The equation of state for two-dimensional hard-sphere gases: Hard-sphere gases as ideal gases with multi-core boundaries

Abstract

The equation of state for a two-dimensional hard-sphere gas is difficult to calculate by usual methods. In this paper we develop an approach for calculating the equation of state of hard-sphere gases, both for two- and three-dimensional cases. By regarding a hard-sphere gas as an ideal gas confined in a container with a multi-core (excluded sphere) boundary, we treat the hard-sphere interaction in an interacting gas as the boundary effect on an ideal quantum gas; this enables us to treat an interacting gas as an ideal one. We calculate the equation of state for a three-dimensional hard-sphere gas with spin $j$, and compare it with the results obtained by other methods. By this approach the equation of state for a two-dimensional hard-sphere gas can be calculated directly.

arXiv comment9 pages, 1 figure

References in corpus (6)

• Bose-Einstein Condensation of Atomic Hydrogen
• Critical Temperature of Bose-Einstein Condensation of Hard Sphere Gases
• Quantum Monte Carlo Calculations for a large number of bosons in a harmonic trap
• Bose-Einstein transition in a dilute interacting gas
• Geometry effects in confined space
• Quantum statistics of ideal gases in confined space

Cited by in corpus (9)

• The difference of boundary effects between Bose and Fermi systems
• Heat-kernel approach for scattering
• Canonical partition functions: ideal quantum gases, interacting classical gases, and interacting quantum gases
• Calculating eigenvalues of many-body systems from partition functions
• The explicit expression of the fugacity for weakly interacting Bose and Fermi gases
• Converting Lattices into Networks: The Heisenberg Model and Its Generalizations with Long-Range Interactions
• Heat kernel approach for confined quantum gas
• The Brownian Motion in an Ideal Quantum Qas
• Statistical problem of ideal gas in general 2-dimensional regions