Abstract
When composite particles---such as small molecules, nuclei, or photogenerated excitons in semiconductors---are scattered by an external potential, energy may be transferred between the c.m. and the internal degrees of freedom. An accurate dynamical modeling of this effect is pivotal in predicting diverse scattering quantities and reaction cross sections, and allows us to rationalize time-resolved energy and localization spectra. Here, we show that time-dependent scattering of a quantum composite particle with an arbitrary, nonperturbative external potential can be obtained by propagating the c.m. degrees of freedom with a properly designed local self-energy potential. The latter embeds the effect of internal virtual transitions and can be obtained by the knowledge of the stationary internal states. The case is made by simulating Wannier-Mott excitons in one- and two-dimensional semiconductor heterostructures. The self-energy approach shows very good agreement with numerically exact Schr\odinger propagation for scattering potentials where a mean-field model cannot be applied, at a dramatically reduced computational cost.
Highlights
Single-particle scattering is a basic exercise in wave quantum mechanics, but becomes a complex far-reaching problem even for the simplest composite system, a bound pair—say a light diatomic molecule or nuclei [1]
The SE method, instead, including in a local potential the virtual transitions to the internal states, provides a TD c.m. wave-packet dynamics which is very close to the results obtained by numerically exact propagation of the full two-body system, at a drastically reduced computational cost
II we describe the physical system under examination, and give the specific parameters used in our simulations for the prototypical case of a Wannier-Mott indirect Wannier-Mott excitons (IXs) in GaAs-based heterostructures
Summary
Single-particle scattering is a basic exercise in wave quantum mechanics, but becomes a complex far-reaching problem even for the simplest composite system, a bound pair—say a light diatomic molecule or nuclei [1]. Even when energy conservation does not allow internal excitations, virtual transitions between internal states cannot be neglected Such mechanisms turn out to be essential in determining scattering coefficients, and should be carefully included for a quantitative evaluation of, e.g., reaction cross sections in heavy-nuclei fusion [1], chemisorption/backscattering ratio in diatomic molecule/surface collisions [3], non-adiabatic electronuclear quantum dynamics [4], lightwave-driven quasiparticle collisions [5], or resonant tunneling of two-particle systems [6]. The SE method, instead, including in a local potential the virtual transitions to the internal states, provides a TD c.m. wave-packet dynamics which is very close to the results obtained by numerically exact propagation of the full two-body system, at a drastically reduced computational cost. The Appendix reports details of the derivation of the Green-function local formulation, which gives rise to the local SE
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