Quantum resonant systems, integrable and chaotic
نویسندگان
چکیده
منابع مشابه
Integrable Systems and Quantum Groups
The main purpose of this lecture is to present the study of quantum integrable systems and its interplay with the study of quantum groups. The history of quantum integrable systems begins, following a certain historical path, with the rst attempts of W. Heisenberg to develop a microscopic theory that could explain ferromagnetism [1]. Later on a method was proposed by H. Bethe [2] in order to ob...
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We prove that any spectral sequence obeying a certain growth law is the quantum spectrum of an equivalence class of classically integrable non-linear oscillators. This implies that exceptions to the BerryTabor rule for the distribution of quantum energy gaps of classically integrable systems, are far more numerous than previously believed. In particular we show that for each finite dimension k,...
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A general program to show quantum-classical correspondence for bound conservative integrable and chaotic systems is described. The method is applied to integrable systems and the nature of the approach to the classical limit, the cancellation of essential singularities, is demonstrated. The application to chaotic systems requires an understanding of classical Liouville eigenfunctions and a Liou...
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We present two applications of quantum integrable systems. First, we predict that it is possible to generate high harmonics from solid state devices by demonstrating that the emission spectrum of a minimally coupled laser field of frequency ω to an impurity system of a quantum wire, contains multiples of the incoming frequency. Second, by evaluating expressions for the conductance in the high t...
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We review briefly some ideas and constructions for dKP (from KP) and its Hamiltonian dynamics, discuss its quantization via Moyal back to KP, and treat the KP hierarchy itself as a sequence of quantum Hamiltonian systems based on the dKP dynamics. Some connections to q-theories are also indicated. The constructions are all well known (cf. [6, 8, 11, 12, 13, 14, 15, 16, 17, 18, 19, 23, 24, 29, 3...
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ژورنال
عنوان ژورنال: Journal of Physics A: Mathematical and Theoretical
سال: 2018
ISSN: 1751-8113,1751-8121
DOI: 10.1088/1751-8121/aaf2a1