双势阱中的玻色子：双模近似与涨落
Bosons in a double well: two-mode approximation and fluctuations
AI总结：
研究双势阱中多相互作用玻色子在粒子数与势阱间距同趋于无穷极限下的基态，推导有效 Bose-Hubbard Hamiltonian，证明含 Bogoliubov 修正的能量展开及粒子数方差界，揭示违反中心极限定理的关联基态特征。
摘要：
我们研究双势阱中多相互作用玻色子的基态，在粒子数与势阱间距同时趋于无穷的联合极限下。两个单粒子轨道（每个势阱一个）被宏观占据，我们关注推导相应的有效 Bose-Hubbard Hamiltonian。我们证明 (i) 能量展开，包括双模 Bose-Hubbard 能量和两个独立的 Bogoliubov 修正（每个势阱一个），(ii) 落在每个势阱内粒子数的方差界。后者是关联基态的标志，因为它违反了中心极限定理。
英文摘要：
We study the ground state for many interacting bosons in a double-well potential, in a joint limit where the particle number and the distance between the potential wells both go to infinity. Two single-particle orbitals (one for each well) are macroscopically occupied, and we are concerned with deriving the corresponding effective Bose-Hubbard Hamiltonian. We prove (i) an energy expansion, including the two-modes Bose-Hubbard energy and two independent Bogoliubov corrections (one for each potential well), (ii) a variance bound for the number of particles falling inside each potential well. The latter is a signature of a correlated ground state in that it violates the central limit theorem.
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