Daphne Gilbert

Daphne Gilbert (née Daphne Jane Mansergh, 1944–2024), was an English mathematician known for pioneering the subordinacy theory of spectral analysis. She codeveloped, with David Pearson, the Gilbert-Pearson Theory of Subordinacy of Schrödinger Operators, a foundational result that provided new methods for analyzing spectral properties of quantum mechanical systems. She later continued the development of the theory to extend it to more general settings, contributing significantly to the mathematical understanding of Schrödinger operators and their applications in quantum mechanics.

Early life and education

Daphne Jane Mansergh was born in 1944 in Working, Surrey, England. She was the second of five children of Philip Nicholas Seton Mansergh, an Anglo-Irish historian, and Diana Mary Keeton, a squash and lawn tennis blue. Her interest in mathematics began when she attended the Perse School For Girls in Cambridge. On her nature walks, she would notice organic geometric patterns. Although her parents encouraged her to pursue domestic sciences, she chose to study mathematics, physics, and chemistry. In 1961, Gilbert began her studies of mathematics at New Hull (now Murray Edwards College) in Cambridge. She paused her studies a year later to devote her time to raising a family. In 1977, she went back to New Hull to continue her study of mathematics, earning her bachelor’s degree in 1980. Gilbert’s doctoral dissertation, completed in 1984 under the supervision of David Pearson, developed what became known as the Gilbert–Pearson theory of Subordinacy for Schrödinger Operators.

Career

Gilbert began her career at New Hull after earning her PhD in 1984. She continued her research and development, publishing an extension to the theory in 1989 called “On subordinacy and analysis of the spectrum of Schrödinger operators with two singular endpoints." Daphne Gilbert extended the subordinacy theory of Schrödinger operators, originally developed with her advisor David Pearson for systems defined on the half-line, to apply to the whole line. This allowed the analysis of particle behavior in both directions rather than only from a fixed starting point.

In 1990, she joined Sheffield Hallam University, in Sheffield, South Yorkshire, England, where she continued her mathematical research. Here, she lectured, supervised PhD candidates with uplifting guidance and dedication, developed new degree programs, and developed new masters programs within mathematics fields. Gilbert then proceeded to become Head of Department of Pure and Applied Mathematics at the Dublin Institute of Technology in 1999, where she rose to professor before her retirement. She continued conducting research and developing the Mathematical Science Department at DIT. Gilbert coauthored numerous research articles between June 2000 and July 2013, including several published after her retirement. She retired in 2008 and was granted emeritus status.

Research

Gilbert and David Pearson developed the Gilbert-Pearson Theory of Subordinacy of Schrödinger Operators, published in 1984. Their theory gave mathematicians and physicists a new way to understand how quantum particles behave over time and how their possible energy states can be identified. In mathematical terms, their theory provides a framework for analyzing and quantifying the behavior of quantum states, and was the first to apply subordinacy theory to continuum half-line Schrödinger operators, establishing a new method for studying their spectral properties. Gilbert continued researching and published “On subordinacy and analysis of the spectrum of Schrödinger operators with two singular endpoints,” which developed the subordinacy theory for the whole continuum of Schrödinger operators.

Notable papers

• On Subordinacy and Analysis of the Spectrum of One-Dimensional Schrödinger Operators, Gilbert and Pearson, August 8, 1985
• On subordinacy and analysis of the spectrum of Schrödinger operators with two singular endpoints, Gilbert, 1989
• The Derivation of Minimal Test Sets for Combinational Logic Circuits using Genetic Algorithms, Takhar and Gilbert, 1997
• Bounds for the points of spectral concentration of Sturm-Liouville problems, Gilbert and Harris, June 2000
• On the Recovery of a Differential Equation from Its Spectral Functions, Gilbert and Harris, October 2001
• Bounds for the Points of Spectral Concentration of One-dimensional Schrödinger Operators, Gilbert and Harris and Riehl, January 2004
• The spectral function for Sturm–Liouville problems where the potential is of Wigner–von Neumann type or slowly decaying, Gilbert and Harris and Riehl, June 2004
• Zeros of the Jost Function for a Class of Exponentially Decaying Potentials, Gilbert and Kerouanton, 2005
• Higher Derivatives of Spectral Functions Associated with One-Dimensional Schrödinger Operators, Gilbert and Harris and Riehl, December 2008
• Higher derivatives of spectral functions associated with one-dimensional Schrödinger operators II, Gilbert and Harris and Riehl, July 2013
• Eigenfunction expansions associated with the one-dimensional Schrödinger operator, Gilbert, October 2015

Influence and legacy works

• Power Law Subordinacy and Singular Spectra. II. Line Operators, Jitomirskaya and Last, 1999
• Solutions, Spectrum, and Dynamics for Schrödinger Operators on Infinite Domains, Kiselev and Last, 1999
• Subordinacy Theory for Extended CMV Matrices, Guo and Damanik and Ong, 2022

Personal life

Gilbert met her husband, Paul Gilbert (1942–2022), a philosophy student turned professor, during her studies at New Hull in 1961. After getting married the next year, Daphne paused her studies to concentrate on her family. Even though Paul supported her ambitions, Daphne stayed home for 15 years. Together they had Benjamin, Hester, Matthew, and Emily Gilbert. Gilbert died on March 12, 2024, at the Claremont House Care Home in Beverley.