scholarly journals Path-integral calculation of the fourth virial coefficient of helium isotopes

2021 ◽  
Vol 154 (10) ◽  
pp. 104107
Author(s):  
Giovanni Garberoglio ◽  
Allan H. Harvey
Keyword(s):  
Path Integral ◽  
Virial Coefficient ◽  
Helium Isotopes

scholarly journals Path-integral calculation of the third dielectric virial coefficient of noble gases

2021 ◽  
Vol 155 (23) ◽  
pp. 234103
Author(s):  
Giovanni Garberoglio ◽  
Allan H. Harvey ◽  
Bogumił Jeziorski
Keyword(s):  
Path Integral ◽  
Virial Coefficient ◽  
Noble Gases ◽  
The Third

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.

Path-integral calculation of the second virial coefficient including intramolecular flexibility effects

2014 ◽  
Vol 141 (4) ◽  
pp. 044119 ◽  
Author(s):  
Giovanni Garberoglio ◽  
Piotr Jankowski ◽  
Krzysztof Szalewicz ◽  
Allan H. Harvey
Keyword(s):  
Path Integral ◽  
Virial Coefficient ◽  
Second Virial Coefficient

The transition temperature in liquid helium. II

1958 ◽  
Vol 247 (1249) ◽  
pp. 225-236 ◽  
Keyword(s):  
Transition Temperature ◽  
Effective Mass ◽  
Path Integral ◽  
Lattice Spacing ◽  
Lattice Structure ◽  
The Other ◽  
Helium Isotopes ◽  
Helium Ii ◽  
Liquid Transition ◽  
Real Mass

The Feynman–Kikuchi theory of the λ -transition, discussed in a previous paper, is improved in various respects. A more general formulation of the approximate path integral for two-atom permutations gives the result that these permutations should be unimportant except below about 1°K, where they may become more important than the other kinds of permutations. The lattice model is generalized by allowing vacant lattice sites (holes) so that there is a gas-liquid transition as well as a λ -transition. If one assumes that the lattice spacing is fixed and the only effect of pressure is to change the number of holes, then one finds that the transition temperature decreases with pressure if the ‘effective mass’ for many-sided polygons is taken to be more than twice the real mass. On the other hand, with such a large effective mass the transition temperature itself comes out too low. If one allowed the lattice spacing and effective mass to vary with pressure, one could obtain better numerical agreement with experiment, but with so many adjustable parameters such agreement would not be significant. The effect of lattice structure on the transition is also discussed, and it is found that the product of effective mass, square of lattice spacing, and transition temperature should increase with the co-ordination number of the lattice. The treatment can also be extended to mixtures of helium isotopes; the effect of small amounts of 3 He or 6 He is similar to that predicted by other theories.

Fifth virial coefficient of a two-component mixture of hard discs

1997 ◽  
Vol 90 (4) ◽  
pp. 679-681
Author(s):  
F. SAIJA ◽  
G. FIUMARA ◽  
P.V. GIAQUINTA
Keyword(s):  
Virial Coefficient ◽  
Component Mixture ◽  
Two Component
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