Transmitter with two probes: Resistance as a functional of the current distribution

Lenk, R.

doi:10.1007/bf01313023

Cited by 8 publications

(15 citation statements)

References 14 publications

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“…This relation must be the mathematical consequence of a simple and general linear relationship between them. There is only one such relation, namely I (1) n = −I (2)…”

Section: The Variational Functionalmentioning

confidence: 99%

“…In a previous paper [1], we addressed anew an old question: what is the resistance of an elastic transmitter between two probes? In the spirit of Landauer-cf.…”

Section: Introductionmentioning

confidence: 99%

“…In [1], the needs to represent the lead kinetics, and to couple it with the reflectiontransmission properties of the transmitter and-mainly-the rather cumbersome procedure to prove the existence of the variational functional and to express it, at least for special cases, explicitly as a functional of the currents themselves has tended to mask the generality of the approach. In this paper we take, in a somewhat axiomatic manner, the variational principle as the starting point.…”

Section: Introductionmentioning

confidence: 99%

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The minimal principle for the current distribution in microstructures and the resistance in long incoherently coupled chains

Lenk¹,

Hauck²

1996

J. Phys.: Condens. Matter

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As in the Landauer-Büttiker approach to transport, a transmitter is, at fixed energy, characterized by its reflection and transmission coefficients. Generalizing a prior approach, we establish a variational principle to determine, without magnetic field, the distribution of the current over the different channels if the transmitter is coupled incoherently to its surroundings. For transmitters coupled with each other, a general demand of additivity defines the form of the variational functional. Contacts are treated as special transmitters, and, as a test, the results of the standard model are reproduced. A typical serial resistance is defined as the resistance within a long incoherently coupled chain, with no regard to contacts and reservoirs. This resistance is strictly additive. It is shown that well within the chain a relaxed current and density distribution is established that is independent of the conditions at the ends of the chain. This distribution coincides with the optimal distribution that minimizes the resistance of each of the single transmitters that are the building blocks of the chain. For a sufficiently long chain, the serial resistance is determined by the linear dependence of the inverse total transmission on the number of single transmitters. The relaxational behaviour of a long chain implies corresponding features of the reflection and transmission matrices in the asymptotic regime, especially a factorization of the transmission matrix, expressing memory loss with respect to the ingoing and outgoing channels.

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“…This relation must be the mathematical consequence of a simple and general linear relationship between them. There is only one such relation, namely I (1) n = −I (2)…”

Section: The Variational Functionalmentioning

confidence: 99%

“…In a previous paper [1], we addressed anew an old question: what is the resistance of an elastic transmitter between two probes? In the spirit of Landauer-cf.…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

The minimal principle for the current distribution in microstructures and the resistance in long incoherently coupled chains

Lenk¹,

Hauck²

1996

J. Phys.: Condens. Matter

View full text Add to dashboard Cite

show abstract

“…For a transmitter between two resistive leads [6] the currents between the leads and the transmitter have been varied, instead of fixed external currents in this case the asymptotic current distribution in the leads is given. For the standard model [7,8] the currents between the contacts and the transmitter are varied, the incident currents are fixed externally at the reservoir side of the contacts.…”

Section: Principle Of Minimum Entropy Productionmentioning

confidence: 99%

“…This principle applies directly to transport in the case of incoherently coupled scatterers of arbitrary internal complexity. It has been constructed at first for a transmitter between two resistive leads [6], then generalized for a network of scatterers and shown to reproduce correctly the well-known basic equations of the standard model [7,8], i.e. employing ideal leads, contacts and reservoirs.…”

Section: Introductionmentioning

confidence: 98%