Lenstra and van Haeringen respond [2]

Lenstra and van Haeringen respond [2]

Citation for published version (APA):

Lenstra, D., & van Haeringen, W. (1987). Lenstra and van Haeringen respond [2]. Physical Review Letters,

58(20). https://doi.org/10.1103/PhysRevLett.58.2151

DOI:

10.1103/PhysRevLett.58.2151

Document status and date:

Published: 01/01/1987

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VOLUME 58, NUMBER 20

PHYSICAL

REVIEW

LETTERS

18MAY 1987

Lenstra and van Haeringen Respond: It seems to us that, in the preceding Comment, Landauer criticizes our usage ofthe adjective "resistive" in the context

of

a

sys-tem which lacks energy dissipation. Let us first point out

why we did use this terminology and to what extent we

claim this to be conceptually relevant indeed. After that

we will reply to a specific point in Landauer's Comment. When labeling our system with "resistive,

"

we were led by the idea that resistance applies to any electronic

system which possesses a linear transport coefficient, i.e.,

a linear relation between current and field, irrespective the nature of the underlying microscopic processes. Hence, to our system we assign resistance in the sense of

a linear relation between (time-independent) current and field, no more, no less.

We are well aware ofthe fact that the above definition

ignores the usual, in most situations existing,

companion-ship between resistive behavior and dissipation

of

energy

(to a surrounding heat bath). The model system studied

by us is free of energy dissipation. Nevertheless, and this is one

of

the points advocated in our Letter, the

in-trinsic phase information

of

the system can be considered to fade away, not in a strict way (as phases evolve in a

fully deterministic manner), but certainly in an eA'ective way (as it leads to current saturation).

If

one likes, this can be seen as inherent "dissipation" of phase informa-tion.

Although a lot more research is yet to be done, we think that the implications of our results will reach

beyond the restricted context in which they are derived

(i.e.,one-dimensional rings with simple scattering). The self-randomization behavior

of

quantum-mechanical par-ticles under the simultaneous influences of accelerating forces and elastic scattering may become a clue towards our understanding of systems exhibiting irreversible

physics although described by a well-defined

Hamiltoni-an operator. This includes the proper understanding

of

the residual resistance phenomenon.

Landauer's Comment suggests that in a realistic po-tential the electrons would approach free behavior with a current linearly increasing with time. This point

of

view is wrong. In fact, we have pointed out in our Letter

that free-electron-like behavior is a very singular currence. In realistic potentials, as well as in higher-dimensionality systems, self-randomization and

accom-panying current saturation will even be more eff'ectively

present.

D.Lenstra and W.van Haeringen

Physics Department

Eindhoven University ofTechnology

NL-5600MB Eindhoven, The Netherlands Received 23 March 1987

PACS numbers: 72.10.Bg,71.55.3v

'R.Landauer, Phys. Rev. Lett. 58, 2150

(1987).

2D. Lenstra and W. van Haeringen, Phys. Rev. Lett. 57,

1623(1986).