Harmonically Trapped Quantum Gases
نویسندگان
چکیده
We solve the problem of a Bose or Fermi gas in d-dimensions trapped by δ ≤ d mutually perpendicular harmonic oscillator potentials. From the grand potential we derive their thermodynamic functions (internal energy, specific heat, etc.) as well as a generalized density of states. The Bose gas exhibits Bose-Einstein condensation at a nonzero critical temperature Tc if and only if d+ δ > 2, and a jump in the specific heat at Tc if and only if d+ δ > 4. Specific heats for both gas types precisely coincide as functions of temperature when d+ δ = 2. The trapped system behaves like an ideal free quantum gas in d+ δ dimensions. For δ = 0 we recover all known thermodynamic properties of ideal quantum gases in d dimensions, while in 3D for δ = 1, 2 and 3 one simulates behavior reminiscent of quantum wells, wires and dots, respectively. PACS: 05.30.Fk; 05.30.Jp; 03.75. Fj; 05.70.Ce
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