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We have derived several relations, which allow the evaluation of the system free energy changes in the leading order in variant Planck's over 2pi(2) along classically generated trajectories. The results are formulated in terms of purely classical Hamiltonians and trajectories, so that semiclassical partition functions can be computed, e.g., via classical molecular dynamics simulations. The Hamiltonians, however, contain additional potential-energy terms, which are proportional to variant Planck's over 2pi(2) and are temperature-dependent. We discuss the influence of quantum interference on the nonequilibrium work and problems with unambiguous definition of the semiclassical work operator.

We have developed a novel method, the equation-of-motion phase-matching approach (EOM-PMA), for the calculation of the response of a quantum system to N coherent laser fields. The N-pulse EOM-PMA is limited to weak fields (its domain of validity is equivalent to the traditional nonlinear response functions approach), but allows for arbitrary pulse durations and automatically accounts for pulse-overlap effects. The N-pulse EOM-PMA allows the evaluation of the time evolution of the N-pulse-induced polarization in any phase-matching direction by performing 2(N)-1 independent propagations of certain auxiliary density matrices. The N-pulse EOM-PMA can straightforwardly be incorporated into codes which provide the time evolution of the density matrix of material systems of interest and can efficiently be implemented on parallel computers.

We investigate the influence of strong femtosecond optical pulses on the ultrafast dynamics of molecular systems. The study is based on a series of generic molecular models of increasing complexity, which incorporate multiple and mutually coupled electronic states, electronic-vibrational interaction, and vibrational relaxation. The influence of vibrational relaxation is treated using multilevel Redfield theory. Comparisons to benchmark results of the multilayer multiconfiguration time-dependent Hartree (ML-MCTDH) method demonstrate the validity of the field-free implementation of Redfield theory employed in this work for weak system-bath interaction. The calculated electronic population and vibrational wave-packet dynamics demonstrate the intricate interplay of strong-field excitation, laser-induced Rabi oscillations, electronic interaction, vibronic coupling, and dissipation. In particular, we show that the interaction with a strong laser pulse may result in pronounced coherent vibrational motion in a dissipative system, even for laser pulses that are longer than the vibrational period. Furthermore, vibrational relaxation in combination with strong laser pulse excitation can lead to revivals of the electronic population after the excitation pulse is over.

We study the influence of the velocity dependence of friction on the escape of a Brownian particle from the deep potential well ($E_{b} \gg k_{B}T$, $E_{b}$ is the barrier height, $k_{B}$ is the Boltzmann constant, $T$ is the bath temperature). The bath-induced relaxation is treated within the Rayleigh model (a heavy particle of mass $M$ in the bath of light particles of mass $m\ll M$) up to the terms of the order of $O(\lambda^{4})$, $\lambda^{2}=m/M\ll1$. The term $\sim 1$ is equivalent to the Fokker-Planck dissipative operator, and the term $\sim \lambda^{2}$ is responsible for the velocity dependence of friction. As expected, the correction to the Kramers escape rate in the overdamped limit is proportional to $\lambda^{2}$ and is small. The corresponding correction in the underdamped limit is proportional to $\lambda^{2}E_{b}/(k_{B}T)$ and is not necessarily small. We thus suggest that the effects due to the velocity-dependent friction may be of considerable importance in determining the rate of escape of an under- and moderately damped Brownian particle from a deep potential well, while they are of minor importance for an overdamped particle.

To describe the contribution of the parent molecule rotation and the interfragment repulsive forces into the rotational excitation of molecular fragments produced through the photodisociation process, a simple model is proposed. The model allows one to estimate the magnitude of the additional angular momentum, that originates from the interfragment repulsive forces, by observation of the polarized luminescence of photoproducts.

An efficient method has been developed for the calculation of third-order time- and frequency-resolved optical signals. To obtain the general four-wave mixing signal, seven auxiliary density matrices have to be propagated in time. For the special cases of two-pulse photon-echo and transient-grating signals, two or three density matrices, respectively, are required. The method is limited to weak laser fields (it is thus valid within the third-order perturbation theory) but allows for any pulse durations and automatically accounts for pulse-overlap effects. To illustrate the method, we present the explicit derivation of the three-pulse photon-echo signal. Any other third-order optical signal can be calculated in the same manner. As an example, two- and three-pulse photon-echo and transient-grating signals for a weakly damped displaced harmonic oscillator have been calculated.