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Full-Text Articles in Physics
Quantum Mechanics With A Quartic Dispersion Law, Joanna Ruhl
Quantum Mechanics With A Quartic Dispersion Law, Joanna Ruhl
Graduate Masters Theses
Creation of three-dimensional matter waves, the three-dimensional analog of one-dimensional solitons, has been a goal of experimental physics for some time. A recent proposal has suggested that changing the dispersion law from quadratic to quartic for ultra cold atoms in a shaken lattice should allow for the creation of these objects. In this thesis, we develop the theoretical basis for quantum mechanics with a quartic dispersion law. The probability current functional is constructed from the corresponding time-dependent Schrödinger equation, and used to derive the junction conditions that connect the derivatives of the wavefunction on one side of a potential discontinuity …
Supersymmetric Origins Of The Properties Of Sech-Pulses And Sine-Gordon Solitons, Andrew Phillip Koller
Supersymmetric Origins Of The Properties Of Sech-Pulses And Sine-Gordon Solitons, Andrew Phillip Koller
Graduate Masters Theses
In this thesis, we show that the members of a class of reflectionless Hamiltonians, namely, Akulin's Hamiltonians, are connected via a supersymmetric (SUSY) chain. While the reflectionless property in question (vanishing reflection coefficients at all values of the spectral parameter, e.g. energy) has been mentioned in the literature for over two decades, the enabling algebraic mechanism was previously unknown. We show that the supersymmetric connection of the Akulin's Hamiltonians to a potential-free Hamiltonian is the origin of this property. As the first application for our findings, we show that the SUSY decomposition of Akulin's Hamiltonians explains a well-known effect in …