By Vladimir M. Akulin
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Extra resources for Coherent Dynamics of Complex Quantum Systems
7) m n ,m now stands for the probability amplitudes of the laser-induced where Vn,m transitions. The nuclear motion of vibrationally excited polyatomic molecules is usually chaotic. This implies that the vibrational wavefunction changes drastically and in an irregular way when we move from a given energy eigenstate to a neighboring one. This is even more the case for the vibrational functions corresponding to diﬀerent electronic terms, which implies that the overlap integrals Φ0m |Φ1m change completely with any change of the indexes m and m .
2 Disordered Solids and Surfaces The description of quantum eﬀects in terms of random matrices is a powerful method to tackle a number of problems in solid state physics and surface science. This approach arises in a natural way if one considers the properties of disordered systems like alloys, glasses, non-ideal metals, or systems with chaotic billiard-like dynamics such as quantum dots.
3. Usually the results of diagonalization are very sensitive to the values of the anharmonicity constants α, β, and γ, and both the eigenvalues EI,m and the eigenstates |mI of the Hamiltonian change drastically with a relatively small change in each of the parameters. 14) I2 ,I3 the expansion coeﬃcients cI,m I2 ,I3 will be complex functions of I1 , I2 , and m that strongly depend on α, β, and γ. Therefore the matrix of dipole transitions among the states |Im 24 2 Examples of Complex Systems |3,m> |3,m'> |3,m''> |3,m'''> |2,m> |2,m'> |2,m''> .
Coherent Dynamics of Complex Quantum Systems by Vladimir M. Akulin