The conductance of a multi-mode ballistic ring: Beyond Landauer and Kubo

Bandopadhyay, Swarnali; Etzioni, Yoav; Cohen, Doron

doi:10.1209/epl/i2006-10360-9

Cited by 8 publications

(27 citation statements)

References 13 publications

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“…Scope: In this paper we analyze an example of a single mode device, while in a follow-up work [12] we analyze an example of a multi-mode ring. The single mode example of this paper (unlike the multi mode example of [12]) possibly seems somewhat artificial. Its advantage is its simplicity.…”

Section: Introductionmentioning

confidence: 99%

Rate of energy absorption by a closed ballistic ring

Cohen¹,

Schanz²

2006

J. Phys. A: Math. Gen.

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We make a distinction between the spectroscopic and the mesoscopic conductance of a closed ring. We show that the latter is not simply related to the Landauer conductance of the corresponding open system. A new ingredient in the theory is related to the non-universal structure of the perturbation matrix which is generic for quantum chaotic systems. These structures may created bottlenecks that suppress the diffusion in energy space, and hence the rate of energy absorption. The resulting effect is not merely quantitative: For a ring-dot system we find that a smaller Landauer conductance implies a smaller spectroscopic conductance, while the mesoscopic conductance increases. Our considerations open the way towards a realistic theory of dissipation in closed mesoscopic ballistic devices. ‡ The response of chaotic systems to weak driving is "linear" in the classical treatment. We look for a quantum mechanical related departure from linear response theory. This should be contrasted with the traditional studies of "quantum chaos" models (such as the 'quantum kicked rotator') where in the absence of driving the system is integrable(!) and consequently the response is manifestly non-linear both classically and quantum mechanically. § The terminology of this paper, and in particular our notion of "conductance" are the same as in the theoretical review [8] and in the experimental work [9].

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Section: Introductionmentioning

confidence: 99%

Rate of energy absorption by a closed ballistic ring

Cohen¹,

Schanz²

2006

J. Phys. A: Math. Gen.

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“…The current manuscript is based and reflects a line of study that has been carried out (in chronological order) in collaboration with [33][34][35][36][37][38][39]…”

Section: Acknowledgmentsmentioning

confidence: 99%

Energy absorption by ‘sparse’ systems: beyond linear response theory

Cohen¹

2012

Phys. Scr.

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The analysis of the response to driving in the case of weakly chaotic or weakly interacting systems should go beyond linear response theory. Due to the "sparsity" of the perturbation matrix, a resistor network picture of transitions between energy levels is essential. The Kubo formula is modified, replacing the "algebraic" average over the squared matrix elements by a "resistor network" average. Consequently the response becomes semi-linear rather than linear. Some novel results have been obtained in the context of two prototype problems: the heating rate of particles in Billiards with vibrating walls; and the Ohmic Joule conductance of mesoscopic rings driven by electromotive force. Respectively, the obtained results are contrasted with the "Wall formula" and the "Drude formula".

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“…See Ref. [9,10] for details. As could be expected the result is in agreement with the Landauer theory [16] provided g ≪ 1.…”

Section: The Lrt Calculationmentioning

confidence: 99%

“…Namely, we assume that the environmental induced relaxation is a slow process, when compared with the EMF-driven transitions [this is in opposite to the LRT limit ε → 0]. Accordingly we have to work within the framework of semi-linear response theory (SLRT) [9,10,11] : This theory (see section 5 below) goes beyond the conventional framework of the Kubo formalism.…”

Section: Introductionmentioning

confidence: 99%

The mesoscopic conductance of disordered rings, its random matrix theory and the generalized variable range hopping picture

Stotland¹,

Budoyo²,

Peer³

et al. 2008

J. Phys. A: Math. Theor.

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The calculation of the conductance of disordered rings requires a theory that goes beyond the Kubo-Drude formulation. Assuming "mesoscopic" circumstances the analysis of the electro-driven transitions show similarities with a percolation problem in energy space. We argue that the texture and the sparsity of the perturbation matrix dictate the value of the conductance, and study its dependence on the disorder strength, ranging from the ballistic to the Anderson localization regime. An improved sparse random matrix model is introduced to captures the essential ingredients of the problem, and leads to a generalized variable range hopping picture. ‡ Hence there is no issue of quantum recurrences which would arise for a strictly linear or periodic driving. From here on we use units such that = 1. § The terminology of this paper, and in particular our notion of "conductance" are the same as in the theoretical review [4] and in the experimental work [5].

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The conductance of a multi-mode ballistic ring: Beyond Landauer and Kubo

Cited by 8 publications

References 13 publications

Rate of energy absorption by a closed ballistic ring

Rate of energy absorption by a closed ballistic ring

Energy absorption by ‘sparse’ systems: beyond linear response theory

The mesoscopic conductance of disordered rings, its random matrix theory and the generalized variable range hopping picture

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