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Annals of Physics

Solving many-body Schrödinger equations with kinetic energy partition method

Yu-Hsin Chen, Sheng Der Chao

Published Nov 7, 2017• 3 citations
Publisher
DOI
10.1016/j.aop.2017.11.002

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Based on the idea of adiabatic symmetry, we present a novel basis set expansion method—the kinetic energy partition (KEP) method—for solving quantum eigenvalue problems. Broken symmetry is responsible for quantum entanglement in many-body systems via parametric non-adiabatic corrections. Starting from simple one-particle-in-one-dimension problems, we gradually increase the complexity in the number of particles and the interaction patterns. Our goal in the mini-review is to advocate for the utility of the KEP method in front-line research, in particular for research beginners in quantum many-body problems.
We present a new approach to quantum kinetics based on a Schr\"odinger's equation formalism. As an example we apply this method to a coupled electron-LO phonon system in a semiconductor. We demonstrate that it is possible to compute the full many-body wave function of the electron-phonon system for short times. The time-dependent electron probability distribution, extracted from the many-body wave function, illustrates the non-Markovian nature of the early time kinetics. The retarded onset of dissipation and kinetic energy overshoots are explained through virtual, nonresonant transitions.