Roman J. W. Petryk

     Department of Physics & Astronomy
     The University of British Columbia
     6224 Agricultural Road, Vancouver BC, V6T 1Z1

     Office: Hennings 414 (west annex) 
     Voice:  (604) 822-2095     
     Fax:    (604) 822-5324
     Email:  petryk@physics.ubc.ca

Course Links

     Course (PHYS 410) Homepage
     Instructor (Matt Choptuik) Homepage

Quantum Teleportation Links

     The Bennett, Brassard, Jozsa, Peres and Wootters Article from the Physical Review Online Archive 
     IBM Research Page
     University of Innsbruck Experimental Group Page
     American Institute of Physics News Article (December 10, 1997) *see the graphic here*
     Scientific American Review Article 
     Alien Technology is Here!
     A different angle...

Course Project

Outline

Title: Electromagnetically Coupled Complex Scalar Fields

Objective: To investigate the behaviour of complex scalar fields with
electomagnetic interaction.

Emphasis was placed on the following aspects of the problem:

deriving the equations of motion from the Lagrangian and solving them using finite-difference techniques
spherically symmetric simulation of one massive complex scalar field and its conjugate on a flat spacetime background
boundary conditions, initial data generation, dissipation, convergence, independent residual testing, conserved quantities

RNPL (Rapid Numerical Prototyping Language) was used to implement finite differencing algorithms, and the initial constraint solver was written in FORTRAN and made use of LAPACK's DGTSV solver. Simulations were run on the bhN.physics.ubc.ca (N=1,2,3,4,5,6) dual processor Pentium computers. Visualization software included scivis and ser.

The Finished Project

The primary initial data set. A movie clip showing evolution of the scalar field components--Phi1 (shown in yellow) is the real component, Phi2 (shon in blue) is the imaginary component--can be found here MPEG. A movie clip of the electromagnetic vector potential components (At--shown in yellow--is the time component, Ar--shown in blue--is the radial component) can be found here MPEG. This example has time symmetric initial data for Phi1 and Phi2, and identical initial gaussian profiles for Phi1, Phi2, At and Ar. An outgoing condition was placed on the outer boundary (to the right of the movie clip frames). The center of spherical symmetry is at the left. A movie clip showing r*Phi1 and r*Phi2 (colours same as above) in MPEG format. A movie clip showing r*At and r*Ar (colours same as above) in MPEG format.

(Although charge is apparently *not* conserved, here are video clips showing how charge density and charge distribute inhomogeneously. rho (charge density) in MPEG format. Q (charge within radius r) in MPEG format. Also, r*rho in MPEG, and r*Q in MPEG.)

A different initial data set. A movie clip showing evolution of the scalar field components (Phi1 is the real component shown in yellow, Phi2 is the imaginary component shown in blue) can be found here MPEG. A movie clip of the electromagnetic vector potential components (At--shown n yellow--is the time component, Ar--shown in blue--is the radial component) can be found here MPEG. This example has time symmetric initial data for Phi1 and Phi2, identical initial gaussian profiles for Phi1 and At, and identical initial gaussian profiles for Phi2 and Ar (but shifted from those of Phi1 and At). An outgoing condition was placed on the outer boundary (to the right of the movie clip frames). The center of spherical symmetry is at the left. A movie clip showing r*Phi1 and r*Phi2 (colours same as above) in MPEG format. A movie clip showing r*At and r*Ar (colours same as above) in MPEG format.

A postscript version of the project is available for download here PS.

The MapleV GRTensorII package was used in the calculation of covariant derivatives. A postscript version of the GRTensorII manual is available for download in five parts PS PS PS PS PS .