Dialogue on analytical and ab initio methods in attoscience

TL;DR

This paper discusses the relationship and misconceptions between analytical and ab initio methods in attoscience, highlighting their roles, advantages, and limitations through a dialogue and case studies.

Contribution

It provides a comprehensive survey of theoretical tools in attoscience and clarifies the misconceptions about analytical and ab initio approaches.

Findings

Analytical and ab initio methods have complementary roles in attoscience.

Misconceptions often hinder the understanding of numerical methods in analytical techniques.

Case studies illustrate the advantages and limitations of different theoretical approaches.

Abstract

The perceived dichotomy between analytical and ab initio approaches to theory in attosecond science is often seen as a source of tension and misconceptions. This Topical Review compiles the discussions held during a round-table panel at the 'Quantum Battles in Attoscience' CECAM virtual workshop, to explore the sources of tension and attempt to dispel them. We survey the main theoretical tools of attoscience -- covering both analytical and numerical methods -- and we examine common misconceptions, including the relationship between ab initio approaches and the broader numerical methods, as well as the role of numerical methods in 'analytical' techniques. We also evaluate the relative advantages and disadvantages of analytical as well as numerical and ab initio methods, together with their role in scientific discovery, told through the case studies of two representative attosecond processes: non-sequential double ionisation and resonant high-harmonic generation. We present the discussion in the form of a dialogue between two hypothetical theoreticians, a numericist and an analytician, who introduce and challenge the broader opinions expressed in the attoscience community.