Relativistic quantum statistical properties of many-fermion system in a mesoscopic ring

The relativistic quantum statistical properties of a charged many-fermion system with single fermion rest mass m0 confined in a mesoscopic ring are investigated. The small ring is threaded by an Aharonov-Bohm magnetic flux φ. We have performed analytical calculations starting from evaluating the logarithm of the grand partition functions by using the Mellin transform. The persistent currents, number densities, total energies, heat capacity and hence the fluctuations of the total energies are obtained both in the weakly degenerate and degenerate situations for finite temperature. These thermodynamic functions oscillate periodically in φ with period φ0=h/q, and they are related to the modified Bessel functions of the second kind Kν(r). For the weakly degenerate case, where the chemical potential μ≤m0, we find they decay exponentially with respect to the decrease in temperature, and their magnitudes also decrease in the form of modified exponential functions as the circumference L increases. In the degenerate case, where μ>m0, these functions behave complicatedly in the form of generalized hypergeometric functions, which decay in the power series forms at very low temperature. The non-relativistic limits are given by considering the asymptotic behaviours of Kν(r). (author)