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We show conduction bands of artificial gauge field assisted atom flow intriangle optical lattice. The conduction bands are result from periodicityboundary condition of artificial magnetic flux induced phases of atoms. Thepositions of conduction bands depend on geometry of the atom trajectory. Weconsider a cell of the triangle optical lattice which is a opened systemconnected to its environment of Fermion atom clouds. The chemical potentials ofthe atom clouds are the same and the atom flow is absolutely created by a clocklaser induced spin-orbit coupling. Our results are important for the control ofatom flow in quantum circuits.

Conduction Bands of Atomic Tunneling Ring in Artificial Gauge Field Assisted Opened Optical Traps