Landauer-B\"uttiker formula and Schr\"odinger conjecture

摘要: We study the entropy flux in stationary state of a finite one-dimensional sample S connected at its left and right ends to two infinitely extended reservoirs distinct temperatures T1, T2 chemical potentials mu1, mu2. The is free lattice Fermi gas confined box [0, L] with energy operator -\Delta + v. Landauer-B\"uttiker formula expresses steady coupled system terms scattering data. behavior this limit L->infinity relate persistence transport norm bounds on transfer matrices limiting half-line Schr\"odinger h. A natural conjecture that set energies which persists precisely essential support absolutely continuous spectrum show equivalent spectral theory operators, thus giving physically appealing interpretation conjecture.