# 2.1. Introduction¶

Tkwant is a Python package for the simulation of quantum nanoelectronics devices on which external time-dependent perturbations are applied. Tkwant is an extension of the Kwant package and can handle the same types of systems: discrete tight-binding like models that consist of an arbitrary central region connected to semi-infinite electrodes, also called leads. For such systems, tkwant provides algorithms to simulate the time-evolution of manybody expectation values, as e.g. densities and currents.

Sketch of a typical open quantum system which can be simulated with Tkwant. A central scattering region (in black) is connected to several leads (in grey). Each lead represents a translationally invariant, semi-infinite system in thermal equilibrium. Sites and hopping matrix elements are represented by dots and lines. The regions in red indicate a time-dependent perturbation, in this example a global voltage pulse $$V_p (t)$$ on lead 0 and a time-dependent voltage $$V_g (t)$$ on a gate inside the scattering region. The figure is taken from Ref. [1].

Input: A tight-binding Hamiltonian of generic form

$\hat{H}(t) = \sum_{ij} H_{ij}(t) \hat{c}^\dagger_i \hat{c}_j$

as well as the chemical potential $$\mu$$ and the temperature $$T$$ in each lead.

Output: Time-dependent manybody expectation values, such as the electron density $$n_i(t) = \langle \hat{c}^\dagger_i \hat{c}_i \rangle$$ an currents $$j_i(t) = i[\langle \hat{c}^\dagger_i \hat{c}_{i+1} \rangle - \langle \hat{c}^\dagger_{i+1} \hat{c}_{i} \rangle]$$. We refer to Tkwant’s main paper Ref. [1] for the technical background.

## 2.1.1. References¶

[1] T. Kloss, J. Weston, B. Gaury, B. Rossignol, C. Groth and X. Waintal, Tkwant: a software package for time-dependent quantum transport, arXiv:2009.03132 [cond-mat.mes-hall].