A splitting scheme for the quantum Liouville-BGK equation
DOI10.3934/krm.2023014zbMath1530.81004arXiv2103.06852MaRDI QIDQ6192355
Sophia Potoczak Bragdon, Olivier Pinaud
Publication date: 12 February 2024
Published in: Kinetic and Related Models (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2103.06852
strang splittingquantum Liouville equationquantum drift-diffusionconstrained free energy minimization
Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) PDEs in connection with quantum mechanics (35Q40) Computational methods for problems pertaining to quantum theory (81-08) Quantum dynamics and nonequilibrium statistical mechanics (general) (82C10) Time-dependent Schrödinger equations and Dirac equations (35Q41)
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- A problem of moment realizability in quantum statistical physics
- Entropy minimization for many-body quantum systems
- An entropic quantum drift-diffusion model for electron transport in resonant tunneling diodes
- On Wigner measures
- Quantum moment hydrodynamics and the entropy principle
- Moment closure hierarchies for kinetic theories.
- The quantum drift-diffusion model: existence and exponential convergence to the equilibrium
- Quantum energy-transport and drift-diffusion models
- Quasi-hydrodynamic semiconductor equations
- A constrained optimization problem in quantum statistical physics
- The quantum Liouville-BGK equation and the moment problem
- Constrained minimizers of the von Neumann entropy and their characterization
- On the minimization of quantum entropies under local constraints
- On quantum hydrodynamic and quantum energy transport models
- A generalization of a lemma of bellman and its application to uniqueness problems of differential equations
- Derivation of New Quantum Hydrodynamic Equations Using Entropy Minimization
- A New Asymptotic Preserving Scheme Based on Micro-Macro Formulation for Linear Kinetic Equations in the Diffusion Limit
- Isothermal Quantum Hydrodynamics: Derivation, Asymptotic Analysis, and Simulation
- Entropic Discretization of a Quantum Drift-Diffusion Model
- A derivation of the isothermal quantum hydrodynamic equations using entropy minimization
- A Model for Collision Processes in Gases. I. Small Amplitude Processes in Charged and Neutral One-Component Systems
- On local quantum Gibbs states
- An inverse problem in quantum statistical physics
This page was built for publication: A splitting scheme for the quantum Liouville-BGK equation
