Common Features in Multi-species Bose–Einstein Condensates and the Origin of the Inherent Critical Phenomena
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A general approach is proposed to solve the coupled Gross–Pitaevskii equations (CGP) for K-species Bose–Einstein condensates under the Thomas–Fermi approximation. We aim at finding out the common features of these condensates different in K. In particular, two types of phase transitions, full-state transition and partial-state transition, are found. In the former, all species are involved in the transition, while in the latter only a few specified species are significantly involved. This leads to the criticality and the hidden criticality (namely, the criticality found in a condensate with fewer species recovers in a condensate with more species). The former originates from the singularity of the whole matrix of the CGP, while the latter originates from the singularity of a specified sub-matrix (which is related to a few specified species). In general, for any many-body system, the singularity inherent in the equations that govern the system is crucial to its critical behavior.
KeywordsMulti-species Bose–Einstein condensates Criticality Singularity of the Gross–Pitaevskii equations Phase transition
Supported by the National Natural Science Foundation of China under Grants Nos. 11372122, 11274393, 11574404, and 11275279; the Open Project Program of State Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, China (No. Y4KF201CJ1); and the National Basic Research Program of China (2013CB933601).
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