By Vladimir M. Akulin

This publication gathers jointly a number of related difficulties that may be encountered in numerous fields of contemporary quantum physics and that experience universal gains in regards to multilevel quantum platforms. the most motivation was once to envision from a uniform viewpoint a number of types and techniques which were constructed in atomic, molecular, condensed subject, chemical, laser and nuclear physics in numerous contexts. The publication might help senior-level undergraduate, graduate scholars and researchers placing specific difficulties in those fields right into a broader medical context and thereby making the most of well-established thoughts utilized in adjoining fields.

This moment variation has been multiplied to incorporate monstrous new fabric (e.g. new sections on Dynamic Localization and on Euclidean Random Matrices and new chapters on Entanglement, Open Quantum platforms, and Coherence Protection). it truly is in response to the author’s lectures on the Moscow Institute of Physics and know-how, on the CNRS objectiveé Cotton Laboratory, and on different classes he has given over the past decades.

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M. Lifshits [146] as well as Quantum mechanics by C. CohenTanoudji, B. Diu, and F. Laloe [58]. The main mathematical tools can be found in the textbook by J. Mathews and R. L. Walker [160] Mathematical methods of physics. For more special aspects of the mathematical technique including algebra and group theory, the books Mathematical methods of classical mechanics by V. I. Arnold, A. Weinstein, and K. Vogtmann [10], Theory of group representations and applications by A. Barut and R. Raczka [14], Integrable systems of classical mechanics and Lie algebras by A.

Thus the sequence of scattering events is a kind of random process which has a direct analogy to the quantum Sinai billiard. 33) k ,n for the amplitudes ψk,n of these states. 18) of k ,n multiphoton transitions from the ground state |0 . The matrix elements Vk,n allow for the probability amplitudes of scattering from the state |k |n to the state |k |n . We note one interesting peculiarity of this process. The Kepler period may change considerably with the change in the energy of the Rydberg electron: the closer the energy to the ionization limit, the longer the period.

33) by the phase factor exp[−i(Ek + En )T (n )], where T (k ) is the Kepler period corresponding to the energy Ek . This phase factor changes drastically from one state to another, and it makes the matrix elements of the neighboring states very different in phase and thereby justifies the use of the random matrix model for this process. We also note one important application of this process: by measuring the yield of zero kinetic energy electrons as a function of the laser frequency one obtains the high-resolution rotational and vibrational spectra of molecular ions.