1998
DOI: 10.1103/physrevlett.80.948
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Coexistence of Ballistic Transport, Diffusion, and Localization in Surface Disordered Waveguides

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Cited by 102 publications
(121 citation statements)
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“…The idea of quantum graphs was introduced by Linus Pauling to model organic molecules [15] and they are also used to simulate, e.g., quantum wires [16], optical waveguides [17] and mesoscopic quantum systems [18,19]. The validity of the BGS conjecture was proven rigourously for graphs with incommensurable bond lengths in Refs.…”
mentioning
confidence: 99%
“…The idea of quantum graphs was introduced by Linus Pauling to model organic molecules [15] and they are also used to simulate, e.g., quantum wires [16], optical waveguides [17] and mesoscopic quantum systems [18,19]. The validity of the BGS conjecture was proven rigourously for graphs with incommensurable bond lengths in Refs.…”
mentioning
confidence: 99%
“…The recent confirmation of the universal thermal conductance in tiny silicon nitride devices [7] is an experimental tour de force. Although verifying the predictions of a universal value of K͞T at low enough temperatures, the experiments showed values of K͞T that decrease as the temperature increases in the range of 0.08 to 0.2 K, before beginning to rise at higher temperatures as more vibrational modes that can carry the heat are excited.We [8] and others [9,10] have previously studied a simplified treatment of this problem using a scalar model for the elastic waves. However, elastic waves in confined geometries have many unusual features, such as modes with a quadratic dispersion relation v~k 2 at small wave numbers k and regions of anomalous dispersion dv͞dk , 0, that are not captured in this simple model and might be expected to have a strong influence on the low temperature transport.…”
mentioning
confidence: 99%
“…We [8] and others [9,10] have previously studied a simplified treatment of this problem using a scalar model for the elastic waves. However, elastic waves in confined geometries have many unusual features, such as modes with a quadratic dispersion relation v~k 2 at small wave numbers k and regions of anomalous dispersion dv͞dk , 0, that are not captured in this simple model and might be expected to have a strong influence on the low temperature transport.…”
mentioning
confidence: 99%
“…[32]. However, we notice that in numerical simulations of transport through surface-disordered wires, step-like corrugated waveguides are more often used [16][17][18][19][33][34][35], among others [13,36]. We also note that here we concentrate on the case of small number of open modes, M = [2,9]; the case of M ≫ 1 has been recently addressed in Ref.…”
Section: Modelmentioning
confidence: 99%
“…For disordered wires, it is well established that (i) for relatively short wire lengths the resistance increases linearly with L as [16,[36][37][38] …”
Section: A Diffusive and Localized Regimesmentioning
confidence: 99%