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arXiv 1303.5529cond-mat.other
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超流体格子模型中涡旋的横向力

Transverse force on a vortex in lattice models of superfluids

E. B. Sonin

摘要:

本文在连续近似下导出了超流体晶格模型中的横向力(马格努斯力和洛伦兹力)。连续近似恢复了原格点模型中缺少的平移不变性,但该理论不是伽利略不变性。因此,计算涡旋上的两个横向力,马格努斯力和洛伦兹力,需要分析两个平衡,即晶格中粒子的真实动量(马格努斯力)和从周期势中粒子的布洛赫理论中已知的准动量(洛伦兹力)。虽然发展的理论产生相同的洛伦兹力,这是众所周知的,以前,一个新的一般表达式的马格努斯力。该理论演示了如何一个小的马格努斯力出现在约瑟夫森结阵列,如果粒子-空穴对称性被打破。发展了玻色-哈伯德模型在超流-绝缘体相变附近的连续近似,并用于计算马格努斯力。理论表明,在玻色-哈伯德模型的相图中,存在一个区域,在该区域中,马格努斯力的符号与速度环流的符号相反。

英文摘要:

The paper derives the transverse forces (the Magnus and the Lorentz forces) in the lattice models of superfluids in the continuous approximation. The continuous approximation restores translational invariance absent in the original lattice model, but the theory is not Galilean invariant. As a result, calculation of the two transverse forces on the vortex, Magnus force and Lorentz force, requires the analysis of two balances, for the true momentum of particles in the lattice (Magnus force) and for the quasimomentum (Lorentz force) known from the Bloch theory of particles in the periodic potential. While the developed theory yields the same Lorentz force, which was well known before, a new general expression for the Magnus force was obtained. The theory demonstrates how a small Magnus force emerges in the Josephson-junction array if the particle-hole symmetry is broken. The continuous approximation for the Bose--Hubbard model close to the superfluid-insulator transition was developed, which was used for calculation of the Magnus force. The theory shows that there is an area in the phase diagram for the Bose--Hubbard model, where the Magnus force has an inverse sign with respect to that which is expected from the sign of velocity circulation.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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