Physical Sciences and Mathematics | Open Access Articles

Quantum Effects Of A Spacetime Varying Alpha On The Propagation Of Electrically Charged Fermions, Alejandro Ferrero, Brett David Altschul

Faculty Publications

A spacetime-varying fine structure constant α(x ^µ) could generate quantum corrections in some of the coefficients of the Lorentz-violating standard model extension (SME) associated with electrically charged fermions. The quantum corrections depend on ∂µα, the spacetime gradient of the fine structure constant. Lorentz-violating operators involving fermions arise from the one-loop corrections to the quantum electrodynamics (QED) vertex function and fermion self-energy. Both g λµν and c µν terms are generated, at O(∂_µα) and O[(∂_{µα) ² ], respectively. The g λµν terms so generated are different in the vertex and self-energy, which represents a radiatively induced violation …}

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Wavepacket Approach To The Cumulative Reaction Probability Within The Flux Operator Formalism, Sophya Garashchuk, Tijo Vazhappilly

Faculty Publications

Expressions for the singular flux operator eigenfunctions and eigenvalues are given in terms of the Dirac δ-function representable as a localized Gaussian wavepacket. This functional form enables computation of the cumulative reaction probability N(E) from the wavepacket time-correlation functions. The Gaussian based form of the flux eigenfunctions, which is not tied to a finite basis of a quantum-mechanical calculation, is particularly useful for approximate calculation of N(E) with the trajectory based wavepacket propagation techniques. Numerical illustration is given for the Eckart barrier using the conventional quantum-mechanical propagation and the quantum trajectory dynamics with the approximate quantum potential. N(E) converges with …

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Bohmian Dynamics On Subspaces Using Linearized Quantum Force, V. A. Rassolov, Sophya V. Garashchuk

Faculty Publications

In the de Broglie–Bohm formulation of quantum mechanics the time-dependent Schrödinger equation is solved in terms of quantum trajectories evolving under the influence of quantum and classical potentials. For a practical implementation that scales favorably with system size and is accurate for semiclassical systems, we use approximate quantum potentials. Recently, we have shown that optimization of the nonclassical component of the momentum operator in terms of fitting functions leads to the energy-conserving approximate quantum potential. In particular, linear fitting functions give the exact time evolution of a Gaussian wave packet in a locally quadratic potential and can describe the dominant …

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Semiclassical Dynamics With Quantum Trajectories: Formulation And Comparison With The Semiclassical Initial Value Representation Propagator, Sophya V. Garashchuk, V. A. Rassolov

Faculty Publications

We present a time-dependent semiclassical method based on quantum trajectories. Quantum-mechanical effects are described via the quantum potential computed from the wave function density approximated as a linear combination of Gaussian fitting functions. The number of the fitting functions determines the accuracy of the approximate quantum potential (AQP). One Gaussian fit reproduces time-evolution of a Gaussian wave packet in a parabolic potential. The limit of the large number of fitting Gaussians and trajectories gives the full quantum-mechanical result. The method is systematically improvable from classical to fully quantum. The fitting procedure is implemented as a gradient minimization. We also compare …

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Full-Text Articles in Physical Sciences and Mathematics

Quantum Effects Of A Spacetime Varying Alpha On The Propagation Of Electrically Charged Fermions, Alejandro Ferrero, Brett David Altschul

Faculty Publications

Wavepacket Approach To The Cumulative Reaction Probability Within The Flux Operator Formalism, Sophya Garashchuk, Tijo Vazhappilly

Faculty Publications

Bohmian Dynamics On Subspaces Using Linearized Quantum Force, V. A. Rassolov, Sophya V. Garashchuk

Faculty Publications

Semiclassical Dynamics With Quantum Trajectories: Formulation And Comparison With The Semiclassical Initial Value Representation Propagator, Sophya V. Garashchuk, V. A. Rassolov

Faculty Publications