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).

Slides from talks:
"A semiclassical model for fermion dynamics (with applications to molecular electronics)". Emerging Technologies in Computational Chemistry Contest Session. 242nd ACS National Meeting, Denver, CO. August 2011. [20 min]
"Dynamics of Classically Mapped Fermions (with applications to molecular electronics)." MolSim Group Meeting, Universiteit van Amsterdam, February 3, 2012. [1 hr]
"Classical dynamics for nonequilibrium quantum transport: The Dynamics for Classically Mapped Fermions method". Dutch Molecular Dynamics Day, Rijksuniversiteit Groningen, March 23, 2012. [20 min]
"A classical model for nonequilibrium quantum transport: The Dynamics for Classically Mapped Fermions method". Spring Symposium of the Amsterdam Center on Multiscale Modeling, Universiteit van Amsterdam, June 28, 2012. [40 min]