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The chemical potential for the inhomogeneous electron liquid in terms of its kinetic and potential parts with special consideration of the surface potential step and BCS-BEC crossover |
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| Authors: | K. Morawetz N.H. March R.H. Squire |
| Affiliation: | a Institute of Physics, Chemnitz University of Technology, 09107 Chemnitz, Germany b Max-Planck-Institute for the Physics of Complex Systems, Nöthnitzer street 38, 01187 Dresden, Germany c Department of Physics, University of Antwerp, Belgium d Oxford University, Oxford, England, UK e Abdus Salam International Centre for Theoretical Physics, Trieste, Italy f Department of Chemistry, West Virginia University, Montgomery, WV 25136, USA |
| Abstract: | The chemical potential μ of a many-body system is valuable since it carries fingerprints of phase changes. Here, we summarize results for μ for a three-dimensional electron liquid in terms of average kinetic and potential energies per particle. The difference between μ and the energy per particle is found to be exactly the electrostatic potential step at the surface. We also present calculations for an integrable one-dimensional many-body system with delta function interactions, exhibiting a BCS-BEC crossover. It is shown that in the BCS regime the chemical potential can be expressed solely in terms of the ground-state energy per particle. A brief discussion is also included of the strong coupling BEC limit. |
| Keywords: | 71.10.Ca 05.30.Jp 73.90.+f 64.10.+h 05.70.Ce |
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