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1 year ago in Physics By Mauli

Physical meaning of the chemical potential in a Bose-Einstein condensate (BEC)?

In standard thermodynamics, μ is the cost to add a particle. But in a BEC below the critical temperature, the ground state population becomes macroscopic. Textbooks often state μ approaches zero from below. I'm confused about what μ actually represents for the condensate itself is it the energy of the condensate? Why is it pinned near zero?

CondensedMatterPhysics

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By Mia Answered 1 year ago

This is a brilliant question that gets to the heart of BEC statistics. Below the critical temperature, the system has a two-component structure: the condensate (ground state) and the thermal cloud. The chemical potential μ is not the energy of the condensate; it's the free energy cost to add a particle to the entire system. In the thermodynamic limit, adding a particle to a BEC costs almost zero free energy because it simply joins the existing macroscopic wavefunction. Thus, μ is pinned just below the energy of the first excited single-particle state (essentially zero for a uniform gas), ensuring that adding further particles only increases the condensate fraction, not the energy per particle.

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Physical meaning of the chemical potential in a Bose-Einstein condensate (BEC)?

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