By Massimiliano Di Ventra
This graduate textbook presents an in-depth description of the delivery phenomena suitable to structures of nanoscale dimensions. different theoretical methods are seriously mentioned, with emphasis on their simple assumptions and approximations. The booklet additionally covers info content material within the size of currents, the function of preliminary stipulations in setting up a gradual nation, and the trendy use of density-functional idea. subject matters are brought by way of easy actual arguments, with specific awareness to the non-equilibrium statistical nature of electric conduction, and through 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
In addition, I have stressed the most important message of this book: electrical transport is a non-equilibrium statistical problem. The reason is that electrons are driven out of their equilibrium state, and our experimental knowledge of their time evolution is generally incomplete. For this reason, I have introduced the statistical operator formalism, which will be central in discussing the information content during a measurement of the current, and, in general, the loss of information in the description of transport phenomena.
For instance, I will show in Chapter 6 that the many-body Hamiltonian of electrons and ions of a given material, can, under speciﬁc approxˆ e , plus a imations, be written as the sum of an electronic Hamiltonian H Hamiltonian describing ionic vibrations (whose quanta are called phonons) ˆ e−ph . 64) where ˆ1e is the identity operator on the Hilbert space He of the electrons only, and ˆ 1ph is the identity operator on the Hilbert space Hph of the phonons. The symbol ⊗ means tensor product of the two Hilbert spaces.
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. No less than ﬁnding the many-body state itself.