Kinetic derivation of the second virial coefficient for a quantum gas

A kinetic equation has been proposed earlier for an inhomogeneous quantum dilute gas obeying Boltzmann statistics. We show here that it leads to the correct equilibrium properties of the gas by computing the second virial coefficient as it can be deduced from the trace of the pressure tensor and by checking the result with the value deduced from various approaches.     

Inversion of the classical second virial coefficient

It is shown that, on the basis of some weak assumptions regarding the nature of the intermolecular pair potential, the classical second virial coefficient determines the potential uniquely.Research supported by NSF Grant GP-19881.     

S matrix poles and the second virial coefficient

For cutoff potentials, a condition which is not a limitation for the calculation of physical systems, the S matrix is meromorphic. It may be expressed in terms of its poles, and then the quantum mechanical second virial coefficient of a neutral gas may be calculated. This paper takes another look at this approach, and discusses the feasibility, attraction and problems of the method. Among concerns are the rate of convergence of the ‘pole’ expansion and the physical significance of the ‘higher’ poles.     

Trace formulas for time delay and the second virial coefficient

A high-temperature expansion for the quantum-mechanical second virial coefficient is derived using newly developed trace formulas for time delay in scattering theory. The known cancellation between the bound state and continuum contributions is explained in this general framework. The method cam be extended to higher virial coefficients.     

On the inversion of the classical second virial coefficient

For a large class of intermolecular potentials, the values of the second virial coefficient at a discrete set of temperature points in an arbitrarily small neighborhood of the origin determine the potential uniquely.     

Radial distribution function and second virial coefficient for interacting bosons

We have studied the radial distribution function and the second virial coefficient of interacting bosons. The second virial coefficient has been deduced theoretically and is in good agreement with experimental values. The third virial coefficient has been calculated from the experimental values of the pressure.     

On the second dielectric virial coefficient of nonspherical polar fluids

The second dielectric virial coefficient is evaluated for nonspherical polar fluids and compared with the experimental data of NH₃ and CH₃F.     

第二位力系数与体积关系的理论证明

用参数变换方法,研究了位形配分函数对体积的一次导数,得到了第二位力系数,从而证明了第二位力系数与体积无关,并对现有教材所给出的条件加以补充。     

The second dielectric virial coefficient of a dipolar sticky hard sphere fluid

We calculate the second dielectric virial coefficient, B _?, of a fluid whose molecules are sticky hard spheres with embedded central point dipoles. The effect of stickiness is to increases B _? markedly.     

Modified 2CLJDQP model and the second virial coefficients for linear molecules

A modified form of 2CLJDQP potential model is proposed to calculate the second virial coefficients of two-center Lennard-Jones molecules. In the presented potential model, the potential parameters σ and ε are considered as the temperature-dependent parameters in the form of hyperbolical temperature function based on the theory of temperaturedependent potential parameters. With this modified model, the second virial coefficients of some homonuclear molecules（such as O2, Cl2, CH3CH3, and CF3CF3） and heteronuclear molecules（such as CO, NO, CH3 F, CH3 Cl, CH3CF3,CH3CHF2, and CF3CH2F） are calculated. Then the Lorentz–Berthelot mixing rule is modified with a temperaturedependent expression, and the second virial coefficients of the heteronuclear molecules（such as CH3 F, CH3 Cl, and CH3CF3） are calculated. Moreover, CO2 and N2O are also studied with the modified 3CLJDQP model. The calculated results from the modified 2CLJDQP model accord better with the experimental data than those from the original model.It is shown that the presented model improves the positive deviation in low temperature range and negative deviation in high temperature range. So the modified 2CLJDQP potential model with the temperature-dependent parameters can be employed satisfactorily in large temperature range.     

Contribution of quantum molecular flexibility to the second virial coefficient of water vapor

The contribution of essentially quantum internal molecular motions to the second virial coefficient B2 of water vapor is analyzed in the framework of the path integral approach. A general purpose ab initio polarizable force field QMPFF2 or a nonpolarizable three-site water model are used with oscillator and Morse valence potentials. It is demonstrated that the contribution may be significant but depends strongly on the form of the intramolecular potential. In the case of the more realistic stretching Morse potential, inclusion of quantum molecular flexibility into the simulation reduces the virial coefficient by 20%-40%. Also, the internal modes make a contribution to the difference in the virial coefficient for light and heavy water, which is opposite to that of the intermolecular motions, so that the net effect can even change the sign at higher temperatures.     

Ab initio calculation of the refractivity and hyperpolarizability second virial coefficients of neon gas

Second virial coefficients for the density dependence of a number of electric properties are calculated for neon gas. Employing an accurate CCSD(T) potential for the Ne² van der Waals dimer and interaction-induced electric dipole polarizabilities and hyperpolarizabilities obtained from CCSD response theory, we evaluated the dielectric, refractivity, Kerr and ESHG second virial coefficients using both a semiclassical and a quantum statistical approach. The results cover a wide range of temperatures and are expected to be more reliable than the available experimental and empirical data. Quantum effects are found to be important only for temperatures below 100 K. The frequency-dependence of the refractivity virial coefficient is found to be small, but not negligible. For frequencies in the visible region it accounts for a few percent of the final results. For the ESHG virial coefficient of neon, frequency dependence is found to be very important, accounting for 20–25% of the second virial coefficient at the typical frequencies employed in experiments.     

Fifth virial coefficient for a system of hard disks

The most accurate value of the fitth virial coefficient B₅ for a system of hard disks has been (0.3338±0.0005) B⁴₂ until now, where B₂ is the second virial coefficient. The present work describes methods of calculation and gives the improved value B₅ = 0.3335561 B⁴₂, the last digit being uncertain.     

Equation of state for the hard sphere model in the third virial coefficient approximation

Exactly solvable systems of infinite-dimensional integral equations are investigated. These systems approximate the hard sphere model and the Ising model for antiferromagnetism. An equation of state for the hard sphere model in the approximation of the third virial coefficient is obtained.     

The calculation of transport properties and density of states of disordered solids

A computational method is presented for the calculation of the conductivity tensor and the density of states of disordered solids. This is a more general and detailed discussion of an algorithm which has been applied to d.c. and a.c. conductivity, Hall effect and density of states of various systems.     

Simple model for the calculation of the coefficient of self-diffusion in a liquid

The coefficient of self-diffusion in three-dimensional classical liquid is computed approximately from the hierarchy of kinetic equations for the time-correlation functions (TCF).     

Functional integrals for QCD at nonzero chemical potential and zero density

In a Euclidean space functional integral treatment of the free energy of QCD, a chemical potential enters only through the functional determinant of the Dirac operator which for any flavor is /D+m-mu(f)gamma(0) (where mu(f) is the chemical potential for the given flavor). Any nonzero mu alters all of the eigenvalues of the Dirac operator relative to the mu=0 value, leading to a naive expectation that the determinant is altered and which thereby alters the free energy. Phenomenologically, this does not occur at T=0 for sufficiently small mu, in contradiction to this naive expectation. The problem of how to understand this phenomenological behavior in terms of functional integrals is solved for the case of an isospin chemical through the study of the spectrum of the operator gamma(0)(/D+m). The case of the baryon chemical potential is briefly discussed.