Dokument

Summary:
In this thesis three possibilities of external influences in wave mechanical systems are analyzed. In all three cases I used microwave devices to study quantum mechanical systems. The first analyzed property is the decay rate from states in so-called regular islands in a billiard system to the chaotic sea. Afterwards I characterize the influence of open decay channels in transport through chaotic wave systems. The last topic is the introduction of a time-dependently changed microwave device. In the first chapter the decay of a wave function from one classically isolated phase space region to another is analyzed. The main interest lies on the influence of additional states corresponding to the same original phase space region. I will show that these states can lead to an enhancement of the decay rate. The decay rates are measured via an indirect absorption process, leading to an increase of the corresponding resonance widths. Alternatively to mode depending width properties, which were typically analyzed in numerical calculations, a parameter depending variation of the system is introduced to verify the demanded effect. The experimental and numerical determination of channel correlations are the subject of the second chapter. After defining the correlation function, an experimental demonstration is presented. The results of the experiment and the describing numerics show that the correlation functions are important for the characterization of universal conductance fluctuations. The last chapter deals with the realization of a periodically driven microwave system. The principal setup is a resonant circuit with a time-dependent capacity. The properties of the setup, e.g. sideband structures for different driving signals, are analyzed experimentally, theoretically and numerically. This is the first step to create a system where a huge subset of resonances is changed. The fulfilled description of the single resonance system is presented and the next steps to realizations of time-dependent driven wave mechanical systems are sketched.

Bibliographie / References

1. T. Kottos and U. Smilansky. Quantum chaos on graphs. Phys. Rev. Lett., 79:4794, 1997.
2. U. Kuhl, R. Höhmann, J. Main, and H.-J. Stöckmann. Resonance widths in open microwave cavities studied by harmonic inversion. Phys. Rev. Lett., 100:254101, 2008.
3. G. L. Celardo, F. M. Izrailev, S. Sorathia, V.G. Zelevinsky, and G. P. Berman. Continuum shell model: From Ericson to conductance fluctuations. In P. Dnielewicz, P. Peicuch, and V. Zelevinsky, editors, Semi-Classical Approxi- mation in Quantum Mechanics. In: Mathematical Physics and Applied Mathematics 7, Contemporary Mathematics 5. Dordrecht etc., volume 995 of AIP Conference Proceedings, page 75. Springer, East Lansing, Michigan, 2008.
4. A. Bäcker, R. Ketzmerick, S. Löck, M. Robnik, G. Vidmar, R. Höhmann, U. Kuhl, and H.-J. Stöckmann. Dynamical tunneling in mushroom billiards. Phys. Rev. Lett., 100:174103, 2008.
5. T. Tudorovskiy, R. Höhmann, U. Kuhl, and H.-J. Stöckmann. On the theory of cavities with point-like perturbations. Part I: General theory. J. Phys. A, 41:275101, 2008.
6. Steffen Löck, Arnd Bäcker, Roland Ketzmerick, and Peter Schlagheck. Regular-to-chaotic tunneling rates: From the quantum to the semiclassical regime. Phys. Rev. Lett., 104:114101, 2010.
7. T. Tudorovskiy, U. Kuhl, and H.-J. Stöckmann. Singular statistics revised. New J. of Physics, 12:123021, 2010.
8. Stöckmann. Probing decoherence through Fano resonances. Phys. Rev. Lett., 105:056801, 2010.
9. B. Köber, U. Kuhl, H.-J. Stöckmann, T. Gorin, D. V. Savin, and T. H. Selig- man. Microwave fidelity studies by varying antenna coupling. Phys. Rev. E, 82:036207, 2010.
10. Arnd Bäcker, Roland Ketzmerick, and Steffen Löck. Direct regular-to-chaotic tunneling rates using the fictitious-integrable-system approach. Physical Re- view E, 82(5):056208, 2010.
11. O. Hul, M. Ławniczak, S. Bauch, A. Sawicki, M. Ku´Ku´s, and L. Sirko. Are scatter- ing properties of graphs uniquely connected to their shapes? Phys. Rev. Lett., 109:040402, 2012.
12. A. Potzuweit, T. Weich, S. Barkhofen, U. Kuhl, H.-J. Stöckmann, and M. Zworski. Weyl asymptotics: From closed to open systems. Phys. Rev. E, 86:066205, 2012.
13. S. Gehler, T. Tudorovskiy, C. Schindler, U. Kuhl, and H.-J. Stöckmann. Mi- crowave realisation of a periodically driven system, 2013. arXiv:1302.1289, accepted at New J. of Physics.
