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Correlation Functions in Open Quantum-Classical Systems
Chemical Physics Theory Group, Department of Chemistry, University of Toronto, Toronto, ON M5S 3H6, Canada
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Received: 25 September 2013; in revised form: 21 October 2013 / Accepted: 22 October 2013 / Published: 27 December 2013
Abstract: Quantum time correlation functions are often the principal objects of interest in experimental investigations of the dynamics of quantum systems. For instance, transport properties, such as diffusion and reaction rate coefficients, can be obtained by integrating these functions. The evaluation of such correlation functions entails sampling from quantum equilibrium density operators and quantum time evolution of operators. For condensed phase and complex systems, where quantum dynamics is difficult to carry out, approximations must often be made to compute these functions. We present a general scheme for the computation of correlation functions, which preserves the full quantum equilibrium structure of the system and approximates the time evolution with quantum-classical Liouville dynamics. Several aspects of the scheme are discussed, including a practical and general approach to sample the quantum equilibrium density, the properties of the quantum-classical Liouville equation in the context of correlation function computations, simulation schemes for the approximate dynamics and their interpretation and connections to other approximate quantum dynamical methods.
Keywords: quantum correlation functions; quantum-classical systems; nonadiabatic dynamics
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Cite This Article
MDPI and ACS Style
Hsieh, C.-Y.; Kapral, R. Correlation Functions in Open Quantum-Classical Systems. Entropy 2014, 16, 200-220.
Hsieh C-Y, Kapral R. Correlation Functions in Open Quantum-Classical Systems. Entropy. 2014; 16(1):200-220.
Hsieh, Chang-Yu; Kapral, Raymond. 2014. "Correlation Functions in Open Quantum-Classical Systems." Entropy 16, no. 1: 200-220.