Correlation function quantum-like formalism

The evaluation of the equilibrium correlation function can be made without a problem. In, fact, adopting a quantum-like formalism we can write, for t2 > t, ... 

The quantum mechanical forms of the correlation function expressions for transport coefficients are well known and may be derived by invoking linear response theory [64] or the Mori-Zwanzig projection operator formalism [66,67], However, we would like to evaluate transport properties for quantum-classical systems. We thus take the quantum mechanical expression for a transport coefficient as a starting point and then consider a limit where the dynamics is approximated by quantum-classical dynamics [68-70], The advantage of this approach is that the full quantum equilibrium structure can be retained. 

Molecular quantum chemistry and quantum mechanical simulation of solids have followed substantially independent paths and strategies for many years, with almost no reciprocal influence. In the implementation of computational schemes and formalisms, they started from different elementary models either the hydrogen or helium atom like, for example, the parameterization of a correlation functional based on accurate He atom calculations by Colle and Salvetti, or the electron gas, which is the reference system of the local density approximation "" (LDA) to density functional theory (DFT). Moreover, if we compare the simplest real crystals, like lithium metal or sodium chloride, with the smallest molecule, H2, the much greater complexity of the solid system is... 

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