14. Martin J Körber, Matthias Michler, Arnd Bäcker, and Roland Ketzmerick. Hi- erarchical fractal weyl laws for chaotic resonance states in open mixed sys- tems. arXiv preprint arXiv:1304.2662, 2013.
15. Hojeong Kwak, Younghoon Shin, Songky Moon, and Kyungwon An. Obser- vation of resonance-assisted dynamical tunneling in an asymmetric microcav- ity, 2013. arXiv:1305.6019.
16. M. L. Mehta. Random Matrices. 2nd edition. Academic Press, San Diego, 1991. XXIX Bibliography
17. E. Persson, I. Rotter, H.-J. Stöckmann, and M. Barth. Observation of resonance trapping in an open microwave cavity. Phys. Rev. Lett., 85:2478, 2000.
18. T. Gorin and T. H. Seligman. Signatures of the correlation hole in total and partial cross sections. Phys. Rev. E, 65:026214, 2002.
19. J. Barthélemy, O. Legrand, and F. Mortessagne. Complete S-matrix in a mi- crowave cavity at room temperature. Phys. Rev. E, 71:016205, 2005.
20. U. Kuhl, H.-J. Stöckmann, and R. Weaver. Classical wave experiments on chaotic scattering. J. Phys. A, 38:10433, 2005.
21. G. L. Celardo, F. M. Izrailev, V. G. Zelevinsky, and G. P. Berman. Open sys- tem of interacting fermions: Statistical properties of cross sections and fluctu- ations. Phys. Rev. E, 76:031119, 2007.
22. Olivier Brodier, Peter Schlagheck, and Denis Ullmo. Resonance-assisted tun- neling in near-integrable systems. Phys. Rev. Lett., 87:064101, 2001.
23. A. Bäcker and R. Schubert. Amplitude distribution of eigenfunctions in mixed systems. J. Phys. A, 35:527, 2002.
24. A. Bäcker and R. Schubert. Autocorrelation function of eigenstates in chaotic and mixed systems. J. Phys. A, 35:539, 2002.
25. O. Brodier, P. Schlagheck, and D. Ullmo. Resonance-assisted tunneling. Ann. Phys., 300:88, 2002.
26. T. Kottos and U. Smilansky. Quantum graphs: a simple model for chaotic scattering. J. Phys. A, 36:3501, 2003.
27. W. T. Lu, S. Sridhar, and M. Zworski. Fractal Weyl laws for chaotic open systems. Phys. Rev. Lett., 91:154101, 2003.
28. R. Schäfer, T. Gorin, T. H. Seligman, and H.-J. Stöckmann. Correlation func- tions of scattering matrix elements in microwave cavities with strong absorp- tion. J. Phys. A, 36:3289, 2003.
29. O. Hul, S. Bauch, P. Pakoñski, N. Savytskyy, K. ˙ Zyczkowski, and L. Sirko. Experimental simulation of quantum graphs by microwave networks. Phys.
30. Christopher Eltschka and Peter Schlagheck. Resonance-and chaos-assisted tunneling in mixed regular-chaotic systems. Phys. Rev. Lett., 94(1):014101, 2005.
31. R. Schäfer, H.-J. Stöckmann, T. Gorin, and T. H. Seligman. Experimental verifi- cation of fidelity decay: From perturbative to Fermi golden rule regime. Phys. Rev. Lett., 95:184102, 2005.
32. John David Jackson. Classical electrodynamics. 1998.
33. W. H. Zurek. Decoherence, einselection, and the quantum origins of the clas- sical. Rev. Mod. Phys., 75:715, 2003.
34. F. Haake. Quantum Signatures of Chaos. 2nd edition. Springer, Berlin, 2001.
35. T. Ericson. A theory of fluctuations in nuclear cross sections. Ann. Phys. (N.Y.), 23:390, 1963.
36. T. Ericson and T. Mayer-Kuckuk. Fluctuations in nuclear reactions. Ann. Rev. Nucl. Sci., 16:183, 1966.
37. H. G. Schuster. Deterministic Chaos: An Introduction. Physik Verlag, Weinheim, 1984.
38. Torleif Ericson. Fluctuations of nuclear cross sections in the "continuum" re- gion. Phys. Rev. Lett., 5:430–431, 1960.
39. H. Alt, H.-D. Gräf, H. L. Harney, R. Hofferbert, H. Lengeler, A. Richter, P. Schardt, and H. A. Weidenmüller. Gaussian orthogonal ensemble statis- tics in a microwave stadium billiard with chaotic dynamics: Porter-Thomas distribution and algebraic decay of time correlations. Phys. Rev. Lett., 74:62, 1995.
