Landauer-Büttiker and Thouless conductance
arXiv:1408.0185 · doi:10.1007/s00220-015-2321-0
Abstract
In the independent electron approximation, the average (energy/charge/entropy) current flowing through a finite sample S connected to two electronic reservoirs can be computed by scattering theoretic arguments which lead to the famous Landauer-Büttiker formula. Another well known formula has been proposed by Thouless on the basis of a scaling argument. The Thouless formula relates the conductance of the sample to the width of the spectral bands of the infinite crystal obtained by periodic juxtaposition of S. In this spirit, we define Landauer-Büttiker crystalline currents by extending the Landauer-Büttiker formula to a setup where the sample S is replaced by a periodic structure whose unit cell is S. We argue that these crystalline currents are closely related to the Thouless currents. For example, the crystalline heat current is bounded above by the Thouless heat current, and this bound saturates iff the coupling between the reservoirs and the sample is reflectionless. Our analysis leads to a rigorous derivation of the Thouless formula from the first principles of quantum statistical mechanics.
References in corpus (5)
- Independent electrons model for open quantum systems: Landauer-Buettiker formula and strict positivity of the entropy production
- Landauer-Büttiker formula and Schrödinger conjecture
- Entropic fluctuations in XY chains and reflectionless Jacobi matrices
- A note on reflectionless Jacobi matrices
- The Spectral Structure of the Electronic Black Box Hamiltonian
Cited by in corpus (6)
- Steady states and universal conductance in a quenched Luttinger model
- Ballistic Transport for Limit-Periodic Jacobi Matrices with Applications to Quantum Many-Body Problems
- Conductance and absolutely continuous spectrum of 1D samples
- A model of Josephson Junctions on Boson Systems - Currents and Entropy Production Rate -
- Crystalline conductance and absolutely continuous spectrum of 1D samples
- Mean--field stability for the junction of quasi 1D systems with Coulomb interactions