Liouville equation electric field

In order to introduce some notation, we first recall a few of the well-known properties of the interaction of light pulses with molecules in the linear approximation. Frequently, the signals in nonlinear optical experiments are expressed in terms of the polarization induced in the medium by the incident pulses. The complex linear polarization P t) vector for a distribution of identical two-level systems is obtained from an elementary calculation of the density matrix using the Liouville equation of a system perturbed by an electric field and proceeding as follows ... 

Nakano and Yamaguchi255-258 are developing a method based on numerical solutions of Liouville s equation to describe the frequency-dependent response of an assembly of dipoles to an electric field. The aggregates are of a size such that retardation effects are significant. One novel result is that there is a sharp change of the polarizability, reminiscent of a phase transition, that occurs as the intensity of a near-resonant field is increased. 

The above example illustrates the development and solution to the singleparticle Liouville equation in cartesian coordinates. As discussed in Chap. 1, for structured particles, it is often more fruitful to work in generalized coordinates. Let s revisit the problem of a dipole in an external electric field. Example 1.1, and develop the generalized coordinates, conjugate momenta, hamiltonian, and associated Liouville equation for this system. 

Let us consider the problem of describing the response of a system to some probe, such as an electric or magnetic field, that can be treated as a classical external force. This problem can be dealt with by starting with the following version of the quantum Liouville equation ... 

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