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The wavefunction in Sec. describes a statistically pure state whereas the density operator in Sec. is concerned with a mixed state causing the correlation among initial states, which resulted in a discrepancy in the treatment of statistical weights. At zero temperature and for the particle number N?1, for example, this discrepancy amounts to C~N and C'~N3, according to our numerical calculations
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The wavefunction in Sec. describes a statistically pure state whereas the density operator in Sec. is concerned with a mixed state causing the correlation among initial states, which resulted in a discrepancy in the treatment of statistical weights. At zero temperature and for the particle number N?1, for example, this discrepancy amounts to C~N and C'~N3, according to our numerical calculations.
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