**Contact Info**

Department of Applied Mathematics

University of Waterloo

Waterloo, Ontario

Canada N2L 3G1

Phone: 519-888-4567, ext. 32700

Fax: 519-746-4319

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Friday, March 19, 2021 2:00 PM EDT

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Andrew Stasiuk | Applied Mathematics, University of Waterloo

Computational and Theoretical Insights into Multi-Body Quantum Systems

In generality, perfect predictions of the structure and dynamics of multi-body quantum systems are few and far between. As experimental design advances and becomes more refined, experimentally probing the interactions of multiple quantum systems has become commonplace. Predicting this behavior is not a ``one size fits all" problem, and has lead to the inception of a multitude of successful theoretical techniques which have made precise and verifiable predictions through, in many cases, clever approximations and assumptions. As the state-of-the-art pushes the quantum frontier to new experimental regimes, many of the old techniques become invalid, and there is often no tractable methodology to fall back on.

This work focuses on expanding the theoretical techniques for making predictions in newly accessible experimental regimes. The transport of quantum information in a room-temperature dipolar spin network is veritably diffusive in nature, but much less is known about the transport properties of such a sample at low temperatures. This work presupposes that diffusion is still a good model for incoherent transport at low temperatures, and proposes a new method to calculate its diffusion coefficient. The diffusion coefficient is reported as a function of the temperature of the ensemble. Further, the interaction of an i.i.d. spin ensemble with a quantized electromagnetic field has long been analyzed via restriction to the Dicke subspace implicit in the Holstein--Primakoff approximation, as well as other within other approximations. This work reanalyzes the conditions under which such a restriction is valid. In regimes where it is shownt that restricting to the Dicke subspace would be invalid, the Hamiltonian structure is thoroughly analyzed. Various predictions can be made by appealing to a reduction in effective dimensionality via a direct sum decomposition.

The main theme of the techniques utilized throughout this work is to appeal to a reduction in difficulty via various theoretical tools in order to prepare for an otherwise intractable computational analysis. Computational insights due to this technique have then gone on to motivate directly provable theoretical results, which might otherwise have remained hidden behind the complexity of the structure and dynamics of a multi-body quantum system.

**Contact Info**

Department of Applied Mathematics

University of Waterloo

Waterloo, Ontario

Canada N2L 3G1

Phone: 519-888-4567, ext. 32700

Fax: 519-746-4319

PDF files require Adobe Acrobat Reader

University of Waterloo

University of Waterloo

43.471468

-80.544205

200 University Avenue West

Waterloo,
ON,
Canada
N2L 3G1

The University of Waterloo acknowledges that much of our work takes place on the traditional territory of the Neutral, Anishinaabeg and Haudenosaunee peoples. Our main campus is situated on the Haldimand Tract, the land granted to the Six Nations that includes six miles on each side of the Grand River. Our active work toward reconciliation takes place across our campuses through research, learning, teaching, and community building, and is co-ordinated within the Office of Indigenous Relations.