Density matrix multidimensional

We conclude that the QCL description represents a promising approach to the treatment of multidimensional curve-crossing problems. The density-matrix... 

To this end, we resort to a novel general approach to the control of arbitrary multidimensional quantum operations in open systems described by the reduced density matrix p(t) if the desired operation is disturbed by linear couplings to a bath, via operators S B (where S is the traceless system operator and B is the bath operator), one can choose controls to maximize the operation fidelity according to the following recipe, which holds to second order in the system-bath coupling (i) The control (modulation) transforms the system-bath coupling operators to the time-dependent form S t) (S) B(t) in the interaction picture, via the rotation matrix e,(t) a set of time-dependent coefficients in the operator basis, (Pauli matrices in the case of a qubit), such that ... 

In Chapter 11 we shall also introduce the product operator formalism, in which the basic ideas of the density matrix are expressed in a simpler algebraic form that resembles the spin operators characteristic of the steady-state quantum mechanical approach. Although there are some limitations in this method, it is the general approach used to describe modern multidimensional NMR experiments. 

All theoretical studies on benzoic acid dimer underlined the need for a multidimensional potential surface. These studies have investigated the temperature dependence of the transfer process They included a density matrix model for hydrogen transfer in the benzoic acid dimer, where bath induced vibrational relaxation and dephasing processes are taken into account [25]. Sakun et al. [26] have calculated the temperature dependence of the spin-lattice relaxation time in powdered benzoic acid dimer and shown that low frequency modes assist the proton transfer. At high temperatures the activation energy was found to be... 

Shaul Mukamel, who is currently the C. E. Kenneth Mees Professor of Chemistry at the University of Rochester, received his Ph.D. in 1976 from Tel Aviv University, follot by postdoctoral appointments at MIT and the University of California at Berkeley and faculty positions at the Weizmann Institute and at Rice University. He has b n the recipient of the Sloan, Dreyfus, Guggenheim, and Alexander von Humboldt Senior Scientist awards. His research interests in theoretical chemical physics and biophysics include developing a density matrix Liouville-space approach to femtosecond spectroscopy and to many body theory of electronic and vibrational excitations of molecules and semiconductors multidimensional coherent spectroscopies of sbucture and folding dynamics of proteins nonlinear X-ray and single molecule spectroscopy electron transfer and energy ftrnneling in photosynthetic complexes and Dendrimers. He is the author of over 400 publications in scientific journals and of the textbook. Principles of Nonlinear OfMical Spectroscopy (Oxford University Press), 1995. 

We conclude that the QCL description represents a promising approach to the treatment of multidimensional curve-crossing problems. The density-matrix formulation yields a consistent treatment of electronic populations and coherences, and the momentum changes associated with an electronic transition can be directly derived from the formalism without the need of ad hoc assumptions. Employing a Monte-Carlo sampling scheme of local classical trajectories, however, we have to face two major complications, that is, the representation of nonlocal phase-space operators and the sampling problem caused by rapidly varying phases. At the present time, the... 

In multidimensional systems, coherently excited vibrational states of an ensemble of molecules probably are described best with the density-matrix formalism. Such a description has been used to rationalize oscillatory features in the dynamics of the initial electron-transfer step in photosynthetic bacterial reaction centers after excitation with sub-picosecond flashes [127, 128]. Vibrational modes that are coupled to electron transfer were identified by recording the fluctuating energy... 

In the density-matrix model, the energy gap between P and P B (U(t)) oscillates as the wavepacket evolves on the multidimensional potential surface of the excited state. The time dependence of the gap is given by... 

R is called the relaxation superoperator. Expanding the density operator in a suitable basis (e.g., product operators [7]), the a above acquires the meaning of a vector in a multidimensional space, and eq. (2.1) is thereby converted into a system of linear differential equations. R in this formulation is a matrix, sometimes called the relaxation supermatrix. The elements of R are given as linear combinations of the spectral density functions (a ), taken at frequencies corresponding to the energy level differences in the spin system. 

Efficient use of symmetry can greatly speed up localized-orbital density-functional-exchange-and-correlation calculations. The local potential of density functional theory makes this process simpler than it is in Hartree-Fock-based methods. The greatest efficiency can be achieved by using non-Abelian point-group symmetry. Such groups have multidimensional irreducible representations. Only one member of each such representation need be used in the calculation. However efficient localized-orbital evaluation of the chosen matrix element requires the sum of the magnitude squared of the components of all the members on one of the symmetry inequivalent atoms, based on Eq. 13. 

---