**Alexander Harvey Barnett
October 2000**

**A thesis presented to the Department of Physics
in partial fulfillment of the requirements
for the degree of
Doctor of Philosophy
in the subject of
Physics
Harvard University
Advisor: Eric J. Heller**

- Frontmatter

- Chapter 1: Introduction and summary
- Structure of this thesis
- Chapters 2,3 and 4: Dissipation rate and deformations of chaotic billiards
- Chapters 5 and 6: Improved billiard quantization methods
- Chapter 7: Quantum point contact conductance and scattering in the half-plane
- Chapter 8: Waveguides for neutral atoms using evanescent light fields

- Chapter 2: Quantum and classical theories of ergodic dissipation
- Review of classical dissipation in a general system
- Review of the linear response theory of quantum dissipation
- Quantum-classical correspondence

- Chapter 3: Dissipation rate in chaotic billiards, and `special' deformations
- The cavity system
- The white noise approximation (WNA)
- `Special' deformations
- The WNA revisited--cavity shape effects

- Chapter 4: Improving upon the white noise approximation: a new `wall formula'

- Chapter 5: Improved sweep methods for billiard quantization
- Introduction and history of quantum eigenproblems
- Definition of the billiard problem
- Representation by a Helmholtz basis
- The choice of norm matrix
- The hunt for local tension minima as a function of
- Conclusion and discussion

- Chapter 6: The scaling method of Vergini and Saraceno
- The basic scaling method
- Higher-order correction and normalization
- Sources of error in the method
- Application: local density of states at finite deformations
- Discussion

- Chapter 7: Conductance of quantum point contacts and half-plane scattering
- Conductance in terms of cross section
- Partial-wave channel modes for a 2-terminal system
- Idealized `slit' aperture point contact
- Point contact coupled to a resonator
- What is the maximum conductance of a single quantum channel?
- Reciprocity and `conductance' of atom waves
- Conclusions

- Chapter 8: Substrate-based atom waveguide using two-color evanescent light fields
- Introduction
- Trap Concept
- Trap properties
- Numerical solution of the light fields
- Further decoherence and loss mechanisms
- Conclusion

- Appendix A: General transformation of the 1D Fokker-Planck equation
- Appendix B:
Numerical evaluation of the classical band profile in billiards
- Trajectories--the issue of exponential divergence
- General system--windowed estimation of correlation spectrum
- Considerations in a billiard system

- Appendix C: Numerical evaluation of quantum band profile in billiards

- Appendix D: How Many Special Deformations Are There?

- Appendix E: Cross correlations I: general-special
- Appendix F: Cross correlations II: normal-general
- Appendix G: Numerical evaluation of wavefunction boundary integrals

- Appendix H:
Boundary evaluation of matrix elements of Helmholtz solutions

- Appendix I: Scaling expansion of eigenfunctions and tension matrix
- Expansion of the dilation operator
- Curvilinear boundary coordinates
- Applying boundary conditions and simplifying
- Tension matrix expansion
- Useful geometric boundary integrals

- Appendix J: Helmholtz basis functions for two-dimensional billiards
- Basis `badness'
- Real plane waves (RPWs)
- Adding evanescent plane waves (EPWs)
- Symmetrization and reduction of effort

- Appendix K: Transmission cross section in the narrow slit limit
- Appendix L: Explicit relation of cross section to Landauer formula
- Bibliography
- About this document ...

Alex Barnett 2001-10-03