# Numerical Analysis of the Transient Behavior of the Non-Equilibrium Quantum Liouville Equation

Title | Numerical Analysis of the Transient Behavior of the Non-Equilibrium Quantum Liouville Equation |

Publication Type | Journal Article |

Year of Publication | 2018 |

Authors | Schulz, Lukas, Schulz, Dirk |

Journal | IEEE Transactions on Nanotechnology |

Volume | 17 |

Pagination | 1197—1205 |

Date Published | nov |

ISSN | 1941-0085 |

Keywords | Boundary conditions, complex absorbing potential, composability, discretization scheme, drift operator, finite volume discretization technique, finite volume methods, heterostructure devices, Liouville equation, Metrics, nonequilibrium quantum Liouville equation, nonphysical reflections, numerical analysis, Numerical models, numerical schemes, oscillating behaviors, Poisson equation, privacy, pubcrawl, Quantum Liouville equation, quantum theory, quantum transport, quantum transport equations, resilience, Resiliency, resonant tunneling devices, Schrodinger equation, statistical density matrix, Transient analysis, transient nonequilibrium solution, transient quantum effects, transient regime |

Abstract | The numerical analysis of transient quantum effects in heterostructure devices with conventional numerical methods tends to pose problems. To overcome these limitations, a novel numerical scheme for the transient non-equilibrium solution of the quantum Liouville equation utilizing a finite volume discretization technique is proposed. Additionally, the solution with regard to the stationary regime, which can serve as a reference solution, is inherently included within the discretization scheme for the transient regime. Resulting in a highly oscillating interference pattern of the statistical density matrix as well in the stationary as in the transient regime, the reflecting nature of the conventional boundary conditions can be an additional source of error. Avoiding these non-physical reflections, the concept of a complex absorbing potential used for the Schrodinger equation is utilized to redefine the drift operator in order to render open boundary conditions for quantum transport equations. Furthermore, the method allows the application of the commonly used concept of inflow boundary conditions. |

URL | https://ieeexplore.ieee.org/document/8464085/ |

DOI | 10.1109/TNANO.2018.2868972 |

Citation Key | schulz_numerical_2018 |

- Boundary conditions
- complex absorbing potential
- composability
- discretization scheme
- drift operator
- finite volume discretization technique
- finite volume methods
- heterostructure devices
- Liouville equation
- Metrics
- nonequilibrium quantum Liouville equation
- nonphysical reflections
- numerical analysis
- Numerical models
- numerical schemes
- oscillating behaviors
- Poisson equation
- privacy
- pubcrawl
- Quantum Liouville equation
- quantum theory
- quantum transport
- quantum transport equations
- resilience
- Resiliency
- resonant tunneling devices
- Schrodinger equation
- statistical density matrix
- Transient analysis
- transient nonequilibrium solution
- transient quantum effects
- transient regime