By Carlo Jacoboni
This ebook describes in information the idea of the electron delivery within the fabrics and buildings on the foundation of recent micro- and nano-electronics. It leads and accompanies the reader, via a step by step derivation of all calculations, from the fundamental legislation of classical and quantum physics as much as the main sleek theoretical options, reminiscent of nonequilibrium eco-friendly services, to check shipping houses of either semiconductor fabrics and smooth low-dimensional and mesoscopic structures.
Read or Download Theory of Electron Transport in Semiconductors: A Pathway from Elementary Physics to Nonequilibrium Green Functions PDF
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Extra resources for Theory of Electron Transport in Semiconductors: A Pathway from Elementary Physics to Nonequilibrium Green Functions
The ﬂuctuations of energy in the systems of a canonical ensemble and the ﬂuctuations of energy and of particle number in the grand-canonical ensemble are often very small so that many statistical results are independent of the ensemble used. 1 Microcanonical Ensemble In the microcanonical ensemble, all systems have the same energy , and, if the system of interest is made of particles, all the systems in the ensemble have the same number of particles. In classical physics, since energy is a continuous variable, it is more convenient to assume, without practical consequences, that the systems of the ensemble have energies contained in an interval δ small with respect to the energy variations of interest.
The temperature in this case is a property of the combined system, the one of interest plus thermal bath. Once the system is again isolated, it will have again well-deﬁned energy and temperature. The latter, however, is not necessarily the same of that of the thermal bath, even though this is the most probable, as seen in the previous section. There are possible diﬀerences that are, in general, extremely small. 6 The Three Fundamental Statistical Ensembles In Sect. 1, the statistical ensembles were presented as large mental sets of systems obtained as replicas of the actual system of interest.
Thus, once the picture is chosen, we still have the choice of the basis to represent vectors and observables with numbers. The choice of the basis is called a representation. 2 Evolution Operator and Its Equation of Motion Let us work, for the time being, in a Schr¨ odinger picture, and let |ΨS (t) be the state vector of the system at time t. 2) This operator must be linear, to preserve the superpositions of states, and must be unitary, to preserve the normalization of the state vectors. 6) From the Schr¨odinger picture, we move to the Heisenberg picture through the unitary transformation U † (t, t◦ ).