Luttinger liquid model

In general, the evaluation of coefficients Cmn presents a major challenge. Remarkably, in the case of ID systems, Cmn can be calculated analytically when the number of carriers, N, is large, but the emission spectrum is stiU discrete [80]. Such systems have recently been manufactured and will be reviewed in the next section. In this case, the luminescence from ID electron-hole system can be described within the finite-size Luttinger-liquid formalism [20]. Note that the Luttinger liquid model was employed earlier for calculations of the Fermi-edge optical properties of infinite ID systems (with and without defects) in Refs. [21-23,81,82]. 

Here we outline the general formulas for recombination of an electron-hole pair belonging to Luttinger liquid rings in conduction and valence bands, (see Fig, 3). We start with the two-component Luttinger liquid model on a ring [108] with Hamiltonian H1 + H2 + Hint, where Hj describe noninter-... 

The only source of drag in the Luttinger liquid is interwire backscattering, associated with a large momentum transfer between the wires. The model predicts a distinctive temperature dependence of the corresponding contribution... 

The parameter A here is related to the conventional interaction parameter g of the Luttinger liquid g = 1/A. This relation follows from the definition g = vp/u in terms of the velocity of the collective mode (plasmon) u, and its value u = (7m/m)A in the Calogero-Sutherland model [14, 13]. For the rational values of A and at T = 0 the density-density correlation function is known exactly [14, 13]. Due to the integrability of the model, Ai k,w) 0 only in a finite interval of u> around u> = Uik [15]. We found this interval for k < 27rnj ... 

J. Sirker, The Luttinger Liquid and Integrable Models, arXiv.org, e-Print Arch., Condens. Matter, 11 Jul 2012, 1-23, arXiv 1207.2582vl [cond-mat.str-el]. Avail. URL http //arxiv.org/PS cache/arxiv/pdf/1207/1207.2582vl.pdf. 

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