Dissertation > Excellent graduate degree dissertation topics show

Spectra Analysis of Circular Billiards Systems

Author: ZhangLiQin
Tutor: ZhangYanHui
School: Shandong Normal University
Course: Atomic and Molecular Physics
Keywords: Periodic orbits theory( Closde-orbits theory) circular billiard system Fourier-transformed spectra quantum spectra function correspondence between quantum and classical
CLC: O561
Type: Master's thesis
Year: 2006
Downloads: 36
Quote: 0
Read: Download Dissertation

Abstract


Since the development of periodic orbit theory for chaotic systems by Gutzwiller, ithas become an important tool of the study of the connections between the quantizedenergy eigenvalues of a bound state and the classical motions for the correspondingpoint particle The study of integrabel and chaotic interface is continue between classicalmechanics and quantum mechanics.The semi-classical method has become a necessaryinstrument to study the classical movement of the particle.For the correspondingconnection of the systems between quantum-classical description,the theory has given adeeper explanation.In recently years the study of “artificial atoms”(quantum well) and nanodevices hasbeen of great interest in the relatively new field. The study of microjunctions and theirtransport behaviors have become an important field.The models have becomeincreasingly interesting and important and will development very well in theory andexperiment during to study the dynamic character and especially quantum chaos.In the early quantum mechanics, the quantized method ofWKB( Wentzel-Kramers-Brillouin) and EBK(Einstein-Brillouin-Keller) presented bysemi-classical technology are apply respective in one-dimension and n-dimensions. Butsemi-classical quantized methods are applicable in integrabel system.Gutzeiller startedfrom the exact expression of trace of Green function insteads of its quantized form, andgained the stated density of semi-classical system. Which made the semi-classical formof Gutzwiller were perfectly applied in complete chaos systems. In quantum mechanicsthere are kinds of semi-classical calculational means. Which may help us to understandthe interface between classical and quantum.We use a recently quantum spectral function popularized it from closed-orbittheory to the opened-orbit theory. The quantum spectra function contain richinformation of all classical orbits connecting two arbitrary points in well. We study thecorrespondence between quantum spectra and classical orbits in the circular.Two-dimensional billiard systems have provided easily visualization examples relevantfor both types of analyses. As a simple example of the application to a billiard or infinitewell system of Periodic orbit theory we compute the Fourier transform( ρ ( L)) of thequantum mechanical energy level density of two-dimensional circular billiard systems.The resulting peaks in plots of ( )ρ L2 versus L are compared to the lengths of theclassical trajectoried in these geometries. The locations of peaks in ρ ( L) agree withthe lengths of classical orbits perfectly,which testifies the correspondence of quantummechanics and classical mechanics.Furthermore, the connections between the energyeigenvalues spectrum of two-dimensional billiard systems and the classical dynamics ofparticle an be explored through the time-dependence of wave packet solutions of theSchrodinger equation. In the thesis, we study the correspondence between quantumspectra and classical orbits in the circular billiard, 1/2 circular and 1/4 circular billiardsby applying the analytic and numerical method. We find that the peak positions in theFourier-transformed quantum spectra match accurately with the lengths of the classical.This thesis id divided into four chapters. The first chapter is summarization,whichbriefly introduces the development of semiclassical Period orbit theory(Closed orbittheory) and quantum packet wave revival theory. In the second chapter we introducedthe periods orbits theory which applied in the infinite-circular well. In the third chapter,we study the correspondence between quantum spectra and classical orbits in thecircular billiard, 1/2 circular and 1/4 circular billiards by applying the analytic andnumerical method. The locations of peaks in ρ ( L) agree with the lengths of classicalorbits perfectly. In which the orbits theory air open fashion. In the last chapter, Weextend the Closed orbits theory to teo-dimensional ciucular billiard. The energyeigenvalues and wavefunctions of the system have been derived in a variety of differentcontext by different groups.We calculate the Fourier transform of the quantum spectraand examine the connections between the length of the classical path and the locationsof the quantum spectral peaks.In addition, in a numerical evaluations one must use afinite number of wave numbers to limit the energy region, witch brings into a resolutionproblem. These examples show evidently that semi-classical methods provides a bridgebetween quantum and classical mechanics.

Related Dissertations

  1. Quantum Transport and Spectral Analysis of Two-dimensional Annular Billiard System,O413.1
  2. Investigation of Self-Assembly of Xanthan Gum with Atomic Force Microscopy,O561
  3. Theoretical Studies on I-V Properties of Organic Molecular Junctions,O561
  4. Study of the Ground-state Geometric Structures of Bimetallic Clusters Fe-Ni with A Genetic Algorithm,O561
  5. Study on the Melting Behavior of Silver Halides Clusters by Molecular Dynamics Simulation,O561
  6. The Influence of Molecular Ground State Wave Function on High-order Harmonic Generation from N2 Molecules in Intense Laser Fields,O561.4
  7. Competition between Two Excitation-dissociation Channels for Molecular Ions and Experimental Study on Collision Frequencies of Electrons Produced by Laser with Molecules,O561.4
  8. Influence of Basis Sets on the Energy-level Calculations of Fullerene Molecules,O561
  9. Study of Asymmetric Frequency Shift of the Fermi Resonance in the Raman Spectra,O561.3
  10. Ab Initio Intermolecular Potential of Hydrogen Sulfide and the Properties of Liquid and Solid: A Monte Carlo Study,O561.4
  11. Theoretical Calculation of Photodissociation of C2F5I,O561.4
  12. The Structure of Hydrogenated Fullerenes under High Pressure and the Fullerenes Doped with Alkali Metals,O561
  13. 1 - fluoro - naphthalene clusters of resonant two -photon ionization and ab initio,O561.3
  14. 1 - naphthol monochromatic two-photon ionization mass spectrometry study,O561.3
  15. BiH (D, T), GaH (D, T) molecular structure and potential function,O561.1
  16. SH , OH and ArH ~ ground state potential energy function,O561.1
  17. Time-dependent Wavepacket Approach to the Influnce of Laser Fields on the Resonance Enhanced Multi-photon Ionization of C1O Radical,O561
  18. QM/MM Study for the Function of Crystal Water in the Binding between HIV-1 Protease and Ligand,O561
  19. The Structures and Electronic Properties of Endohedral Metallofullerenes: A Theoretical Investigation,O561
  20. Nitrobenzene and 2 - nitro- toluene multiphoton dissociation mass spectrometry study,O561
  21. O - bromotoluene and bromotoluene multiphoton ionization mass spectrometry,O561.3
  22. Compute Protein Charge by ABEEMσπ Model and Parallelized Implementation of the ABEEMσπ Method,O561

CLC: > Mathematical sciences and chemical > Physics > Molecular physics, atomic physics > Molecular Physics
© 2012 www.DissertationTopic.Net  Mobile