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.
Highlights
Modern developments in laser technologies have kickstarted the attosecond revolution, which formed the field of attoscience, dealing with dynamics on the attosecond (10−18 s) timescale [1,2,3]
In this Topical Review, we present an exploration of this dichotomy, which collects the arguments presented in the panel discussion ‘Quantum Battle 3— Numerical versus Analytical Methods’ held during the online conference ‘Quantum Battles in Attoscience’ [7]
We tackle the subtleties in the definitions of ‘ab initio’, ‘numerical’ and ‘analytical’ methods: we detail their differences, and we present a rough classification of the various theoretical methods used in attosecond science
Summary
Modern developments in laser technologies have kickstarted the attosecond revolution, which formed the field of attoscience, dealing with dynamics on the attosecond (10−18 s) timescale [1,2,3]. The meteoric progress of attoscience has been fuelled, on the one hand, by formidable experimental efforts, and, on the other hand, it has been supported by a matching leap in our theoretical capabilities These theoretical advances have come in a wide variety, forming two opposing families of analytical and numerical approaches. While these two families generally work together, the dichotomy between analytical and numerical methods is sometimes perceived as a source of tension within the attoscience community. Our main purpose is to resolve the tension caused by this dichotomy, by identifying the critical tension points, developing the different viewpoints involved, and finding a common ground between them This process forms a natural dialogue between the analytical and numerical perspectives. Numerio and Analycia discuss the friction points they have with each other’s methods
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