Geometry effects in confined space

Abstract

In this paper we calculate some exact solutions of the grand partition functions for quantum gases in confined space, such as ideal gases in two- and three-dimensional boxes, in tubes, in annular containers, on the lateral surface of cylinders, and photon gases in three-dimensional boxes. Based on these exact solutions, which, of course, contain the complete information about the system, we discuss the geometry effect which is neglected in the calculation with the thermodynamic limit $V\to \infty$, and analyze the validity of the quantum statistical method which can be used to calculate the geometry effect on ideal quantum gases confined in two-dimensional irregular containers. We also calculate the grand partition function for phonon gases in confined space. Finally, we discuss the geometry effects in realistic systems.

Revtex,15 pages, no figure

References in corpus (2)

• Quantum statistics of ideal gases in confined space
• Metal nanoring and tube formation on carbon nanotubes

Cited by in corpus (23)

• The difference of boundary effects between Bose and Fermi systems
• How does geometry affect quantum gases?
• Quantum shape effects and novel thermodynamic behaviors at nanoscale
• Discrete nature of thermodynamics in confined ideal Fermi gases
• The equation of state for two-dimensional hard-sphere gases: Hard-sphere gases as ideal gases with multi-core boundaries
• Fermions on a torus knot
• Quantum shape oscillations in the thermodynamic properties of confined electrons in core-shell nanostructures
• Dimensional transitions in thermodynamic properties of ideal Maxwell-Boltzmann gases
• Thermosize potential in semiconductors
• The explicit expression of the fugacity for weakly interacting Bose and Fermi gases
• Characterization of density oscillations in confined and degenerate Fermi gases
• Origin of quantum shape effect
• Discrete and Weyl density of states for photons and phonons
• Bose-Einstein condensation temperature of finite systems
• Inherent correlations between thermodynamics and statistic physics in extensive and nonextensive systems
• Spectral properties of size-invariant shape transformation
• Quantum gases on a torus
• Remarks on the thermodynamics and the vacuum energy of a quantum Maxwell gas on compact and closed manifolds
• Covariant perturbation expansion of off-diagonal heat kernel
• Electron gases in toroidal shells: mode coupling and state functions
• Quantum Shape Effects
• Statistical problem of ideal gas in general 2-dimensional regions
• Heat kernel approach for confined quantum gas