BOSE-EINSTEIN CONDENSATION OF THE MAGNETIZED IDEAL BOSE-GAS

We study the charged non-relativistic Bose gas interacting with a cons tant magnetic field but which is otherwise free. The notion of Bose-Ei nstein condensation for the three-dimensional case is clarified, and w e show that although there is no condensation in the sense of a phase transition, there is still a maximum in the specific heat which can be used to define a critical temperature. Although the absence of a phas e transition persists for all values of the magnetic field, we show ho w as the magnetic field is reduced the curves for the specific heat ap proach the free field curve. For large values of the magnetic field we show that the gas undergoes a ''dimensional reduction'' and behaves e ffectively as a one-dimensional gas except at very high temperatures. These general features persist for other spatial dimensions D and we s how results for D = 5. Finally we examine the magnetization and the Me issner-Ochsenfeld effect. (C) 1998 Elsevier Science B.V.