Todd Timberlake's Physics 381C Web Page

Todd K. Timberlake

     Center for Statistical Mechanics 
     Department of Physics
     The University of Texas at Austin
     Austin, Texas 78712-1081
     
     Voice:  (512) 471-1834     
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     Email:  [email protected]

Exploring the Driven Triangle Well

This work was done as a project in Matt Choptuik's Computational Physics Course (Physics 381C).

Computational Work
- Collision Maps
  - Fortran Source Code
    - twcmap.f: Main program for generating the collision map.
    - fcn.f: Subroutine that defines equations of motion.
    - g.f: Subroutine that monitors collsions with the infinite wall.
    - Makefile for running the above programs on charon.
  - Postscript Plots
    - Collision map for field strength of 0.01.
    - Collision map for field strength of 0.1.
    - Collsion map for field strength of 0.2.
    - Collision map for field strength of 0.3.
    - Collision map for field strength of 0.5. (Spooky eyes!)
- Strobe Plots
  - Fortran Source Code
    - twsplt.f: Main program for generating the strobe plot.
    - fcn.f: Subroutine that defines equations of motion.
    - g.f: Subroutine that monitors collsions with the infinite wall.
    - out.f: Subroutine that writes output at t = NT.
    - fcn.inc: Common block include file.
    - Makefile for running the program on charon.
  - Postscript Plots
    - Strobe plot for field strength of 0.01.
    - Strobe plot for field strength of 0.1.
    - Strobe plot for field strength of 0.2.
    - Strobe plot for field strength of 0.5.
- Radiation Spectra
  - Fortran Source Code
    - accel.f: Main program for generating the acceleration time series and output of wavefunction and variance.
    - fcn.f: Subroutine defining ODEs for the coefficients in the energy expansion of the wavefunction.
    - fcn.inc: Common block include file.
    - powspec.f: Program that computes the Fourier transform of the acceleration times series (i.e. it computes the radiation spectrum.
    - triwev.f: Program that calculates the energy eigenvalues of the (undriven) triangle well.
    - Makefile for running these programs on charon.
  - Postscript Plots
    - Spectrum for field strength of 0.01. This spectrum uses a static field strength of 0.4, a driving frequency of 2.52, a 12-cycle turn-on time, a acceleration times series that's 256 cycles long, and 400 basis states.
    - Spectrum for field strength of 0.1. Otherwise the same as above.
    - Spectrum for field strength of 0.2. Otherwise the same.
    - Spectrum showing the cutoff of the harmonics for field strength of 0.2 and all other parameters as above, except the integration times was only 128 cycles.
    - Spectrum for field strength of 0.3. All else is the same.
    - Spectrum for field strength of 0.5. This spectrum also uses in instant turn-on of the field. Note the shifted harmonics that result because the system goes into a combination of several Floquet states. Other parameters are the same as above.
    - Spectrum for field strength of 0.5 and driving frequency of 0.6. This is in the delocalized regime (see below) and required the use of 800 basis states. As a result, the program ran rather poorly. Do not trust this data!
    - Plot of the variance of the wavefunction vs. time. This plot uses the same parameters as the spectrum with 0.5 field and 2.52 frequency. In fact it was generated by the same run of accel as that spectrum. Notice that the variance plateaus after a while. That's "dynamic Anderson localization"!
    - Plot of the variance of the wavefunction in the delocalized regime. Uses same parameters as delocalized spectrum above. Again, do not trust this data!
- Quasienergy Spectrum
  - Work still in progress but semiclassical quasienergy spectra have been produced for the driven harmonic oscillator
  - Fortran Source Code for Driven Harmonic Oscillator
    - orbitnt.f: Main program for finding periodic orbits, calculating residues, and calculating actions.
    - fcn.f: Subroutine defining equations of motion.
    - fcn.inc: Common block include file.
    - Makefile for running orbitnt on einstein.
    - ho60.res: Output of orbitnt for first 60 repetitions of the periodic orbit.
    - ho60.er: Error file showing Newton iterations for finding periodic orbits with orbitnt.
    - dhonqp.f: Program that generates a plot of the quasienergy density of states using output from orbitnt.
    - dhoqp.f: Program that generates a plot of the quasienergy density of states using analytical formulae.
    - diffp.f: Program that generates a plot of the difference between the outputs of dhonqp and dhoqp.
  - Postscript Plots for Driven Harmonic Oscillator
    - A plot of the only periodic orbit whose period is an integer multiple of the driving period. This plot uses an oscillator frequency of 4 and a driving frequency of 4*PI. If the frequencies were commensurate then there would be a value of N for which the entire phase space is periodic with period N times the driving period. By keeping the frequencies incommensurate we limit the system to only a single periodic orbit and its repetitions.
    - A plot of the quasienergy density of states. This plot shows both numerical and analytical results. Pretty good agreement, eh?
    - Well, don't get cocky. Here's a plot of the error in the numerical result. It seems to run at about 1% of the correct value. Most of this error comes from the error in numerically approximating the residue of the N=22 and N=44 orbits. These orbits are near resonance (because the frequency ratio is PI which is almost equal to 22/7), and thus have the most influence on the density of states.
Final Project
- Project Outline (Latex source file)
- Presentation Transparencies (Latex source file)
- Final paper (Latex source file)
Acknowledgements
- I would like to thank the instructor of this course, Matt Choptuik, and my research adviser, Linda Reichl for their help and advice on this project.