Trotter

As in the case of the propagator, we shall be applying a symmetrical version of the Trotter fomuila [48] to the high-temperature density matrix... 

Trotter H F 1959 On the product of semi-groups of operators Proc. Am. Math. Soc. 10 545-51... 

Spence T G, Trotter B T, Burns T D and Posey L A 1998 Metal-to-ligand charge transfer in the gas phase cluster limit J. Phys. Chem. A 102 6101... 

With this break up the reversible Trotter factorization of the propagator is... 

The system defined by the Liouvillian is called the reference system. Now applying the Trotter factorization to the propagator exp iLs + Fi arising from this subdivision gives the new propagator,[17]... 

Analogously, pyrazolyl-aluminate and -indate ligands have been prepared <75JCS(D)749) and their chelating properties evaluated with cobalt, nickel, copper and zinc. Gallyl derivatives of pyrazoles and indazoles have been extensively studied by Storr and Trotter e.g. 75CJC2944) who determined several X-ray structures of these compounds. These derivatives exist in the solid state as dimers, such as (212) and (288). A NMR study in acetone solution showed the existence of a slow equilibrium between the dimer (212) and two identical tautomers (289) and (290) (Section 4.04.1.5.1) (81JOM(215)157). 

The idea is now to replace the formal solution of the Liouville equation by the discretized version. The middle term gf the propagator in Eq. (51) can be further decomposed by an additional Trotter factorization to obtain... 

Path integral Monte Carlo simulations were performed [175] for the system with Hamiltonian (Eq. (25)) for uj = ujq/J = A (where / = 1) with N = 256 particles and a Trotter dimension P = 64 chosen to achieve good computer performance. It turned out that only data with noise of less than 0.1% led to statistically reliable results, which were only possible to obtain with about 10 MC steps. The whole study took approximately 5000 CPU hours on a CRAY YMP. 

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