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Extra info for An extensible model of the electron
R The possibility of fabricating multiple quantum wells close enough to interact and/or exchange electrons has led to the study of the layered electron liquid and the exploration of new concepts such as coulomb drag, interlayer coherence, and charge-transfer instability. The technological applications of 2DELs have been equally impressive. Just to limit ourselves to a single example, in Fig. 6 we show the schematics of an MOS-based field-effect transistor (MOSFET) which replaces the time-honored bipolar transistor of 17 18 The standard measure of cleanness of an electronic system is the electron mobility µ, which gives the average drift velocity of the electrons in response to an applied electric field E: vd = µE.
Actually, we now show that in three and two dimensions there is only one fundamental parameter, the dimensionless electronic density, n¯ = na dB , where d (2 or 3) is the number of spatial dimensions and a B is the Bohr radius h¯ 2 . 21) me2 To prove this, we express the electronic coordinates in terms of the “natural” length scale rs a B – the “typical” distance between two electrons. It is customary to define this typical distance as the radius of the d-dimensional sphere that encloses, on the average, exactly one electron.
N . 54) i=1 Here the ket |α1 , . . , αi → β, . . , α N denotes the state obtained from |α1 , . . , αi , . . , α N upon replacing φαi by φβ . Now observe that |α1 , . . , αi → β, . . , α N is obtained from |α1 , . . , αi , . . , α N † through the application of the operators aˆ β and aˆ αi in the following manner: † |α1 , . . , αi → β, . . , α N = aˆ β aˆ αi |α1 , . . , αi , . . , α N . 33) of the basis states, and going through the following chain of transformations: † aˆ β aˆ αi (aˆ α† 1 aˆ α† 2 .