the present day by briefly discussing the observation of interference effects in graphene. Persistent currents are described starting from the Schrödinger equation for a ring and developing theory for wave functions satisfying periodic boundary conditions. The chapter also discusses recent experiments of persistent currents in light of the model developed for them.

*Pier A. Mello and Narendra Kumar*

- Published in print:
- 2004
- Published Online:
- September 2007
- ISBN:
- 9780198525820
- eISBN:
- 9780191712234
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198525820.003.0007
- Subject:
- Physics, Condensed Matter Physics / Materials

This chapter treats the problem of finding the probability distribution of quantities related to quantum transport through a strictly one-dimensional (i.e., 1-channel) and through an N-channel ...
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This chapter treats the problem of finding the probability distribution of quantities related to quantum transport through a strictly one-dimensional (i.e., 1-channel) and through an N-channel quasi-one-dimensional disordered system. It uses the maximum entropy approach wherein the distribution for the random transfer matrix for an elementary building block is determined by maximizing the associated Shannon entropy, subject to the physically relevant constraints of flux conservation, time-reversal symmetry (when relevant), and the Ohmic small length-scale limit. The contents of this chapter include ensemble of transfer matrices; universality classes — the orthogonal and the unitary classes; invariant measure; the Fokker-Planck equation for a disordered one-dimensional conductor; the maximum-entropy ansatz for the building block; construction of the probability density for a system of finite length; the Fokker-Planck equation for a quasi-one-dimensional multi-channel disordered conductor; the diffusion equation for the orthogonal universality class, β = 1; the diffusion equation for the unitary universality class, β = 2; and universal conductance fluctuations in the good-metallic limit.Less

This chapter treats the problem of finding the probability distribution of quantities related to quantum transport through a strictly one-dimensional (i.e., 1-channel) and through an *N*-channel quasi-one-dimensional disordered system. It uses the maximum entropy approach wherein the distribution for the random transfer matrix for an elementary building block is determined by maximizing the associated Shannon entropy, subject to the physically relevant constraints of flux conservation, time-reversal symmetry (when relevant), and the Ohmic small length-scale limit. The contents of this chapter include ensemble of transfer matrices; universality classes — the orthogonal and the unitary classes; invariant measure; the Fokker-Planck equation for a disordered one-dimensional conductor; the maximum-entropy ansatz for the building block; construction of the probability density for a system of finite length; the Fokker-Planck equation for a quasi-one-dimensional multi-channel disordered conductor; the diffusion equation for the orthogonal universality class, β = 1; the diffusion equation for the unitary universality class, β = 2; and universal conductance fluctuations in the good-metallic limit.