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I want to study about order parameter and symmetry breaking related to bose einstein condensation in interacted system. Which book i should read? also i want to learn this in second quantization notation.

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I mean the two main textbooks for this are:

  • Pethic & Smith, Bose Einstein condensation in dilute gases

  • Stringary & Pitaevski, Bose Einstein condensation (and Superfluidity)

which cover both the theory and the experimental stuff.

Otherwise, any lecture notes online cover the basics of BEC.

As a quick answer to the key words in your title/question:

  • The order parameter is usually chosen as the population in the ground state $|\Psi_0|^2$ which is $\sim 0$ for $T>T_c$ and $\underbrace{\neq}_{\text{macroscopically}} 0$ for $T<T_c$ and $1$ at $T=0$.

  • The symmetry broken is $U(1)$, since the BEC is a single mega-wavefunction with just one phase. The choice of a single phase breaks the $U(1)$ (the group of phase factors) symmetry of the thermal state.

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