40. U. Fano. Effects of configuration interaction on intensities and phase shifts. Phys. Rev., 124:1866, 1961.
41. I. C. Percival. Regular and irregular spectra. J. Phys. B, 6:229, 1973.
42. D. Dubbers and H.-J. Stöckmann. Quantum Physics: The Bottom-Up Approach. Springer, Berlin Heidelberg, 2013.
43. U. Fano. Sullo spettro di assorbimento dei gas nobili presso il limite dello spettro d'arco. Nuov. Cim., 12:154, 1935.
44. XXX Bibliography [21] P. M. Koch. Microwave " ionization " of excited hydrogen atoms: How non- classical local stability brought about by scarred matrix states is affected by broadband noise and by varying the pulse envelope. Physica D, 83:178, 1995.
45. D Agassi, H.A Weidenmüller, and G Mantzouranis. The statistical theory of nuclear reactions for strongly overlapping resonances as a theory of transport phenomena. Physics Reports, 22(3):145 – 179, 1975.
46. J. J. M. Verbaarschot, H. A. Weidenmüller, and M. R. Zirnbauer. Grassmann in- tegration in stochastic quantum physics: The case of compound-nucleus scat- tering. Phys. Rep., 129:367, 1985.
47. B. Eckhardt. Quantum mechanics of classically non-integrable systems. Phys. Rep., 163:205, 1988.
48. N. Lehmann, D. Saher, V. V. Sokolov, and H.-J. Sommers. Chaotic scatter- ing: the supersymmetry method for large number of channels. Nucl. Phys. A, 582:223, 1995.
49. D. L. Shepelyansky. Localization of diffusive excitation in multi-level systems. Physica D, 28:103, 1987.
50. M. V. Berry. Regular and irregular semiclassical wavefunctions. J. Phys. A, 10:2083, 1977.
51. James D. Hanson, Edward Ott, and Thomas M. Antonsen. Influence of finite wavelength on the quantum kicked rotator in the semiclassical regime. Phys. Rev. A, 29:819–825, 1984.
52. Paul S. Linsay. Period doubling and chaotic behavior in a driven anharmonic oscillator. Phys. Rev. Lett., 47:1349–1352, 1981.
53. F. L. Moore, J. C. Robinson, C. F. Bharucha, P. E. Williams, and M. G. Raizen. Observation of dynamical localization in atomic momentum transfer: A new testing ground for quantum chaos. Phys. Rev. Lett., 73:2974, 1994.
54. J. Stein, H.-J. Stöckmann, and U. Stoffregen. Microwave studies of billiard Green functions and propagators. Phys. Rev. Lett., 75:53, 1995.
55. U. Kuhl, M. Martínez-Mares, R. A. Méndez-Sánchez, and H.-J. Stöckmann. Direct processes in chaotic microwave cavities in the presence of absorption. Phys. Rev. Lett., 94:144101, 2005.
56. O. Bohigas, M. J. Giannoni, and C. Schmit. Characterization of chaotic spectra and universality of level fluctuation laws. Phys. Rev. Lett., 52:1, 1984.
57. M. Kopp and H. Schomerus. Fractal Weyl laws for quantum decay in dynam- ical systems with a mixed phase space. Phys. Rev. E, 81:026208, 2010.
58. Steven Tomsovic, Maurice Grinberg, and Denis Ullmo. Semiclassical trace formulas of near-integrable systems: resonances. Phys. Rev. Lett., 75(24):4346– 4349, 1995.
59. H.-J. Stöckmann and P. Šeba. The joint energy distribution function for the Hamiltonian H = H 0 − iWW † for the one-channel case. J. Phys. A, 31:3439, 1998. XXXII Bibliography
60. I. Rotter. A non-Hermitian Hamilton operator and the physics of open quan- tum systems. J. Phys. A, 42:153001, 2009. XXXIII Bibliography [61] C. H. Lewenkopf and H. A. Weidenmüller. Stochastic versus semiclassical approach to quantum chaotic scattering. Ann. Phys. (N.Y.), 212:53, 1991.
61. S. Fishman, D. R. Grempel, and R. E. Prange. Chaos, quantum recurrences and Anderson localization. Phys. Rev. Lett., 49:509, 1982.
62. G. Binnig, H. Rohrer, Ch. Gerber, and E. Weibel. Surface studies by scanning tunneling microscopy. Phys. Rev. Lett., 49:57–61, 1982.
63. H.-J. Stöckmann and J. Stein. " Quantum " chaos in billiards studied by mi- crowave absorption. Phys. Rev. Lett., 64:2215, 1990.
