6 research outputs found
Hamiltonian Dynamics of Semiclassical Gaussian Wave Packets in Electromagnetic Potentials
We extend our previous work on symplectic semiclassical Gaussian wave packet
dynamics to incorporate electromagnetic interactions by including a vector
potential. The main advantage of our formulation is that the equations of
motion derived are naturally Hamiltonian. We obtain an asymptotic expansion of
our equations in terms of and show that our equations have
corrections to those presented by Zhou, whereas ours also
recover the equations of Zhou in the case of a linear vector potential and
quadratic scalar potential. One and two dimensional examples of a particle in a
magnetic field are given and numerical solutions are presented and compared
with the classical solutions and the expectation values of the corresponding
observables as calculated by the Egorov or Initial Value Representation (IVR)
method. We numerically demonstrate that the correction
terms improve the accuracy of the classical or Zhou's equations for short times
in the sense that our solutions converge to the expectation values calculated
using the Egorov/IVR method faster than the classical solutions or those of
Zhou as .Comment: 16 pages, 6 figure
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Classical and Quantum Mechanical Models of Many-Particle Systems
This meeting was focused on recent results on the mathematical analysis of many-particle systems, both classical and quantum-mechanical in scaling regimes such that the methods of kinetic theory can be expected to apply. Thus, the Boltzmann equation is in many ways the central equation investigated in much of the research presented and discussed at this meeting, but the range of topics naturally extended from this center to include other non-linear partial differential and integro-differential equations, especially macroscopic/fluid-dynamical limits of kinetic equations modeling the dynamics of many-particle systems. A significant subset of the talks focused on propagation of chaos, and the validation and derivation of kinetic equations from underlying stochastic particle models in which there has been much progress and activity. Models were discussed with applications not only in physics, but also engineering, and mathematical biology. While there were a number of new participants, especially younger researchers, an interesting aspect of the conference was the number of talks presenting progress that had its origins in the previous meeting in this series held in 2010