Path-integral Mayer-sampling calculations of the quantum Boltzmann contribution to virial coefficients of helium-4

2012 ◽  
Vol 137 (18) ◽  
pp. 184101 ◽  
Author(s):  
Katherine R. S. Shaul ◽  
Andrew J. Schultz ◽  
David A. Kofke
Keyword(s):  
Path Integral ◽  
Virial Coefficients ◽  
Helium 4

scholarly journals Path-Integral Calculation of the Second Dielectric and Refractivity Virial Coefficients of Helium, Neon, and Argon

2020 ◽  
Vol 125 ◽  
Author(s):  
Giovanni Garberoglio ◽  
Allan H. Harvey
Keyword(s):  
Path Integral ◽  
State Of The Art ◽  
Virial Coefficients ◽  
Quantum Statistical Mechanics ◽  
Quantum Calculations ◽  
Path Integral Monte Carlo ◽  
Straightforward Manner ◽  
Helium 4 ◽  
Pair Potentials ◽  
Helium Neon

We present a method to calculate dielectric and refractivity virial coefficients using the path-integral Monte Carlo formulation of quantum statistical mechanics and validate it by comparing our results with equivalent calculations in the literature and with more traditional quantum calculations based on wavefunctions. We use state-of-the-art pair potentials and polarizabilities to calculate the second dielectric and refractivity virial coefficients of helium (both 3He and 4He), neon (both 20Ne and 22Ne), and argon. Our calculations extend to temperatures as low as 1 K for helium, 4 K for neon, and 50 K for argon. We estimate the contributions to the uncertainty of the calculated dielectric virial coefficients for helium and argon, finding that the uncertainty of the pair polarizability is by far the greatest contribution. Agreement with the limited experimental data available is generally good, but our results have smaller uncertainties, especially for helium. Our approach can be generalized in a straightforward manner to higher-order coefficients.

scholarly journals THE FOURTH VIRIAL COEFFICIENT OF ANYONS

1998 ◽  
Vol 13 (21) ◽  
pp. 3723-3747 ◽  
Author(s):  
ANDERS KRISTOFFERSEN ◽  
STEFAN MASHKEVICH ◽  
JAN MYRHEM ◽  
KÅRE OLAUSSEN
Keyword(s):  
Monte Carlo ◽  
Fourier Series ◽  
Monte Carlo Method ◽  
Path Integral ◽  
Virial Coefficient ◽  
Path Integrals ◽  
Second Virial Coefficient ◽  
Virial Coefficients ◽  
Partition Functions ◽  
Two Dimensional

We have computed by a Monte Carlo method the fourth virial coefficient of free anyons, as a function of the statistics angle θ. It can be fitted by a four term Fourier series, in which two coefficients are fixed by the known perturbative results at the boson and fermion points. We compute partition functions by means of path integrals, which we represent diagramatically in such a way that the connected diagrams give the cluster coefficients. This provides a general proof that all cluster and virial coefficients are finite. We give explicit polynomial approximations for all path integral contributions to all cluster coefficients, implying that only the second virial coefficient is statistics dependent, as is the case for two-dimensional exclusion statistics. The assumption leading to these approximations is that the tree diagrams dominate and factorize.

scholarly journals Fully quantum calculation of the second and third virial coefficients of water and its isotopologues from ab initio potentials

2018 ◽  
Vol 212 ◽  
pp. 467-497 ◽  
Author(s):  
Giovanni Garberoglio ◽  
Piotr Jankowski ◽  
Krzysztof Szalewicz ◽  
Allan H. Harvey
Keyword(s):  
Monte Carlo ◽  
Heavy Water ◽  
Path Integral ◽  
Monte Carlo Methods ◽  
Virial Coefficients ◽  
Quantum Calculation ◽  
Path Integral Monte Carlo ◽  
The Third ◽  
Ab Initio Potentials ◽  
State Of Art

Path-Integral Monte Carlo methods were applied to calculate the second, B(T), and the third, C(T), virial coefficients for water and heavy water from state-of-art flexible potentials.

A path integral centroid molecular dynamics study of nonsuperfluid liquid helium-4

1999 ◽  
Vol 110 (9) ◽  
pp. 4523-4532 ◽  
Author(s):  
Shinichi Miura ◽  
Susumu Okazaki ◽  
Kenichi Kinugawa
Keyword(s):  
Molecular Dynamics ◽  
Liquid Helium ◽  
Path Integral ◽  
Helium 4
Sign in / Sign up

Export Citation Format

Share Document