Liouville equation vibrational relaxation

The above theory is usually called the generalized linear response theory because the linear optical absorption initiates from the nonstationary states prepared by the pumping process [85-87]. This method is valid when pumping pulse and probing pulse do not overlap. When they overlap, third-order or X 3 (co) should be used. In other words, Eq. (6.4) should be solved perturbatively to the third-order approximation. From Eqs. (6.19)-(6.22) we can see that in the time-resolved spectra described by x"( ), the dynamics information of the system is contained in p(Af), which can be obtained by solving the reduced Liouville equations. Application of Eq. (6.19) to stimulated emission monitoring vibrational relaxation is given in Appendix III. 

Both vibrational and rotovibrational relaxation can be described analyti-caDy as multiplicative stochastic processes. For these processes, RMT is equivalent to the stochastic Liouville equation of Kubo, with the added feature that RMT takes into account the back-reaction from the molecule imder consideration on the thermal bath. The stochastic Liouville equation has been used successfully to describe decoupling in the transient field-on condition and the effect of preparation on decay. When dealing with liquid-state molecular dynamics, RMT provides a rigorous justification for itinerant oscillator theory, widely applied to experimental data by Evans and coworkers. This implies analytically that decoupling effects should be exhibited in molecular liquids treated with strong fields. In the absence of experimental data, the computer runs described earlier amount to an independent means of verifying Grigolini s predictions. In this context note that the simulation of Oxtoby and coworkers are semistochastic and serve a similar purpose. 

Contributions from terms like Cs pyare smaU and ignored in the summation. Starting from the von Neumann-Liouville equation, a reduced density matrix for the system mode is derived using the time-dependent perturbation theory after tracing over the bath degrees of freedom. The commonly employed Markov approximation is avoided and no assumption of a separation in timescales between system and bath mode relaxation is invoked in this theory [84]. The ultimate result for the evolution of the ground state vibrational population is... 

From a quantum mechanical perspective, the transient vibrational relaxation dynamics is often studied within a reduced density matrix formalism. The dissipative dynamics of the so-called open system is described by a Liouville von Neumann equation that includes implicitly the effects of the surroundings on the dynamics... 

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