Using the Chebychev expansion in quantum transport calculations

Area of Science:

• Quantum physics
• Molecular electronics
• Computational chemistry

Background:

• Time-dependent quantum transport theories are computationally challenging.
• Existing methods using Lorentzian function decomposition have limitations in molecule-lead coupling forms and temperature ranges.
• A Chebychev expansion approach was recently proposed to address some of these limitations.

Purpose of the Study:

• To develop a novel theoretical framework for time-dependent quantum transport.
• To overcome limitations of existing methods regarding molecule-lead coupling and temperature.
• To present a numerically accurate and stable formalism for quantum transport calculations.

Main Methods:

• Utilized a Chebychev expansion for time-dependent quantum transport calculations.
• Derived a new set of coupled differential equations based on Bessel function properties.
• Performed test calculations to validate the numerical accuracy and stability of the formalism.

Main Results:

• The new formalism demonstrates excellent numerical accuracy and stability.
• The Chebychev expansion scheme is valid for a wide range of spectral densities and temperatures.
• The applicable time span of the scheme can be determined a priori.

Conclusions:

• The presented Chebychev expansion-based formalism offers a robust and accurate method for studying time-dependent quantum transport.
• This approach overcomes key limitations of previous theoretical models.
• The method has potential for broader applications in molecular electronics and quantum systems.