Many-Body Effects in Models with Superexponential Interactions

TL;DR

This paper investigates the complex scattering dynamics of many-body systems with superexponential potentials, revealing a transition from direct to multiple backscattering as energy increases, with detailed trajectory and statistical analysis.

Contribution

It introduces a detailed analysis of scattering behavior in superexponential many-body systems, highlighting the transition in dynamics and statistical properties with energy.

Findings

Transition from direct to multiple backscattering with increasing energy

Distribution of reflection times shifts from two-plateau to broad peak

Momentum-time maps evolve from two-valued curves to broad distributions

Abstract

Superexponential systems are characterized by a potential where dynamical degrees of freedom appear in both the base and the exponent of a power law. We explore the scattering dynamics of many-body systems governed by superexponential potentials. Each potential term exhibits a characteristic crossover via two saddle points from a region with a confining channel to two regions of asymptotically free motion. With increasing scattering energy in the channel we observe a transition from a direct backscattering behaviour to multiple backscattering and recollision events in this channel. We analyze this transition in detail by exploring both the properties of individual many-body trajectories and of large statistical ensembles of trajectories. The recollision trajectories occur for energies below and above the saddle points and typically exhibit an intermittent oscillatory behaviour with strongly varying amplitudes. In case of statistical ensembles the distribution of reflection times into the channel changes with increasing energy from a two-plateau structure to a single broad asymmetric peak structure. This can be understood by analyzing the corresponding momentum-time maps which undergo a transition from a two-valued curve to a broad distribution. We close by providing an outlook onto future perspectives of these uncommon model systems.