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- W3022110257 abstract "In this short chapter, which is the end of Part I, we continue focusing on LRO and SSB in ground states, but in a system of many bosonic particles which exhibits Bose–Einstein condensation (BEC), namely, the system of hard-core bosons on the d-dimensional hypercubic lattice with (dge 2). For background, see, e.g., [4, 14, 15, 17]. We will see that, while the mathematical structure of the ground state and low-lying states is exactly parallel to that in quantum antiferromagnets, its physical interpretation is drastically different. Although we do not discuss superconductivity in the present book, this phenomenon is (at least mathematically) very similar to BEC as long as LRO and SSB are concerned. After defining the problem in Sect. 5.1 and discussing the important notion of off-diagonal long-range order in Sect. 5.2, we show in Sect. 5.3 the results about low-lying states and symmetry breaking, parallel to those obtained for quantum spin systems. In Sect. 5.4, we discuss a fundamental difference between quantum spin systems and particle systems, and develop a picture about physically realistic ground state of a large but finite system exhibiting BEC. Finally, in Sect. 5.5, we describe an interesting phenomenon of “SSB” in coupled Bose–Einstein condensates." @default.
- W3022110257 created "2020-05-13" @default.
- W3022110257 creator A5029759804 @default.
- W3022110257 date "2020-01-01" @default.
- W3022110257 modified "2023-09-24" @default.
- W3022110257 title "Long-Range Order and “Spontaneous Symmetry Breaking” in Bose–Einstein Condensates" @default.
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- W3022110257 doi "https://doi.org/10.1007/978-3-030-41265-4_5" @default.
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