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enFermion Dynamics from a Classical Hamiltonian
http://www.hyperblazer.net/research/fermion-dynamics-classical-hamiltonian
<p>While he was on sabbatical in Berkeley, Prof. Eran Rabani approached Prof. Miller about the idea of developing a semiclassical approach to study molecular electronics. Together, we developed what we eventually called the Dynamics for Classically Mapped Fermions (DCMF) method, which generates classical model Hamiltonian that can describe the dynamics of fermionic systems. Fermion dynamics are particularly challenging for a classical model because of the Pauli exclusion principle and because of the anticommutivity of fermionic operators.</p><p><a href="http://www.hyperblazer.net/research/fermion-dynamics-classical-hamiltonian">read more</a></p>ResearchFri, 25 Feb 2011 06:48:58 -070028 at http://www.hyperblazer.netPrecision Finite Difference Monodromy Matrix
http://www.hyperblazer.net/research/precision-finite-difference-monodromy-matrix
<p>While at the University of California, Berkeley, I developed a new method for calculating the monodromy matrix. The monodromy (or stability) matrix is a quantity of central importance in many semiclassical theories; it is required to calculate the semiclassical prefactor, which helps capture many quantum effects in semiclassical calculations. Calculating it is one of the most computationally difficult parts of many semiclassical calculations.</p>
<p><a href="http://www.hyperblazer.net/research/precision-finite-difference-monodromy-matrix">read more</a></p>ResearchMon, 22 Nov 2010 19:09:23 -070025 at http://www.hyperblazer.netModeling the potential energy surface of H2-benzene
http://www.hyperblazer.net/research/modeling-potential-energy-surface-h2-benzene
<p> Under the direction of <a href="http://chem.iupui.edu/Faculty/Dykstra/">Prof. Clifford E. Dykstra</a> of <a href="http://www.iupui.edu/">Indiana University-Purdue University Indianapolis</a>, I used the Molecular Mechanics for Clusters [1] scheme to develop an approximate version of the H<sub>2</sub>-benzene <i>ab initio</i> potential energy surface. Using previously developed parameters for the H<sub>2</sub>-H<sub>2</sub> interaction, [2] I was able to show that our model represented clusters of H<sub>2</sub> around a benzene with good accuracy.</p>
<p><a href="http://www.hyperblazer.net/research/modeling-potential-energy-surface-h2-benzene">read more</a></p>ResearchMon, 21 Jan 2008 09:16:24 -07009 at http://www.hyperblazer.net