A Path Integral Approach to Nano-Scale Electronics

By John Shumway

Department of Physics, Arizona State University, Tempe, AZ

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Path integral Quantum Monte Carlo (pi-qmc) allow many-body nanoscale simulations involving all thermal and quantum fluctuations. This allows the direct simulation of quantum phenomena such as exchange tunneling between quantum dots or Luttinger liquid behavior in quantum wires. In the path integral formulation of statistical mechanics developed by Richard Feynman, particles are represented by closed imaginary-time trajectories of duration ℏ/kT. Monte Carlo methods are used to efficiently sample an ensemble of such paths. Simulations of pi-qmc are able to compute total energies, correlation functions, charge distribution, and linear response functions for thermal equilibrium. Our application, pi-qmc, is well-suited for modeling conduction electrons and holes in quantum dots, quantum wires, and quantum wells. Simple ab-initio calculations, such as hydrogen molecules and helium atoms, connect the pi-qmc method to quantum chemistry. In this talk I give a brief overview of the pi-qmc method and our efforts to deploy the simulations on nanoHUB. Some technical details of our approach include the use of python scripts, matplotlib graphing, and XML processing within the Rappture framework.


John Shumway is a professor of physics at Arizona State University and a senior computational scientist at Stone Ridge Technology. His research focuses on the intersection of high performance computing, physics, and energy technology. As a professor at Arizona State University, he developed pi-qmc, an open-source quantum simulation program that is applicable to a wide range of physical systems, including nanoscale electronics. He received his Ph. D. in physics from the University of Illinois and studied self-assembled quantum dots as a postdoctoral researcher at the National Renewable Energy Laboratory. He has maintained a lifelong interest in software design, especially the practical application of agile design methodologies to high-performance software. Currently he is working for Stone Ridge Technology, a Maryland start-up company focusing on the delivery of hardware-accelerated solutions to the oil and gas, finance, and bio-informatics industries.

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Researchers should cite this work as follows:

  • John Shumway (2014), "A Path Integral Approach to Nano-Scale Electronics," https://nanohub.org/resources/21162.

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nanoHUB user conference, Phoenix, AZ