Dynamics of Quantum Fluids: Path integral and Semiclassical Methods

By Nancy Makri

University of Illinois at Urbana-Champaign

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The interplay of many-body nonlinear interactions and quantum mechanical effects such as zero-point motion or identical particle exchange symmetries lead to intriguing phenomena in low-temperature fluids, some of which remain poorly understood. Recent advances in theory and methodology have established the framework that has recently enabled the simulation of time-dependent processes in such systems. This lecture focuses on the development of path integral and semiclassical methods and their application to the dynamics of quantum fluids.

Forward-backward semiclassical dynamics (FBSD) is a rigorous and efficient methodology for capturing quantum mechanical effects in the time evolution of condensed phase systems through classical trajectory information. FBSD expressions for time-dependent expectation values or correlation functions take the form of phase space integrals with respect to trajectory initial conditions, weighted by the coherent state transform of a corrected density operator. Full quantization of the initial density is feasible by employing the discretized path integral representation of statistical mechanics, thus ensuring a proper treatment of zero point energy and identical particle exchange effects, while capturing important imaginary components. The FBSD approximation satisfies the detailed balance property of time autocorrelation functions and reverts to the exact quantum mechanical result at zero time.

Traditional path integral calculations of real-time properties are impractical for application to many-particle systems because of extensive phase cancellation. We have been able to obtain accurate, fully quantum mechanical results for the early dynamics of neat liquids by using a pair-product approximation to evaluate the complex-time propagator in a single step, circumventing the sign problem.

These methods have been employed to investigate the dynamics of low-temperature fluids, ranging from the nearly-classical supercritical argon to highly quantum mechanical systems such as liquid neon, para-hydrogen and superfluid helium. The results of these calculations are in very good agreement with experimental results on diffusion coefficients and dynamic structure factors probed by neutron scattering. The FBSD simulations provide novel insights into the separate roles of quantum mechanical and quantum statistical effects on the dynamics of these fluids.


Nancy Makri Nancy Makri received her B.S. from the University of Athens in 1985 and her Ph.D. from the University of California at Berkeley in 1989. She spent two years as a Junior Fellow at Harvard before joining the faculty at Illinois in the spring of 1992. She is the Gutgsell professor in the University of Illinois Department of Chemistry and Physics and a part-time faculty member in the Beckman Institute Nanoelectronics and Biophotonics group. Her field of interest is quantum dynamics of polyatomic systems.

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  • Nancy Makri (2008), "Dynamics of Quantum Fluids: Path integral and Semiclassical Methods," http://nanohub.org/resources/4584.

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