# Quantum chaos and electron transport properties in a quantum waveguide

dc.contributor.advisor | Reichl, L. E. | en |

dc.creator | Lee, Hoshik, 1975- | en |

dc.date.accessioned | 2008-08-29T00:18:55Z | en |

dc.date.accessioned | 2017-05-11T22:19:27Z | |

dc.date.available | 2008-08-29T00:18:55Z | en |

dc.date.available | 2017-05-11T22:19:27Z | |

dc.date.issued | 2008-05 | en |

dc.description | text | en |

dc.description.abstract | We numerically investigate electron transport properties in an electron waveguide which can be constructed in 2DEG of the heterostructure of GaAs and AlGaAs. We apply R-matrix theory to solve a Schrödinger equation and construct a S-matrix, and we then calculate conductance of an electron waveguide. We study single impurity scattering in a waveguide. A [delta]-function model as a single impurity is very attractive, but it has been known that [delta]-function potential does not give a convergent result in two or higher space dimensions. However, we find that it can be used as a single impurity in a waveguide with the truncation of the number of modes. We also compute conductance for a finite size impurity by using R-matrix theory. We propose an appropriate criteria for determining the cut-off mode for a [delta]-function impurity that reproduces the conductance of a waveguide when a finite impurity presents. We find quantum scattering echoes in a ripple waveguide. A ripple waveguide (or cavity) is widely used for quantum chaos studies because it is easy to control a particle's dynamics. Moreover we can obtain an exact expression of Hamiltonian matrix with for the waveguide using a simple coordinate transformation. Having an exact Hamiltonian matrix reduces computation time significantly. It saves a lot of computational needs. We identify three families of resonance which correspond to three different classical phase space structures. Quasi bound states of one of those resonances reside on a hetero-clinic tangle formed by unstable manifolds and stable manifolds in the phase space of a corresponding classical system. Resonances due to these states appear in the conductance in a nearly periodic manner as a function of energy. Period from energy frequency gives a good agreement with a prediction of the classical theory. We also demonstrate wavepacket dynamics in a ripple waveguide. We find quantum echoes in the transmitted probability of a wavepacket. The period of echoes also agrees with the classical predictions. We also compute the electron transmission probability through a multi-ripple electron waveguide. We find an effect analogous to the Dicke effect in the multi-ripple electron waveguide. We show that one of the S-matrix poles, that of the super-radiant resonance state, withdraws further from the real axis as each ripple is added. The lifetime of the super-radiant state, for N quantum dots, decreases as [1/N] . This behavior of the lifetime of the super-radiant state is a signature of the Dicke effect. | en |

dc.description.department | Physics | en |

dc.format.medium | electronic | en |

dc.identifier | b70670249 | en |

dc.identifier.oclc | 243863152 | en |

dc.identifier.uri | http://hdl.handle.net/2152/3914 | en |

dc.language.iso | eng | en |

dc.rights | Copyright is held by the author. Presentation of this material on the Libraries' web site by University Libraries, The University of Texas at Austin was made possible under a limited license grant from the author who has retained all copyrights in the works. | en |

dc.subject.lcsh | Scattering (Physics)--Mathematical models | en |

dc.subject.lcsh | Electron transport--Mathematical models | en |

dc.subject.lcsh | Wave guides | en |

dc.subject.lcsh | Quantum chaos | en |

dc.subject.lcsh | Matrix mechanics | en |

dc.title | Quantum chaos and electron transport properties in a quantum waveguide | en |

dc.type.genre | Thesis | en |