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Faculty of Graduate Studies

Jeffrey Morais

  • B.Sc. (McGill University, 2023)
Notice of the Final Oral Examination for the Degree of Master of Science

Topic

Scaling Analysis and Ensemble Measures in Quantum Systems

Department of Physics and Astronomy

Date & location

  • Tuesday, August 11, 2026
  • 10:00 A.M.
  • Virtual Defence

Examining Committee

Supervisory Committee

  • Dr. Thomas Baker, Department of Physics and Astronomy, University of Victoria (Supervisor)
  • Dr. Jesse Mumford, Department of Physics and Astronomy, UVic (Member)

External Examiner

  • Dr. Marcelo Laca, Department of Mathematics and Statistics, UVic

Chair of Oral Examination

  • Dr. Annalee Lepp, Department of Gender Studies, UVic

Abstract

We investigate equilibration and dephasing timescales in the one-dimensional models using exact diagonalization and tensor network methods. While these models are integrable and evade thermalization, they provide a well-controlled framework for studying the scaling of relaxation dynamics in isolated finite quantum systems. We formally define and compare two complementary timescales, the relaxation time and the equilibration time, and analyze their scaling relative to Hilbert space dimension. We perform a systematic comparison of exact diagonalization and two-site time-dependent variational principle tensor network time evolution across several system sizes, multiple local observables, and bond dimensions. We find that the tensor network generates relative to exact diagonalization results. Our results are consistent with a sub-polylogarithmic scaling trend for the equilibration time. We further examine the dependence on initial states, showing that high-energy states with maximal eigenstate participation (e.g., the Hadamard state) dephase fastest, whereas eigenstates exhibit no dynamics. In the spinless fermion model, we exploit particle-number conservation to restrict dynamics to specific symmetry sectors, observing consistent sub-scaling for both even- and odd-site charge density wave initial states. These results provide a quantitative baseline for understanding coherence preservation and relaxation timescales in scalable quantum simulation architectures.

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