Noah Graham

Assistant Professor of Physics and Junior Faculty Fellow, Middlebury College

McCardell Bicentennial Hall, with telescope and cooling fan

Contact info:

Department of Physics
McCardell Bicentennial Hall
Middlebury College
Middlebury, VT 05753

Phone: (802) 443-3423
Fax: (802) 443-2072

email: ngraham [at] middlebury [dot] edu

Education:

Research:

My research centers around applications of quantum mechanics and classical and quantum field theory to a variety of problems in elementary particle physics, physics of solitons and oscillons, and the Casimir effect. I am also interested in applications of physics techniques to applications in computer science. Here are some possible thesis topics on these subjects, or you can read my fascinating papers.

Here is some code that does a lattice simulation of oscillons in the electroweak Standard Model, as shown in this paper and this paper. It includes SU(2)xU(1) gauge fields and a fundamental Higgs field and allows for parallel processing using MPI, threads, or both. It has been adapted to a number of other situations, including SU(2) adjoint gauge fields, abelian Higgs models, and expanding universe backgrounds -- please contact me if you are interested in the details. By downloading or using this code you agree to the following license terms, which are also included with the package.

All contents of this package are copyright © Noah Graham, 2006-2007, all rights reserved. This program may be used and modified for noncommercial research purposes, provided that citation to N. Graham, hep-th/0610267, "An Electroweak Oscillon," Phys. Rev. Lett. 98 (2007) 101801 and/or N. Graham, arXiv:0706.4125 [hep-th], "Numerical Simulation of an Electroweak Oscillon," Phys. Rev. D 76 (2007) 085017 or equivalent is included in all publications or other products in which the program or any programs derived from it were used. This program and all accompanying materials are provided "AS IS," WITHOUT WARRANTY OF ANY KIND, EITHER EXPRESSED OR IMPLIED, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE.

I have also extensively modified the package of Falloon for computing spheroidal functions in Mathematica. The resulting code is much faster for common cases and fixes a number of bugs; see the readme for details.

These changes were developed with assistance from Pavlo Levkiv.

Spheroidal package for Mathematica 4
Spheroidal package for Mathematica 5
Spheroidal package for Mathematica 6

By downloading or using any of these packages you agree to the following license terms, also which are also given in the license file.

This package is based on previous work of Falloon (see P. E. Falloon, P. C. Abbott, and J. B. Wang, J. Phys. A36 (2003) 5477), which does not indicate any license restrictions or copyright. Modifications are copyright © Noah Graham, 2005-2008, all rights reserved. The modified packages may be used and modified for noncommercial research or educational purposes, provided that citation to

T. Emig, N. Graham, R. L. Jaffe and M. Kardar, "Casimir Manipulations: The Orientation Dependence of Fluctuation-Induced Forces," arXiv:0811.1597, Phys. Rev. D77 (2008) 025005.

is included in all publications or other products in which the modified program or any programs derived from it was used. Commercial use or inclusion in a commercial product is prohibited. This program and all accompanying materials are provided "AS IS," WITHOUT WARRANTY OF ANY KIND, EITHER EXPRESSED OR IMPLIED, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE.

Update: The package for Version 6 also appears to work in Version 7 as well. To use it with the parallel capabilites of Version 7, however, you must include a command to load the package in your user init.m file (in /usr/share/Mathematica/Kernel for my installation) and also delete the "-noinit" option from the subkernel's init.m file (in /usr/local/Wolfram/Mathematica/7.0/AddOns/Applications/SubKernels/Kernel for my installation). Although the performance of the built-in spheroidal functions is considerably improved in Version 7, the package here is still much faster.

I gratefully acknowledge the National Science Foundation, Research Corporation, Vermont EPSCoR, and Middlebury College for grants supporting my research.

Teaching:

Below are lessons on quantum mechanics I have developed for the course "Quantum Mechanics From a Linear Algebra Point of View." They assume knowledge of linear algebra (at the level of Strang's book, for example) and basic familiarity with introductory mechanics and electromagnetism. Rather than the usual wave-mechanics approach used in most textbooks and quantum mechanics courses (such as PH401), they use the more physically abstract but mathematically simpler picture of finite dimensional matrices. My hope is they can provide a complement to standard undergraduate quantum mechanics references such as Gasiorowicz, Griffiths, and Liboff. This approach is also more directly applicable to problems in quantum computing.

All materials are copyright © 2002-2007, Noah Graham. These materials may be used for noncommercial purposes with proper attribution, including this notice.

Lesson 1
Lesson 2
Lesson 3
Lesson 4
Lesson 5
Lesson 6
Lesson 7
Lesson 7 (advanced version)
Lesson 8
Lesson 9

Having worked in industry doing research in speech recognition, I am also interested in applications of scientific computing, both to physics and to subjects like speech and vision. Below are the first three projects from PH120, Computers in the Physical Sciences. These are designed to provide introductions to the applications of an object-oriented approach using Mathematica© and C++ to problems in the physical sciences. Other examples of computational assignments from PH301, Intermediate Electrodynamics, PH350, Statistical Mechanics, and PH401, Quantum Mechanics, are below as well.

All materials are copyright © 2002-2007, Noah Graham. These materials may be used for noncommercial purposes with proper attribution, including this notice.

Project 1
Project 2
Project 3
PH301 Project
PH350 Project
PH401 Project
Weybridge, VT