Interacting many-body simulations
Already the solution of the interacting classical many-body problem is difficult to achieve, since the integration of the equations of motions couples all positions of the particles contained in the system. Quantum mechanics only adds to the difficulty of the problem and makes approximations unavoidable. Classical and quantum-mechanical equations of motions can be related by the time-dependent variational principle as we detail in [27] for Coulombic interacting electrons in a magnetic field. Interacting systems require to carefully consider the questions of self-consistency, since all particles must be linked together and it is not possible to run one particle trajectory after each other. The emergence of an mean-field potential out of a large (10000 electrons!) many-body calculation is shown in [25]. The calculation is only possible due to our usage of graphics processing units, which are ideal tools to study interacting systems.
| [28] | Time dependent approach to transport and scattering in atomic and mesoscopic systems | |||
| T. Kramer | ||||
| AIP Conf. Proc., 1334, 142 (2011) | article | arxiv | NASA | |
| [27] | Two interacting electrons in a magnetic field: comparison of semiclassical, quantum, and variational solutions | |||
| T. Kramer | ||||
| AIP Conf. Proc., 1323, 178 (2010) | article | arxiv | NASA | |
| [25] | Self-consistent calculation of electric potentials in Hall devices | |||
| T. Kramer, V. Krueckl, E. Heller, and R. Parrott | ||||
| Phys. Rev. B, 81, 205306 (2010) | article | arxiv | NASA | |