University of Lethbridge

Biography

Mark is a professor in the Department of Physics and Astronomy. He has been a faculty member since January 1991. Prof. Walton is a theoretical and mathematical physicist. His B.Sc. (Honours) is from Dalhousie University in Halifax, and his M.Sc and Ph.D. (1987) were both completed at McGill University in Montreal. Mark's M.Sc. research was in elementary particle physics (or high energy physics) and his Ph.D. research was in string theory. During an NSERC Postdoctoral Fellowship at the Stanford Linear Accelerator Center he switched research fields to conformal field theory and related topics (a fairly non-technical introduction to conformal field theory is: J. Cardy, Physics World, June, 1993, pg 29). His 2nd postdoctoral position, at Université Laval, was shortened when he was offered the faculty position here at the U of L. In recent years, Prof. Walton has been studying quantum mechanics, and in particular, its phase-space formulation. Mark is interested in how classical mechanics emerges from quantum theory, and in the foundations of quantum mechanics. Throughout his research career, Prof. Walton has applied the math of Lie groups and algebras to various physical systems.

Selected Publications

J Rasmussen, M A Walton, Weight-Polytope Sums for A_n , J Math Phys 62 (2022) 101702 (Editor's Pick)

M Amin*, M A Walton, Quantum-Classical Dynamical Brackets, Phys Rev A 104 (2021) 032216

M Amin*, M A Walton, An Illustration of Canonical Quantum-Classical Dynamics, J Comput Electron 20 (2021) 2141

M P G Robbins*, M A Walton, Can Star Products be Augmented by Classical Physics? , J Phys Commun 2 (2018) 125002

* students

Research Interests

Phase-Space Quantum Mechanics and the Quantum-Classical Relation

Quantum mechanics (QM) describes physics at short, "microscopic'' distances. Classical mechanics (CM) applies at macroscopic scales. Each works eminently well in its regime. The quantum-classical (QC) relation, however, is not well understood.

For example, if one imagines moving from the microscopic to the macroscopic, QM does not morph into CM.
Even worse, the so-called classical limit becomes singular, and it is difficult to understand how classical can emerge from quantum.

My research program is aimed at understanding the QC relation better. Improved understanding would represent an advance in the foundations of physics. It would also be important for many experiments now being done and the technology being developed in the QC regime.

My work uses phase space quantum mechanics (PSQM). It is the formulation of QM best suited to studying the QC relation. Both PSQM and CM live in phase space, for example, and neither uses operators.

Hybrid QC systems point to problems. Many different systems exist in nature that appear to be composed of a quantum part interacting with a classical part. However, attempts to formulate consistently their dynamics have failed. The first part of my research proposal exploits recent progress on this problem made with my student Amin.

Additional effects have been conjectured to play a role in the emergence of CM from QM. These include measurement uncertainties, thermal effects, decoherence by interaction with the environment, and spontaneous state collapse. All will be studied in PSQM to help distinguish them in experiments.

If QM is valid at all scales, then macroscopic quantum systems, "Schrodinger cats'', must exist. An intense hunt is now underway for them. I propose work to help identify candidate measures of macroscopic quantumness.

A second aim of my proposed research is to improve and generalize the methods and tools of PSQM.

Current Research and Creative Activity

Title	Location	Grant Information	Principal Investigator	Co Researchers
NSERC Alliance - Alberta Innovates Advance Programs		Discovery Grant Supplement, $16,000/year for 2 years, 2022-2024.
Phase-Space Quantum Mechanics and the Quantum-Classical Relation		Natural Sciences and Engineering Research Council (NSERC), Discovery Grant (DG), $24,000/year for 5 years, 2022-2027.

Previous Research

Title	Grant Agency	Completion Date
NSERC Grantholder since 1992.