Fermion Dynamics from a Classical Hamiltonian

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.

Our model, based on earlier work by Miller and White [1], gave astonishingly good results when applied to the resonant level (Landauer) model for a wide range of bias voltages, gate voltages, and temperatures.

After the first paper was written, I wrote a rough description of this work for non-scientists.

Following the early success of this approach, Prof. Rabani invited me to continue this work with him at Tel Aviv University. During my five months there, we extended the DCMF approach to systems with a phonon bath, and to systems which include electron correlation.

References:
[1] William H. Miller and Kim A. White. J. Chem. Phys. 84, 5059 (1986).

Publications:
Swenson, Levy, Cohen, Rabani, and Miller. "Application of a semiclassical model for the second-quantized many-electron Hamiltonian to nonequilibrium quantum transport: The resonant level model" J. Chem. Phys. 134, 164103 (2011).
Swenson, Cohen, and Rabani. "A semiclassical model for the nonequilibrium quantum transport of a many-electron Hamiltonian coupled to phonons." Mol. Phys.. (accepted)

Slides from talks:
"". Emerging Technologies in Computational Chemistry Contest Session. 242nd ACS National Meeting, Denver, CO. August 2011.
"Dynamics of Classically Mapped Fermions (with applications to molecular electronics)." MolSim Group Meeting, Universiteit van Amsterdam, February 3, 2012.