64. G. Casati, B. V. Chirikov, F. M. Izrailev, and J. Ford. Stochastic behavior of a quantum pendulum under a periodic perturbation. In G. Casati and J. Ford, editors, Stochastic Behaviour in Classical and Quantum Hamiltonian Sys- tems, Volta mem. Conf. , Como 1977, Lect. Notes Phys. 93, page 334, Berlin, 1979. Springer.
65. R. Blümel and U. Smilansky. A simple model for chaotic scattering. II. Quan- tum mechanical theory. Physica D, 36:111, 1989. XXXIV Bibliography [75] E. Doron, U. Smilansky, and A. Frenkel. Experimental demonstration of chaotic scattering of microwaves. Phys. Rev. Lett., 65:3072, 1990.
66. Stefan Gehler, Bernd Köber, and Ulrich Kuhl. Channel correlation in transport through chaotic wave mechanical system. to be published, 2013.
67. H. G. Schuster. Deterministisches Chaos. VCH Verlagsgesellschaft, Weinheim, 1994. XXXV Bibliography [87] Thomas Klinker, Werner Meyer-Ilse, and Werner Lauterborn. Period doubling and chaotic behavior in a driven toda oscillator. Physics Letters A, 101:371–375, 1984.
68. R. A. Méndez-Sánchez, U. Kuhl, M. Barth, C. H. Lewenkopf, and H.-J. Stöck- mann. Distribution of reflection eigenvalues in absorbing chaotic microwave cavities. Phys. Rev. Lett., 91:174102, 2003.
69. Raizen. Dynamical localization of ultracold sodium atoms. Phys. Rev. E, 60:3881, 1999.
70. Stefan Gehler, Ulrich Kuhl, Hans-Jürgen Stöckmann, Steffen Löck, Arnd Bäcker, and Roland Ketzmerick. Experimental realization of resonance assited tunneling. to be published, 2013.
71. U. Kuhl. Microwave scattering on complex systems, 2008. Habilitationsschrift, Philipps-Universität Marburg.
72. M. Allgaier. Microwave studies on quantum graphs, 2012. Bachelor Thesis, Philipps-Universität Marburg.
73. Bruno K. Meyer. native copper oxide on copper. private communication, 2013.
74. Denis Ullmo, Maurice Grinberg, and Steven Tomsovic. Near-integrable sys- tems: Resonances and semiclassical trace formulas. Phys. Rev. E, 54:136–152, 1996.
75. H.-J. Stöckmann. Quantum Chaos -An Introduction. University Press, Cam- bridge, 1999.
76. D. Waltner and U. Smilansky. Quantum graphs with time dependent bond lengths, 2013. Talk on DPG spring session DY 26.7, DPG Verhandlungen.
77. L. D. Landau and E. M. Lifshitz. Quantum Mechanics: (Nonrelativistic Theory).
78. A. Messiah. Quantum Mechanics, Volume I. North-Holland, Amsterdam, 1961.
79. V. P. Maslov and N. V. Fedoriuk. Semi-Classical Approximation in Quantum Me- chanics. Reidel, Dordrecht, 1981.
80. C. Mahaux and H. A. Weidenmüller. Shell-Model Approach to Nuclear Reactions. North-Holland, Amsterdam, 1969.
81. H. P. Baltes and E. R. Hilf. Spectra of Finite Systems. BI-Wissenschaftsverlag, Mannheim, 1976.
82. T. Tudorovskiy, S. Gehler, U. Kuhl, and H.-J. Stöckmann. Time-dependent point-like perturbations. to be published, 2013.
83. P. A. Lee and A. Douglas Stone. Universal conductance fluctuations in metals. Phys. Rev. Lett., 55:1622–1625, 1985.
84. L. Bittrich. Flooding of Regular Phase Space Islands by Chaotic States. PhD thesis, Technische Universität Dresden, 2010. XXXI Bibliography
85. P. A. Lee and T. V. Ramakrishnan. Disordered electronic systems. Rev. Mod. Phys., 57:287, 1985.
86. M. J. Davis and E. J. Heller. Quantum dynamical tunneling in bound states. J. Chem. Phys., 75:246, 1981.
87. C. Dembowski, H.-D. Gräf, A. Heine, T. Hesse, H. Rehfeld, and A. Richter. First experimental test of a trace formula for billiard systems showing mixed dynamics. Phys. Rev. Lett., 86:3284, 2001.

Das Dokument ist im Internet frei zugänglich - Hinweise zu den Nutzungsrechten