TY - JOUR

T1 - Conductance and Absolutely Continuous Spectrum of 1D Samples

AU - Bruneau, L.

AU - Jakšić, V.

AU - Last, Y.

AU - Pillet, C. A.

N1 - Publisher Copyright:
© 2015, Springer-Verlag Berlin Heidelberg.

PY - 2016/6/1

Y1 - 2016/6/1

N2 - We characterize the absolutely continuous spectrum of the one-dimensional Schrödinger operators h= - Δ + v acting on ℓ2(Z+) in terms of the limiting behaviour of the Landauer–Büttiker and Thouless conductances of the associated finite samples. The finite sample is defined by restricting h to a finite interval [ 1 , L] ∩ Z+ and the conductance refers to the charge current across the sample in the open quantum system obtained by attaching independent electronic reservoirs to the sample ends. Our main result is that the conductances associated to an energy interval I are non-vanishing in the limit L→ ∞ iff sp ac(h) ∩ I≠ ∅. We also discuss the relationship between this result and the Schrödinger Conjecture (Avila, J Am Math Soc 28:579–616, 2015; Bruneau et al., Commun Math Phys 319:501–513, 2013).

AB - We characterize the absolutely continuous spectrum of the one-dimensional Schrödinger operators h= - Δ + v acting on ℓ2(Z+) in terms of the limiting behaviour of the Landauer–Büttiker and Thouless conductances of the associated finite samples. The finite sample is defined by restricting h to a finite interval [ 1 , L] ∩ Z+ and the conductance refers to the charge current across the sample in the open quantum system obtained by attaching independent electronic reservoirs to the sample ends. Our main result is that the conductances associated to an energy interval I are non-vanishing in the limit L→ ∞ iff sp ac(h) ∩ I≠ ∅. We also discuss the relationship between this result and the Schrödinger Conjecture (Avila, J Am Math Soc 28:579–616, 2015; Bruneau et al., Commun Math Phys 319:501–513, 2013).

UR - http://www.scopus.com/inward/record.url?scp=84947941867&partnerID=8YFLogxK

U2 - 10.1007/s00220-015-2501-y

DO - 10.1007/s00220-015-2501-y

M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???

AN - SCOPUS:84947941867

SN - 0010-3616

VL - 344

SP - 959

EP - 981

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

IS - 3

ER -