2015/10/20 by Joseph Weston, Xavier Waintal · 28 citations
Engineering · Mathematics · Physics and Astronomy · #Advancements in Semiconductor Devices and Circuit Design #Computational physics #Condensed matter physics #Hamiltonian (control theory) #Josephson effect #Mathematics #Perturbation (astronomy) #Physics #Physics of Superconductivity and Magnetism #Quadratic equation #Quantum #Quantum and electron transport phenomena #Quantum mechanics #Scaling #Scattering #Statistical physics #Superconductivity #Voltage #cond-mat.mes-hall #cond-mat.supr-con
paper · pdf · doi:10.1103/physrevb.93.134506
published in Physical review. B./Physical review. B 93(13) (American Physical Society) · 13 pages, 12 figures
arxiv created 2015/10/20 · openalex publication_date 2016/04/14 · arxiv updated 2016/04/18 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We report on a ``source-sink'' algorithm which allows one to calculate time-resolved physical quantities from a general nanoelectronic quantum system (described by an arbitrary time-dependent quadratic Hamiltonian) connected to infinite electrodes. Although mathematically equivalent to the nonequilibrium Green's function formalism, the approach is based on the scattering wave functions of the system. It amounts to solving a set of generalized Schr"odinger equations that include an additional ``source'' term (coming from the time-dependent perturbation) and an absorbing ``sink'' term (the electrodes). The algorithm execution time scales linearly with both system size and simulation time, allowing one to simulate large systems (currently around 106 degrees of freedom) and/or large times (currently around 105 times the smallest time scale of the system). As an application we calculate the current-voltage characteristics of a Josephson junction for both short and long junctions, and recover the multiple Andreev reflection physics. We also discuss two intrinsically time-dependent situations: the relaxation time of a Josephson junction after a quench of the voltage bias, and the propagation of voltage pulses through a Josephson junction. In the case of a ballistic, long Josephson junction, we predict that a fast voltage pulse creates an oscillatory current whose frequency is controlled by the Thouless energy of the normal part. A similar effect is found for short junctions; a voltage pulse produces an oscillating current which, in the absence of electromagnetic environment, does not relax.