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Jarov, Seraphim

Given a set of self-adjoint operators {Oi} n i=1 acting on some Hilbert space H, we aim to characterize the space of allowable quantum expectation values, {(⟨O1⟩ρ, ...,⟨On⟩ρ)|ρ ∈ D} ⊂ R n where D is the set of density operators. Our study constrains the problem by considering maximum entropy states and a central theme in our work is finding geometrical characterization of this space of expectation values. In this project, we have proven a number of general results in this direction including a complete description of the space of expectation values for commuting operators and 2 × 2 operators. We also prove generalizations of classical results from statistical mechanics as well as discuss how the generalized uncertainty principle could be used in our geometrical characterization. Finally, we apply the concepts of this thesis to the energy and pressure calculations of a special type of fermion lattice.

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University of British Columbia. PHYS 449

Vancouver : University of British Columbia Library

10.14288/1.0433569

Science, Faculty of; Physics and Astronomy, Department of

Undergraduate

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