The well-known physicist Chen Ning Yang[1]once summarized that the three main themes of 20th-century physics are quantization,the phase factor,and symmetry.Phase,as a fundamental characteristic of quantum mechanics,se...The well-known physicist Chen Ning Yang[1]once summarized that the three main themes of 20th-century physics are quantization,the phase factor,and symmetry.Phase,as a fundamental characteristic of quantum mechanics,serves as the cornerstone for all interference phenomena.In 1984,Berry pointed out that when the parameters in the Hamiltonian evolve slowly enough(adiabatically)to return to their original values,the wave function of a two-level system acquires a pure geometric phase factor,known as the Berry phase[2].This phase factor is precisely the holonomy in a Hermitian line bundle[3].In 1987,Aharonov and Anandan[4]further discovered that,in non-adiabatic conditions,there exists a geometric phase factor known as the A-A phase,arising in a process called cyclic evolution,which can be regarded as a non-adiabatic generalization of the Berry phase.展开更多
基金the National Key Research and Development Program of China(2022YFA1405100)the National Natural Science Foundation of China(12241405,12174384,and 12404146)。
文摘The well-known physicist Chen Ning Yang[1]once summarized that the three main themes of 20th-century physics are quantization,the phase factor,and symmetry.Phase,as a fundamental characteristic of quantum mechanics,serves as the cornerstone for all interference phenomena.In 1984,Berry pointed out that when the parameters in the Hamiltonian evolve slowly enough(adiabatically)to return to their original values,the wave function of a two-level system acquires a pure geometric phase factor,known as the Berry phase[2].This phase factor is precisely the holonomy in a Hermitian line bundle[3].In 1987,Aharonov and Anandan[4]further discovered that,in non-adiabatic conditions,there exists a geometric phase factor known as the A-A phase,arising in a process called cyclic evolution,which can be regarded as a non-adiabatic generalization of the Berry phase.
