Projects / Programmes
Quantum localization in chaotic systems
| Code |
Science |
Field |
Subfield |
| 1.02.00 |
Natural sciences and mathematics |
Physics |
|
| Code |
Science |
Field |
| P190 |
Natural sciences and mathematics |
Mathematical and general theoretical physics, classical mechanics, quantum mechanics, relativity, gravitation, statistical physics, thermodynamics |
| Code |
Science |
Field |
| 1.03 |
Natural Sciences |
Physical sciences |
nonlinear dynamics, classical and quantum chaos, Hamilton (mixed type) systems, quantum localization, applications in mesoscopic and nano systems
Researchers (9)
Organisations (2)
Abstract
The project is in the domain of quantum or wave chaos. Quantum or dynamical localization is one of the key phenomena in quantum classically chaotic systems, opposite to the other important phenomenon, namely the quantum resonance. Quantum dynamics in the classically chaotic systems follows the classical diffusion up to the Heisenberg time, when the evolution operator does not yet detect its own spectral discreteness, while for longer times the discreteness of the spectrum becomes manifested, the intereference phenomena occur, which typically are destructive and lead to the stopping of diffusion, thus to the quantum localization. This phenomenon is manifested also in the structure of the eigenstates of both time-independent systems as well as in the time-periodic (Floquet) systems. The central theme of our research will be the detailed analysis of the localization, not only the average value of the localization measures, but also their distributions. Furthermore we shall perform a detailed study of the relationship between the localization of the eigenstates and the spectral statistics (of the energy or quasi-energy). For example, we shall study the relationship between the degree of localization and the Brody parameter beta. Important model systems are such as the s.c. Robnik billiard, the epsilon-stadium of Bunimovich, and the hydrogen atom in strong magnetif field, as the time-independent systems, and the quantum kicked rotator as the time-periodic (Floquet) system, and in addition also other nonlinear one-dimensional Floquet systems, like e.g. the periodically driven quartic oscillator. In the latter case we have chaos in the classical phase space, chaotic diffusion, the energy of the particle can increase unbounded (Fermi acceleration), and we are interested in the conditions for the occurence of both the quantum resonance and the quantum localization. We shall investigate also the time-evolution of quantm states in the classically chaotic regime, and shall verify how it is quantitatively dependent on the relation between the classical transport time and the Heisenberg time. We shall propose experiments in the microwave resonators, which could be implemented in the group of Prof. Hans-Juergen Stoeckmann at the University of Marburg, Germany, and in the laboratory of Prof. Ulrich Kuhl at the University of Nice, France. In the end we shall also study the higher-dimensional paradigmatic systems, like e.g. Prosen billiards (1998). The quantum localization of chaotic states leads also to the generalization of the Berry-Robnik theory of the spectral statistics in the mixed-type systems.
The results will be published in well established international scientific journals, and presented at numerous international conferences, including those regularly organized by Prof. Robnik at CAMTP, which are also world-top, like e.g. "Let's Face Chaos through Nonlinear Dynamics" and other symposia (Japan-Slovenia Seminars, Christmas Symposia, European Advanced Studies Conferences, etc.). Problems in the classically chaotic quantum systems, thus also in the systems of the mixed type, are very complex, at the same time extremely important, as all generic Hamiltonian systems are precisely of the mixed type. Understanding the detailed quantum localization mechanisms of chaotic eigenstates is of extreme importance. Our results will contribute to the new knowledge on the theoretical, experimental and applied side (atomic, molecular and mesoscopic and nano systems, and classical wave systems, electromagnetic, acoustic, elastic, etc.).
Significance for science
We presume, that our results, on the world top level, like up to now, will fundamentally contribute to the advances and knowledge in this field of theoretical physics, namely in the nonlinear dynamics of classical and quantum Hamilton systems, especially in the mixed type regime. The results will be published in reputed international scientific journals, and presented at numerous international conferences, including those regularly organized by CAMTP, which are also world-top, like e.g. "Let's Face Chaos through Nonlinear Dynamics" and other symposia (Japan-Slovenia Seminars, Christmas Symposia, European Advanced Studies Conferences, etc.). Problems in the chaotic systems, which includes the mixed-type systems, are very complex, at the same time extremely important, as all generic Hamiltonian systems are precisely of the mixed type. Understaning the detailed quantum localization mechanisms of chaotic eigenstates is of extreme importance. Our results will contribute to the new knowledge on the theoretical, experimental and applied side (atomic, molecular and mesoscopic and nano systems, and classical wave systems, electromagnetic, acoustic, elastic, etc.).
Significance for the country
We presume, that our results, on the world top level, like up to now, will fundamentally contribute to the advances and knowledge in this field of theoretical physics, namely in the nonlinear dynamics of classical and quantum Hamilton systems, especially in the mixed type regime. The results will be published in reputed international scientific journals, and presented at numerous international conferences, including those regularly organized by CAMTP, which are also world-top, like e.g. "Let's Face Chaos through Nonlinear Dynamics" and other symposia (Japan-Slovenia Seminars, Christmas Symposia, European Advanced Studies Conferences, etc.). Problems in the chaotic systems, which includes the mixed-type systems, are very complex, at the same time extremely important, as all generic Hamiltonian systems are precisely of the mixed type. Understaning the detailed quantum localization mechanisms of chaotic eigenstates is of extreme importance. Our results will contribute to the new knowledge on the theoretical, experimental and applied side (atomic, molecular and mesoscopic and nano systems, and classical wave systems, electromagnetic, acoustic, elastic, etc.).
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