A central problem in the theory of the dynamics of open quantum systems is the derivation of a rigorous and computationally tractable master equation for the reduced system density matrix. Most generally, the evolution of an open quantum system is described by a completely positive linear map. We show how to derive a completely positive Markovian master equation (the Lindblad equation) from such a map by a coarse graining procedure. We provide a novel and explicit recipe for calculating the coefficients of the master equation, using perturbation theory in the weak-coupling limit. The only parameter external to our theory is the coarse-graining time-scale. We illustrate the method by explicitly deriving the master equation for the spin-boson model. The results are evaluated for the exactly solvable case of pure dephasing, and an excellent agreement is found within the timescale where the Markovian approximation is expected to be valid. The method can be extended in principle to include non-Markovian effects.

A new krypton-containing compound, HKrF, has been prepared in a low-temperature Kr matrix via VUV photolysis of the HF precursor and posterior thermal mobilization of H and F atoms. All three fundamental vibrations have been observed in the FTIR spectra at ∼1950 cm−1 (H–Kr stretch), ∼650 cm−1 (bending), and ∼415 cm−1 (Kr–F stretch). Two distinct sites of HKrF have been identified. The energy difference between the H–Kr stretching vibrations for the two sites is remarkably large (26 cm−1), indicating a strong influence of the environment. In annealing after the photolysis of the precursor, HKrF is formed in two different stages: at 13–16 K from closely trapped H+F pairs and at T>24 K due to more extensive mobility of H and F atoms in the matrix. HKrF in a less stable site decreases at temperatures above 32 K, the other site being stable up to the sublimation temperature of the matrix. The photodecomposition cross section for HKrF has been measured between 193 and 350 nm and compared with the cross sections of the previously reported HArF and HKrCl molecules. The condensed-phase VSCF (vibrational self-consistent field) calculations suggest that the more stable form is a single-substitutional site and the less stable form is a double-substitutional site of HKrF in solid Kr. The gas to matrix shifts for these sites are predicted to be +(9–26) cm−1 for the H–Kr stretching and the bending vibrations and −(7–10) cm−1 for the Kr–F stretching vibrations.

The vibrational spectroscopy and the matrix-site geometries of several novel rare-gas compounds in the matrix environment were computed theoretically, and compared with experiment. Ab initio calculations are used in the fitting of analytical potential surfaces for the HRgY molecules and for the interactions between HRgY and the matrix atoms Rg. With these potentials, matrix-site geometries for the molecule in the solid are computed. Finally, the vibrational spectroscopy of HRgY in the Rg matrix is computed using the vibrational self-consistent field (VSCF) method. The VSCF includes anharmonic effects, that are essential in this case. The version of VSCF used here includes coupling between HRgY and the vibrations of the solid atoms. The vibrations of 72 matrix atoms are treated. The main results are: (1) The matrix shifts are considerably greater than typically found for neutral, strongly bond molecules, but are much smaller than discrepancies between theory and experiment. This can be attributed to the insufficient accuracy of the potentials used for the HRgY molecules. This calls for better future description of the electronic structure of HRgY. (2) The matrix shifts and splitting effects are interpreted by the calculations in terms of the site geometries involved. These effects are very different for HArF, HKrF than for HXeCl, HXeI. (3) The computed matrix-site splittings are in semiquantitative accord with experiment. This supports the interaction potentials used between HRgY and the matrix. The results provide insights on the effects of the matrix on the rare-gas molecules.

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Time-Frequency Resolved Coherent Anti-Stokes Raman Scattering (TFRCARS) was recently proposed as a means to implement quantum logic using the molecular ro-vibrational manifold as a quantum register [R. Zadoyan et al., Chem. Phys. 266, (2001) 323]. We give a concrete example of how this can be accomplished through an illustrative algorithm that solves the Deutsch-Jozsa problem. We use realistic molecular parameters to recognize that, as the problem size expands, shaped pulses must be tailored to maintain fidelity of the algorithm.