Discussion Overview
The discussion centers on the behavior of the Liouville-von-Neumann equation in the context of time-dependent dynamics of an electron in coherently coupled states, specifically addressing the occurrence of negative values in the diagonal elements of the density matrix during numerical simulations.
Discussion Character
- Exploratory
- Technical explanation
- Debate/contested
Main Points Raised
- One participant reports unexpected negative values for diagonal elements of the density matrix while solving the Liouville-von-Neumann equations, questioning the interpretation of this behavior.
- Another participant expresses concern over the implications of negative probabilities and suggests providing additional details for further assistance.
- A different participant suggests that the issue may stem from the numerical method used, recommending a smaller step size and a recheck of the code.
- The original poster acknowledges using a Runge-Kutta solver and questions whether the introduction of a constant dephasing time could lead to violations of causality, as it is not derived from the density matrix formalism.
- Further advice is given to test the numerical method with simpler cases, such as pure states and incoherent mixtures, to ensure the algorithm's correctness before reintroducing dephasing effects.
Areas of Agreement / Disagreement
Participants express varying opinions on the source of the problem, with some attributing it to the numerical method and others to the artificial introduction of dephasing time. No consensus is reached on the exact cause of the negative values in the density matrix.
Contextual Notes
The discussion highlights potential limitations in the numerical approach, including the dependence on the chosen dephasing parameter and the need for careful validation against known cases. Specific assumptions about the behavior of the density matrix and the numerical method remain unresolved.