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A basis set expansion is employed to calculate spectra and eigenstates ofcharge carriers within a toroidal volume characterized by major radius $R$ andminor radius $a$ immersed in an azimuthally symmetric magnetic field. Theangular variables appearing in the Schrodinger equation are eliminated bycontour methods, yielding effective potentials that reduce computational timeby a large factor. An approximation formula for the single particle spectrum ispresented that allows efficient construction of the partition functionnecessary for rapid calculation of thermodynamic quantities. The heat capacityfrom as a function of torus aspect ratio and temperature is calculated. Thetransition from ring-type to bulk-type behavior of the heat capacity ispresented.

Wave functions for a toroidal quantum dot in the presence of an axially  symmetric magnetic field: transition from ring to bulk states as a function  of aspect ratio