Quantum corrections for thermodynamics

E. P. Wigner

V. E. Korepin, John Terilla

Subhasis Sinha

We calculate the quantum corrections of the thermodynamic quantities of a system of confined bosons at finite temperature. Systematically quantum corrections are written in a series of $\ensuremath{\Elzxh},$ which is convergent when $\mathrm{kT}$ is much larger than the spacing between energy levels of the system. We apply this method to the different physical systems. First we calculate the thermodynamic potential of spin-1 bosons confined in a general power-law potential, and calculate the paramagnetic susceptibility of the gas including the quantum corrections. Local-density approximation for charged bosons in the weak magnetic field is improved by the semiclassical expansion. Diamagnetic susceptibility of a system of confined charged bosons is calculated using this method. Finally we apply this method to calculate analytically the thermodynamic potential of a weakly interacting Bose-gas confined in at three-dimensional harmonic-oscillator potential. For a large number of particles, quantum corrections become small, and contribute to the finite-size corrections to scaling.

Felix C. Binder, Luis Alfonso Correa, Christian Gogolin +2 more

Jochen Gemmer B, M. Michel, Günter Mahler A

Charlie Harper

A simplified derivation of Wigner's quantum-mechanical correction for thermodynamic equilibrium is presented. The analysis is restricted to the quantum statistics of systems with classical analogs.