Finite-size effects on the Bose–Einstein condensation critical temperature in a harmonic trap

• We obtain finite-size effects on the Bose–Einstein condensation critical temperature.
• The setting is the general anisotropic harmonic trap.
• We extend the known analytical first order result to higher orders.
• The new results are very accurate throughout a wide regime.
• These results are particularly important for low particle numbers.

We obtain second and higher order corrections to the shift of the Bose–Einstein critical temperature due to finite-size effects. The confinement is that of a harmonic trap with general anisotropy. Numerical work shows the high accuracy of our expressions. We draw attention to a subtlety involved in the consideration of experimental values of the critical temperature in connection with analytical expressions for the finite-size corrections.