Physics Commons^™

Unbounded Derivations Of C*-Algebras And The Heisenberg Commutation Relation, Lara M. Ismert

Department of Mathematics: Dissertations, Theses, and Student Research

This dissertation investigates the properties of unbounded derivations on C*-algebras, namely the density of their analytic vectors and a property we refer to as "kernel stabilization." We focus on a weakly-defined derivation δ_D which formalizes commutators involving unbounded self-adjoint operators on a Hilbert space. These commutators naturally arise in quantum mechanics, as we briefly describe in the introduction.

A first application of kernel stabilization for δ_D shows that a large class of abstract derivations on unbounded C*-algebras, defined by O. Bratteli and D. Robinson, also have kernel stabilization. A second application of kernel stabilization provides a sufficient condition …

Free Electron Sources And Diffraction In Time, Eric R. Jones

Department of Physics and Astronomy: Dissertations, Theses, and Student Research

The quantum revolution of the last century advanced synergistically with technology, for example, with control of the temporal and spatial coherence, and the polarization state of light. Indeed, experimental confirmation of the quirks of quantum theory, as originally highlighted by Einstein, Podolsky, and Rosen, through Bohm, and then Bell, have been performed with photons, i.e., electromagnetic wave packets prepared in the same quantum states. Experimental tests of quantum mechanics with matter wave packets have been limited due to challenges in preparing all of the packets with similar quantum states. While great strides have been made for trapped atoms and Bose-Einstein …

Testing Quantum Coherence In Stochastic Electrodynamics With Squeezed Schrödinger Cat States, Wayne Cheng-Wei Huang, Herman Batelaan

Department of Physics and Astronomy: Faculty Publications

The interference pattern in electron double-slit diffraction is a hallmark of quantum mechanics. A long-standing question for stochastic electrodynamics (SED) is whether or not it is capable of reproducing such effects, as interference is a manifestation of quantum coherence. In this study, we used excited harmonic oscillators to directly test this quantum feature in SED. We used two counter-propagating dichromatic laser pulses to promote a ground-state harmonic oscillator to a squeezed Schrödinger cat state. Upon recombination of the two well-separated wavepackets, an interference pattern emerges in the quantum probability distribution but is absent in the SED probability distribution. We thus …

Duality And Free Energy Analyticity Bounds For Few-Body Ising Models With Extensive Homology Rank, Yi Jiang, Ilya Dumer, Alexey Kovalev, Leonid Pryadko

Department of Physics and Astronomy: Faculty Publications

We consider pairs of few-body Ising models where each spin enters a bounded number of interaction terms (bonds) such that each model can be obtained from the dual of the other after freezing k spins on large-degree sites. Such a pair of Ising models can be interpreted as a two-chain complex with k being the rank of the first homology group. Our focus is on the case where k is extensive, that is, scales linearly with the number of bonds n. Flipping any of these additional spins introduces a homologically nontrivial defect (generalized domain wall). In the presence of …