By Massimiliano Di Ventra
This graduate textbook presents an in-depth description of the delivery phenomena appropriate to structures of nanoscale dimensions. the various theoretical techniques are significantly mentioned, with emphasis on their easy assumptions and approximations. The e-book additionally covers details content material within the dimension of currents, the position of preliminary stipulations in developing a gentle nation, and the fashionable use of density-functional thought. themes are brought by means of uncomplicated actual arguments, with specific awareness to the non-equilibrium statistical nature of electric conduction, and by way of a close formal derivation. This textbook is perfect for graduate scholars in physics, chemistry, and electric engineering.
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Extra info for Electrical Transport in Nanoscale Systems
Example text
Viewpoint 2 is generally referred to as the Landauer approach (Landauer, 1957). What about the discharge of a closed capacitor across a nanojunction I have discussed at the beginning of this chapter? This alternative viewpoint to transport – I call it micro-canonical (Di Ventra and Todorov, 2004) for 53 Indeed, the knowledge of the exact many-body state of the system is not, by itself, necessarily that useful. This state contains a huge amount of information. Therefore, extracting from it the relevant macroscopic properties of the system would be a formidable task.
As anticipated, unlike for the discrete spectrum, a measurement in the continuum does not specify the state of the system with absolute precision, but provides a linear combination of states in a given interval of values of the spectrum. This interval can be made very small, but never exactly zero. This means that a measurement of the current for the majority of systems I consider in this book is always affected by an intrinsic (unavoidable) error of quantum-mechanical origin. 4 Complete measurement and pure states There is yet another point I need to make regarding the measurement of currents.
More generally Hamiltonian H we can write Eq. 73) where L is known as the Lindbladian,42 and Eq. 73 as the Lindblad equation, or quantum master equation. I derive this equation in Appendix C, where I also discuss some of its general properties. In particular, I stress here that the Hamiltonian appearing in Eq. 72 may not necessarily coincide with the Hamiltonian of the electrons in the absence of the bath. The bath, via interaction with the system, may also contribute to the unitary part of the system evolution by “shifting” (or renormalizing) its energy states (see Appendix C).