ISSN:
1434-6079
Keywords:
PACS. 05.30.Fk Fermion systems and electron gas – 05.30.Jp Boson systems – 03.75.Fi Phase coherent atomic ensembles; quantum condensation phenomena – 05.70.Ce Thermodynamic functions and equations of state
Source:
Springer Online Journal Archives 1860-2000
Topics:
Physics
Notes:
Abstract: 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 T c if and only if d + δ 〉 2, along with a jump in the specific heat at T c 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 anddots, respectively. Good agreement is found between experimental critical temperatures for the trapped boson gases 37 87Rb, 3 7Li, 37 85Rb, 2 4He, 19 41K and the known theoretical expression which is a special case for d = δ = 3, but only moderate agreement for 11 27Na and 1 1H.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1140/epjd/e2003-00005-1
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