Cayley transform applied to non-interacting quantum transport
Abstract
We extend the Landauer-B\"uttiker formalism in order to accommodate both unitary and self-adjoint operators which are not bounded from below. We also prove that the pure point and singular continuous subspaces of the decoupled Hamiltonian do not contribute to the steady current. One of the physical applications is a stationary charge current formula for a system with four pseudo-relativistic semi-infinite leads and with an inner sample which is described by a Schr\"odinger operator defined on a bounded interval with dissipative boundary conditions. Another application is a current formula for electrons described by a one dimensional Dirac operator; here the system consists of two semi-infinite leads coupled through a point interaction at zero.
Keywords
Cite
@article{arxiv.1212.4965,
title = {Cayley transform applied to non-interacting quantum transport},
author = {Horia D. Cornean and Hagen Neidhardt and Lukas Wilhelm and Valentin A. Zagrebnov},
journal= {arXiv preprint arXiv:1212.4965},
year = {2012}
}
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