Quantum chaos
The term quantum chaos describes an interdisciplinary field of physics . Analogous to the area of classical mechanics , where deterministic chaos can occur for certain systems , e.g. B. for the Navier-Stokes equations , which are important for weather forecasting and climate prognoses (see butterfly effect ), there are also systems in quantum mechanics with chaotic behavior, namely in the following areas:
- Nuclear physics
- Atomic physics
- Molecular physics
- Solid state physics
- optics
- Microwaves and
- Acoustics .
The correspondence principle describes the transition from the quantum mechanical view to the classical borderline case, the area between classical and quantum mechanical systems is called semiclassical .
The chaotic behavior of quantum systems is z. B. determined by analyzing the spectral distribution function , which differs from deterministic quantum systems. In chaotic quantum systems, e.g. B. Fixed level repulsion or increased probabilities of stay where the classic system only has unstable trajectories . Another possibility is the temporal development of the quantum system and its reaction to external influences (forces) with irregular amplitude distributions.
For example, the Hamilton operator with stochastic (random) potential has critical wave functions as a solution and a Cantor distribution as a spectrum with the Lebesgue measure zero. In practice, these quantum systems show strong fluctuations on the mesoscopic level.
As an alternative name for quantum chaos, Sir Michael Berry suggested "quantum chaology". Significant methods used to study quantum chaos are Oriol Bohigas' random matrix theory and Martin Gutzwiller's periodic orbit theory .
See also
literature
- A. Einstein (1917): On the quantum theorem by Sommerfeld and Epstein. In: Negotiations of the German Physical Society. 19: 82-92. Reprinted in The Collected Papers of Albert Einstein, A. Engel translator, (1997) Princeton University Press, Princeton. 6 p.434. (Provides an elegant reformulation of the Bohr-Sommerfeld quantization conditions, as well as an important insight into the quantization of non-integrable (chaotic) dynamical systems.)
- Martin C. Gutzwiller: Chaos in Classical and Quantum Mechanics. (1990) Springer-Verlag, New York ISBN = 0-387-97173-4.