Effective Large-Scale Descriptions for Non-Equilibrium Many-Body Quantum Systems

This PhD project at King’s College London, Department of Mathematics, focuses on developing effective large-scale descriptions for non-equilibrium many-body quantum systems. Quantum systems with many interacting particles present significant analytical challenges, especially when spatial homogeneity and time-independence assumptions are broken—conditions that are common in modern quantum experiments. While several frameworks such as generalized hydrodynamics, inhomogeneous time-dependent Luttinger liquid approaches, and ballistic fluctuation theory have been developed to address specific regimes, a unified theoretical description remains elusive. The research aims to clarify the relationships among these approaches, uncover common mathematical structures, and develop new analytic predictions for observables, particularly in strongly interacting models. The project is highly interdisciplinary, bridging quantum mechanics, theoretical physics, and advanced mathematical methods. Students will engage with cutting-edge research in non-equilibrium physics, integrable systems, and analytical techniques relevant to quantum experiments. Supervision is provided by Dr PR Ruggiero and Prof BD Doyon, both experts in the field. The position is fully funded, including a stipend, study fees, and a Research Training Support allowance. Applicants should have a strong academic background in physics, mathematics, or a closely related discipline, with particular strengths in theoretical and mathematical physics. Experience with many-body systems and non-equilibrium phenomena is advantageous. The application deadline is January 23, 2026. Prospective candidates should prepare their CV, academic transcripts, and a statement of research interest, and apply via the King’s College London application portal. For further information, candidates may contact the supervisors directly. This opportunity is ideal for students seeking to contribute to foundational advances in quantum theory and mathematical physics within a leading UK research institution.