# Evaluation of coherent-state path integrals in statistical mechanics by matrix multiplication

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## Date

1998-01-22

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American Institute of Physics

## Abstract

The numerical evaluation of coherent-state path-integral representations for partition functions and other quantities in equilibrium quantum statistical mechanics is discussed. Several coherent-state path-integral schemes are introduced, which differ from each other by the order of approximation and by the operator ordering employed in the high-temperature approximation of the density operator. Simple one-dimensional systems are used to test these schemes. For the harmonic oscillator, finite-dimensional approximations to the coherent-state path integral are calculated analytically and compared to each other and to the real-space path integral. For anharmonic systems, integrations must be approximated by quadrature formulas. This leads to a matrix multiplication scheme which is tested for the double-well potential. The results obtained are accurate from zero temperature way up into the high-temperature regime where quantum effects become negligible. This is a significant advantage over traditional real-space path integral schemes which break down at low temperatures.

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## Citation

Burghardt, Bernd; Eicke, Joachim; Stolze, Joachim: In: Evaluation of coherent-state path integrals in statistical mechanics by matrix multiplication. In: Journal of Chemical Physics Nr. 4, Jg. 108(1998), S. 1562-1569, doi: 10.1063/1.475527.