S. K. Sinha

Quantum corrections to the equation of state of a fluid using hard‐sphere basis functions

We develop the expansion for the Slater sum, using a hard‐sphere potential as a reference potential and the hard‐sphere wavefunction as a basis set, which replaces the usual Wigner–Kirkwood series. Expressions are given for the first and second quantum corrections to the free energy arising due to perturbation potential. Results are given for the first and second quantum corrections to the second and third virial coefficients. We find that the quantum corrections to the higher virial coefficients depend on the potential at the core as well as the shape of the well. The general expression for the third virial coefficient of a gas at high temperature is given by Bq3 =Bc3+(5π2d6/18)[(3/√2) BI3(λ/d) +1.708 BII3(λ/d)2+⋅⋅⋅], where BI3 and BII3 are constants depending upon the shape and nature of the perturbation potential and equal to unity in the limit of the hard sphere [i.e., up(r) →0].

Quantum corrections to the equilibrium properties of dense fluids: Application to hard‐sphere fluids

A simple theory for the equation of state of dense fluids in the semiclassical limit, where the quantum effects are small, is developed, based on an interpretation of the reciprocal of the activity. The theory has been applied to calculate the quantum effect on the equation of state of a dense hard‐sphere fluid.

Semiclassical statistical mechanics of a two dimensional fluid

Expansions are obtained for the two and three body ‘modified’ Ursell functions for a hard disc fluid in the semiclassical limit. These results are used to obtain a high temperature expansion for the density independent part of the radial distribution function and the first order density correction to it. Quantum corrections to the second and third virial coefficients are also discussed.

Quantum corrections to the equation of state of a fluid with square‐well plus hard‐core potential

A method developed in the previous paper for evaluation of quantum corrections to the equations of state of a fluid is extended to cover the case of the square‐well plus hard‐core potential. Explicit expressions are given for the first two quantum corrections to the third virial coefficient at high temperature. We find that the quantum corrections to the higher virial coefficients depend on the depth and breadth of the well.

Quantum mechanical second virial coefficient of a gas with square‐well plus hard‐core potential

The quantum mechanical second virial coefficient of a gas with square‐well plus hard‐core potential is evaluated at low and high temperatures. The low temperature result is given in a series in the ascending powers of (a/λ), and the first four coefficients are given. The direct part of the second virial coefficient at high temperature is given in a series in the ascending powers of (λ/a), and the first three coefficients are given. Our result for the first coefficient in the high temperature series is in agreement with the result of previous workers.

Quantum corrections to the equilibrium properties of a dense fluid with square‐well plus hard‐core potential

Using the modified WK expansion of Slater sum, a simple theory for evaluating thermodynamic properties of a dense semiclassical fluid is developed. The theory has been applied to calculate the quantum corrections to the equation of the state and excess Helmholtz free energy of a dense fluid with square‐well plus hard‐core potential. The results for the first two quantum corrections are reported in analytic form.

Quantum corrections to the second virial coefficient of a gas using hard sphere basis functions

The quantum corrections to the second virial coefficient for a gas at high temperature are calculated using the modified Wigner–Kirkwood expansion method, developed by Derderian and Steele. We find that the higher corrections depend both on the shape of the well and the value of the potential at the core. The general expression for the second virial coefficient of a gas at high temperature is given as Bdir=Bdirc + (2πa3/3) e−βup(a) [(3/2√2) (λ/a) + (BII/π)(λ/a)2 + BIII/16√2π) (λ/a)3 + ...], where BII and BIII are constants depending upon the shape and nature of the perturbation potential and equal to unity in the limit of hard sphere [i.e., up(r) →0].

Equilibrium properties of hard‐sphere fluid mixture in the semiclassical limit

High‐temperature expansions for the density independent part of the to it are obtained for a hard‐sphere binary mixture. The ‘‘excess’’ quantum corrections to the excess properties, such as excess second and third virial coefficients and excess free energy, are also reported. It is found that the excess quantum effect depends on the concentration and the particle diameter ratio.

Semiclassical statistical mechanics of a v-dimensional fluid of hard v-Spheres

The quantum corrections to the properties of a dense v-dimensional fluid of hard v-spheres are estimated at high temperature. Explicit expressions for the first quantum corrections to the free energy and equation of state are given. Numerical results are reported for hard v-spheres with 1 ˇ- v ˇ- 5. The behaviour of the radial distribution function near the hard core is also studied. A significant feature is the large increase in quantum correction with increasing dimensionality.

Semiclassical statistical mechanics of a v-dimensional fluid of hard v-spheres: I. Equilibrium properties of dilute hard v-sphere gas

The problem of calculating quantum corrections to the equilibrium properties of v-dimensional fluids of hard v-spheres is studied. Asymptotic expressions, valid at high temperatures, are derived for the density independent radial distribution function and second virial coefficient. Expressions for the first order quantum corrections to the free energy, pressure and the nth virial coefficients are also given. Significant features are the large increase in quantum correction with increasing dimensionality.