Abstract
We improve the Bardeen-Cooper-Schrieffer wave function with a fixed particle number so as to incorporate many-body correlations beyond the mean-field treatment. It is shown that the correlations lower the ground-state energy far more than Cooper-pair condensation in the weak-coupling region. Moreover, they naturally bring a superposition over the number of condensed particles. Thus, Cooper-pair condensation is special among the various bound-state formations of quantum mechanics in that number fluctuations are necessarily present in the condensate through the dynamical exchange of particles with the non-condensate reservoir. On the basis of this result, we propose $\varDelta N_{\rm con}\cdot \varDelta \phi\gtrsim 1$ as the uncertainty relation relevant to the number-phase fluctuations in superconductors and superfluids, where the number of condensed particles $N_{\rm con}$ is used instead of the total particle number $N$. The formula implies that a macroscopic phase $\phi$ can be established even in number-fixed superconductors and superfluids since $\varDelta N_{\rm con}\gg 1$.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
