Using the Chebychev expansion in quantum transport calculations
Abstract
Irradiation by laser pulses and a fluctuating surrounding liquid environment can, for example, lead to time-dependent effects in the transport through molecular junctions. From the theoretical point of view, time-dependent theories of quantum transport are still challenging. In one of these existing transport theories, the energy-dependent coupling between molecule and leads is decomposed into Lorentzian functions. This trick has successfully been combined with quantum master approaches, hierarchical formalisms, and non-equilibrium Green’s functions. The drawback of this approach is, however, its serious limitation to certain forms of the molecule-lead coupling and to higher temperatures. Tian and Chen [J. Chem. Phys. 137, 204114 (2012)] recently employed a Chebychev expansion to circumvent some of these latter problems. Here, we report on a similar approach also based on the Chebychev expansion but leading to a different set of coupled differential equations using the fact that a derivative of a zeroth-order Bessel function can again be given in terms of Bessel functions. Test calculations show the excellent numerical accuracy and stability of the presented formalism. The time span for which this Chebychev expansion scheme is valid without any restrictions on the form of the spectral density or temperature can be determined a priori.
- Authors:
-
- Department of Physics and Earth Sciences, Jacobs University Bremen, Campus Ring 1, 28759 Bremen (Germany)
- Publication Date:
- OSTI Identifier:
- 22415654
- Resource Type:
- Journal Article
- Journal Name:
- Journal of Chemical Physics
- Additional Journal Information:
- Journal Volume: 142; Journal Issue: 15; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0021-9606
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; BESSEL FUNCTIONS; COUPLING; DIFFERENTIAL EQUATIONS; ELECTRIC CONTACTS; ENERGY DEPENDENCE; GREEN FUNCTION; LASER RADIATION; LIQUIDS; MOLECULES; PULSED IRRADIATION; SPECTRAL DENSITY; TIME DEPENDENCE; TRANSPORT THEORY
Citation Formats
Popescu, Bogdan, Rahman, Hasan, and Kleinekathöfer, Ulrich. Using the Chebychev expansion in quantum transport calculations. United States: N. p., 2015.
Web. doi:10.1063/1.4917198.
Popescu, Bogdan, Rahman, Hasan, & Kleinekathöfer, Ulrich. Using the Chebychev expansion in quantum transport calculations. United States. https://doi.org/10.1063/1.4917198
Popescu, Bogdan, Rahman, Hasan, and Kleinekathöfer, Ulrich. 2015.
"Using the Chebychev expansion in quantum transport calculations". United States. https://doi.org/10.1063/1.4917198.
@article{osti_22415654,
title = {Using the Chebychev expansion in quantum transport calculations},
author = {Popescu, Bogdan and Rahman, Hasan and Kleinekathöfer, Ulrich},
abstractNote = {Irradiation by laser pulses and a fluctuating surrounding liquid environment can, for example, lead to time-dependent effects in the transport through molecular junctions. From the theoretical point of view, time-dependent theories of quantum transport are still challenging. In one of these existing transport theories, the energy-dependent coupling between molecule and leads is decomposed into Lorentzian functions. This trick has successfully been combined with quantum master approaches, hierarchical formalisms, and non-equilibrium Green’s functions. The drawback of this approach is, however, its serious limitation to certain forms of the molecule-lead coupling and to higher temperatures. Tian and Chen [J. Chem. Phys. 137, 204114 (2012)] recently employed a Chebychev expansion to circumvent some of these latter problems. Here, we report on a similar approach also based on the Chebychev expansion but leading to a different set of coupled differential equations using the fact that a derivative of a zeroth-order Bessel function can again be given in terms of Bessel functions. Test calculations show the excellent numerical accuracy and stability of the presented formalism. The time span for which this Chebychev expansion scheme is valid without any restrictions on the form of the spectral density or temperature can be determined a priori.},
doi = {10.1063/1.4917198},
url = {https://www.osti.gov/biblio/22415654},
journal = {Journal of Chemical Physics},
issn = {0021-9606},
number = 15,
volume = 142,
place = {United States},
year = {Tue Apr 21 00:00:00 EDT 2015},
month = {Tue Apr 21 00:00:00 EDT 2015}
}