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Symmetrized correlation function for liquid para-hydrogen using complex-time pair-product propagators
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View: Figures


Image of FIG. 1.
FIG. 1.

Schematic illustration of the complex-time plane. The disk bounded by the dotted circle shows the complex-time points for which . The dashed line indicates the contour along which the symmetrized correlation function is obtained at .

Image of FIG. 2.
FIG. 2.

Expectation value of the (a) total and (b) kinetic energy per atom as a function of time at . The solid circles show the results of the pair-product approximation, Eq. (5.2). The hollow triangles show results obtained using the Trotter formula for the complex-time propagators. The solid square shows the result of the PIMC calculation.

Image of FIG. 3.
FIG. 3.

Radial distribution function as a function of time for liquid para-hydrogen at . Solid circles: . Hollow squares: . Up triangles: . Down triangles: . Hollow circles: . The solid line shows the results obtained from a numerically exact PIMC simulation. The dotted line shows the results of the single-step Trotter approximation.

Image of FIG. 4.
FIG. 4.

The partition function as a function of time obtained from Eq. (5.9).

Image of FIG. 5.
FIG. 5.

The velocity autocorrelation function for liquid para-hydrogen at . Solid circles: quantum mechanical results obtained from Eq. (5.10). Hollow triangles: results obtained using the single-bead Trotter approximation to the complex-time propagator. The arrow shows the converged results of a PIMC calculation at using 30 beads.

Image of FIG. 6.
FIG. 6.

Comparison of the accurate quantum mechanical results for the symmetrized velocity autocorrelation function of liquid para-hydrogen at to those obtained using the FBSD approximation. Black circles: quantum PP propagator results obtained from Eq. (5.10). Solid line: transformed FBSD results. Dashed line: scaled transformed FBSD results.

Image of FIG. 7.
FIG. 7.

The normalized self-intermediate scattering function, Eq. (5.15), for liquid para-hydrogen at . Hollow triangles: . Hollow diamonds: . Hollow circles: . Solid squares: .

Image of FIG. 8.
FIG. 8.

Numerical (points) and fitted (line) forms of the normalized self-intermediate scattering function at .

Image of FIG. 9.
FIG. 9.

The normalized dynamic structure factor, Eq. (5.15), for liquid para-hydrogen for at . Solid line: PPP results. Dashed line: results using the FBSD velocity autocorrelation function in the Gaussian approximation.


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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Symmetrized correlation function for liquid para-hydrogen using complex-time pair-product propagators