Anomalous behavior of ideal Fermi gas below two dimensions

Abstract

Normal behavior of the thermodynamic properties of a Fermi gas in d> 2 dimensions, integer or not, means monotonically increasing or decreasing of its specific heat, chemical potential or isothermal sound velocity, all as functions of temperature. However, for 0 < d < 2 dimensions these properties develop a “hump ” (or “trough”) which increases (or deepens) as d → 0. Though not the phase transition signaled by the sharp features (“cusp ” or “jump”) in those properties for the ideal Bose gas in d> 2 (known as the Bose-Einstein condensation), it is nevertheless an intriguing structural anomaly which we exhibit in detail. 1 PACS: 71.10.Pm; 05.30.Fk; 05.70.Ce; 71.10.-w; 71.10.Ca

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