Dresden 2020 – scientific programme

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DY: Fachverband Dynamik und Statistische Physik

DY 7: Statistical Physics (General) I

DY 7.1: Talk

Monday, March 16, 2020, 10:00–10:15, ZEU 160

Climbing the Jacob’s ladder of path integral approaches: quantum effects by classical polymer theory — •Péter Szabó and Alexandre Tkatchenko — University of Luxembourg, 1511 Luxembourg, Luxembourg

Path integral formalism provides an elegant way to evaluate thermal quantum expectation values in the language of classical physics. In ring polymer path integral methods a quantum object is mapped into a classical polymer ring in an extended, high dimensional phase space, where the beads of the polymer are the replicas of the classical system. The equilibrium averages of this polymer give the corresponding thermal properties of the quantum mechanical system.[1]

We have developed a classical polymer theory for imaginary path integrals to get an exact, low dimensional phase space representation of thermal quantum systems. This new picture preserves the classical description, but it allows us to get rid of the curse of dimensionality. The computational complexity of the problem does not depend anymore on the number of replicas. The quantum expectation values can be evaluated by the sampling of the original, classical phase space. The performance of this method is tested in molecular systems, where we calculated the quantum partition functions and compared them to the exact results.

[1] D. Chandler and P. G. Wolynes, J. Chem. Phys. 74, 4078 (1981)