The phase-number commutation for macroscopic order parameters emerges from second quantization in the thermodynamic limit, unifying BEC, BCS superconductivity, and their crossover as coherent-state dynamics.
Chapter I The Josephson Effect and Quantum Coherence Measurements in Superconductors and Superfluids
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Third Quantization for Order Parameter (I): BCS-BEC crossover with macroscopically coherent state
The phase-number commutation for macroscopic order parameters emerges from second quantization in the thermodynamic limit, unifying BEC, BCS superconductivity, and their crossover as coherent-state dynamics.