Physics

Operator (biology)

Pure mathematics

Mathematics

Domain (mathematical analysis)

Transcription factor

Gene

Algorithm

Mathematical analysis

Repressor

Chemistry

Geometry

Computer science

Quantum mechanics

Field (mathematics)

Biochemistry

Radiative transfer

Electromagnetism

Physical Review Research

We show how the central equality of scattering theory, the definition of the $\mathbb{T}$ operator, can be used to generate hierarchies of mean-field constraints that act as natural complements to the standard electromagnetic design problem of optimizing some objective with respect to structural degrees of freedom. Proof-of-concept application to the problem of maximizing radiative Purcell enhancement for a dipolar current source in the vicinity of a structured medium, an effect central to many sensing and quantum technologies, yields performance bounds that are frequently more than an order of magnitude tighter than all current frameworks, highlighting the irreality of these models in the presence of differing domain and field-localization length scales. Closely related to domain decomposition and multi-grid methods, similar constructions are possible in any branch of wave physics, paving the way for systematic evaluations of fundamental limits beyond electromagnetism.

Hierarchical mean-field<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi mathvariant="double-struck">T</mml:mi></mml:math>operator bounds on electromagnetic scattering: Upper bounds on near-field radiative Purcell enhancement

Hierarchical mean-fieldToperator bounds on electromagnetic scattering: Upper bounds on near-field radiative Purcell enhancement