By D. E. Khmelnitskii (auth.), R. Fazio, V. F. Gantmakher, Y. Imry (eds.)
An advent and finished survey of the most matters in mesosocopic physics. issues lined contain quantum corridor results, delivery via quantum wires and dots, coherence in mesoscopic platforms, spintronics, disordered platforms, and reliable country quantum computation. a few contributions are devoted to the connections among nanoscience and biophysics and quantum optics.
Although the themes pointed out have many elements in universal, they span a large region of physics. it's as a result particularly vital to supply a huge view of this speedily increasing box. because of the superb shows, the e-book should be came across appropriate either for younger researchers who are looking to input the sphere and stimulating for more matured scientists.
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Extra info for New Directions in Mesoscopic Physics (Towards Nanoscience)
Example text
We shall discuss the last two points. 1. T OMOGRAPHIC L UTTINGER MODEL We want to determine at which dimension the Luttinger liquid crosses over to a Fermi liquid. To this purpose, we can generalize to d > 1 the method proposed by Dzyaloshinskii and Larkin [32], by showing how the additional Ward identities can still be used asymptotically near the Fermi surface, provided 1 ≤ d < 2.
Introduction The low-energy behavior of most interacting fermionic systems can be discussed within a small number of universality classes. This classification can be understood if one imagines to derive the effective asymptotic theory by means of an iterated elimination of the high-energy degrees of freedom within a Wilson renormalization-group scheme [1]. This procedure selects few types of dominant scattering processes near the Fermi surface [2, 3, 4, 5] and allows for a full description of the low-energy behavior of the system in terms of few parameters.
A†α 1 ,σ1 (k1 , t1 )ρα1 ,σ1 (k1 , t1 ) . . ραl ,σl (kl , tl ) , where aα,σ ,a†α,σ , and ρα,σ , are the operators in the Heisenberg representation, and T is the time-ordering operator. , the one-particle irreducible contributions. In the free case, the Fourier transform of the single-particle Green’s function (2,0) Gασ (k, t) ≡ Gασ;ασ = −i T aα,σ (k, t)a†α,σ (k, 0) with respect to the time (0,2) variable leads to the expression (1) with Z = 1. The functions Gασ,α σ describe the various charge- and spin-density correlations, which are dominated by the collective modes for small wave-vectors |q| kF .