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Full-Text Articles in Biological and Chemical Physics
The Schrödinger Equation With Friction From The Quantum Trajectory Perspective, Sophya V. Garashchuk, Vaibhav Dixit, Bing Gu, James Mazzuca
The Schrödinger Equation With Friction From The Quantum Trajectory Perspective, Sophya V. Garashchuk, Vaibhav Dixit, Bing Gu, James Mazzuca
Faculty Publications
Similarity of equations of motion for the classical and quantum trajectories is used to introduce afriction term dependent on the wavefunction phase into the time-dependent Schrödingerequation. The term describes irreversible energy loss by the quantum system. The force offriction is proportional to the velocity of a quantum trajectory. The resulting Schrödinger equationis nonlinear, conserves wavefunction normalization, and evolves an arbitrary wavefunction into the ground state of the system (of appropriate symmetry if applicable). Decrease in energy is proportional to the average kinetic energy of the quantum trajectory ensemble. Dynamics in the high friction regime is suitable for simple models of …
Geminal Model Chemistry Ii. Perturbative Corrections, V. A. Rassolov, F. Xu, Sophya V. Garashchuk
Geminal Model Chemistry Ii. Perturbative Corrections, V. A. Rassolov, F. Xu, Sophya V. Garashchuk
Faculty Publications
We introduce and investigate a chemical model based on perturbative corrections to the product of singlet-type strongly orthogonal geminals wave function. Two specific points are addressed (i) Overall chemical accuracy of such a model with perturbative corrections at a leading order; (ii) Quality of strong orthogonality approximation of geminals in diverse chemical systems. We use the Epstein–Nesbet form of perturbation theory and show that its known shortcomings disappear when it is used with the reference Hamiltonian based on strongly orthogonal geminals. Application of this model to various chemical systems reveals that strongly orthogonal geminals are well suited for chemical models, …
Semiclassical Dynamics With Quantum Trajectories: Formulation And Comparison With The Semiclassical Initial Value Representation Propagator, Sophya V. Garashchuk, V. A. Rassolov
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 …