6,461 research outputs found
Geometry effects in confined space
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 , 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.Comment: Revtex,15 pages, no figur
Heat-kernel approach for scattering
An approach for solving scattering problems, based on two quantum field
theory methods, the heat kernel method and the scattering spectral method, is
constructed. This approach converts a method of calculating heat kernels into a
method of solving scattering problems. This allows us to establish a method of
scattering problems from a method of heat kernels. As an application, we
construct an approach for solving scattering problems based on the covariant
perturbation theory of heat-kernel expansions. In order to apply the
heat-kernel method to scattering problems, we first calculate the off-diagonal
heat-kernel expansion in the frame of the covariant perturbation theory.
Moreover, as an alternative application of the relation between heat kernels
and partial-wave phase shifts presented in this paper, we give an example of
how to calculate a global heat kernel from a known scattering phase shift
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