Field-driven dynamics

In the section on nonequilibrium molecular dynamics, the equations of motion for field-driven dynamics were introduced. We have also noted that for bulk fluids, the field must be accompanied by boundary conditions that are... 

In the absence of shearing periodic boundary conditions (of the type introduced earlier) the system is totally isolated that is, all the degrees of freedom of the system are explicitly accounted for in the equations of motion. In this case, it is possible to obtain a conserved quantity for field-driven dynamics in general and SLLOD in particular. The approach we employ is similar to that introduced in the section on Molecular Dynamics and Equilibrium Statistical Mechanics. The SLLOD equations of motion are... 

The fast-forward protocol can be regarded as a prescription for finding a shortcut in state space, [50] from the initial state to the target state. There are, of course, many possible shortcuts in state space but very few proposals to find those shortcuts. In this section, we generalize the fast-forward protocol in a two-level system, developing different shortcuts in which, in contrast to fast-forward field (FFE)-driven dynamics, the amplitude and the phase of the wave function of the intermediate state are modulated [50]. 

One may note that covalent changes that are dealt with in the functioning of this motor are, under the conditions of the reaction, irreversible (kinetically controlled reactions). Thus, the steps of this chemically driven motor do not belong to the field of dynamic covalent chemistry (that is based on covalent changes under equilibrium conditions). 

Figure 32. Field-driven rotational motion Quantum mechanical and classical dynamics for an excitation from the ground state. The quantum mechanical probability density is compared to an ensemble of classical trajectories. Here, a preferential rotation in the counterclockwise direction is found.

For a complete treatment of a laser-driven molecule, one must solve the many-body, multidimensional time-dependent Schrodinger equation (TDSE). This represents a tremendous task and direct wavepacket simulations of nuclear and electronic motions under an intense laser pulse is presently restricted to a few bodies (at most three or four) and/or to a model of low dimensionality [27]. For a more general treatment, an approximate separation of variables between electrons (fast subsystem) and nuclei (slow subsystem) is customarily made, in the spirit of the BO approximation. To lay out the ideas underlying this approximation as adapted to field-driven molecular dynamics, we will consider from now on a molecule consisting of Nn nuclei (labeled a, p,...) and Ne electrons (labeled /, j,...), with position vectors Ro, and r respectively, defined in the center of mass (rotating) body-fixed coordinate system, in a classical field E(f) of the form Eof t) cos cot). The full semiclassical length gauge Hamiltonian is written, for a system of electrons and nuclei, as [4]... 

In each case, we first studied the laser driven dynamics of the system in the framework of the Floquet formalism, described in Sect. 6.5 of Chap. 6, which provides a geometrical interpretation of the laser driven dynamics and its dependence on the frequency and amplitude of the laser field, through the analysis of the eigenvalues of the Floquet operator, called quasienergies. Various effective models were used for that purpose. This analysis allowed us to explain the shape of the relevant quasienergy curves as a function of the laser parameters, and to obtain the parameters of the laser field that induce the CDT. We then used the MCTDH method to solve the TDSE for the molecule in interaction with the laser field and compare these results with those obtained from the effective Hamiltonian described in Sect. 8.2.3 above. 

This model gives a simple, analytic description of the phenomenon of CDT. However, it does not account for the possible effect of the higher vibrational states on the laser driven dynamics. In the present case, the frequency of the laser field is far from any resonance. Therefore, one does not expect it to induce population transfers among the vibrational states. Nevertheless, the presence of higher vibrational states can influence the dynamics through vibrational Stark shifts. These Stark shifts can... 

The results presented in this chapter show that the use of proper effective models, in combination with calculations based on the exact vibrational Hamiltonian, constitutes a promising approach to study the laser driven vibrational dynamics of polyatomic molecules. In this context, the MCTDH method is an invaluable tool as it allows to compute the laser driven dynamics of polyatomic molecules with a high accuracy. However, our models still contain simplifications that prevent a direct comparison of our results with potential experiments. First, the rotational motion of the molecule was not explicitly described in the present work. The inclusion of the rotation in the description of the dynamics of the molecule is expected to be important in several ways. First, even at low energies, the inclusion of the rotational structure would result in a more complicated system with different selection rules. In addition, the orientation of the molecule with respect to the laser field polarization would make the control less efficient because of the rotational averaging of the laser-molecule interaction and the possible existence of competing processes. On the other hand, the combination of the laser control of the molecular alignment/orientation with the vibrational control proposed in this work could allow for a more complete control of the dynamics of the molecule. A second simplification of our models concerns the initial state chosen for the simulations. We have considered a molecule in a localized coherent superposition of vibrational eigenstates but we have not studied the preparation of this state. We note here that a control scheme for the localiza-... 

Farrow, 1982 Etchepare et al., 1982 Halbout and Tang, 1982 Ho et al., 1976). Motivated by our previous experimental work on probing interactions and dynamics via nonlinear laser spectroscopy and four-wave mixing (Kenney-Wallace and Wallace, 1983 Golombok et al., 1985 Dickson et al., 1987 Kenney-Wallace et al., 1987), we have particularly focused on the intense laser interaction with the molecules and subsequent field-driven changes in their orientational distribution. The application of this kind of result is not only to advance the interpretation of... 

Jones, G. A., Acocella, A., Zerbetto, R (2008). On-the-fly, electric-field-driven, coupled electron-nuclear dynamics. The Journal of Physical Chemistry A, 112(40), 9650-9656. doi 10.1021/ Jp805360v. 

This probability is nonzero only if the population of the /th state is decreasing and the population of the A th state is increasing, which is represented by the 0 function. The summation in the denominator is performed over all states L whose population is also growing. It should be pointed out that this equation requires only the calculation of the hopping probabilities at each nuclear time step due to the fact that populations generally vary more slowly than the coherences (t)C/(t) which are employed in Eq. 17.4. This is particularly useful in the context of field-driven multistate dynamics during which the laser field is varying very fast as it will be shown in Sect. 17.6. 

Once the piston-driven flow field is known, the flame-driven flow field is found by fitting in a steady flame front, with the condition that the medium behind it is quiescent. This may be accomplished by employing the jump conditions which relate the gas-dynamic states on either side of a flame front. The condition that the reaction products behind the flame are at rest enables the derivation of expressions for the density ratio, pressure ratio, and heat addition... 

Dynamical chaos in periodically driven systems has become attractive topic in many areas of contemporary physics such as atomic, molecular, nuclear and particle physics. Dynamical systems which can exhibit chaotic dynamics can be divided into two classes time independent and time-dependent systems. Billiards, atoms in a constant magnetic field, celestial systems with chaotic dynamics are time independent systems, whose dynamics can be chaotic. 

Thus we have treated the chaotic dynamics of the quarkonium in a time periodic field. Using the Chirikov s resonance overlap criterion we obtain estimates for the critical value of the external field strength at which chaotization of the quarkonium motion will occur. The experimental realization of the quarkonium motion under time periodic perturbation could be performed in several cases in laser driven mesons and in quarkonia in the hadronic or quark-gluon matter. 

---