Broken gauge equivalence of Hamiltonians due to time-evolution and the Berry phase

Jiu‐Qing Liang, Harald J W Müller-Kirsten

Theoretical Physics

Li Zhi-Jian, Cheng Jian－gang, Liang Jiu-Qing +1 more

In this paper we investigate the time evolution of a time－dependent oscillator in finite－dimensional Hilbert space. By performing appropriate time－dependent gauge transformation closed formulas for the time evolution of quantum states an d Berry phases are obtained. Finally we discuss the influence of the driving te rm in the Hamiltonian on the squeezed feature of coherent states.

许长谭, 贺明明, Chen Gang

In this paper, we investigate the Berry phase of two coupled arbitrary spins driven by a time-varying magnetic field where the Hamiltonian is explicitly time-dependent. Using a technique of time-dependent gauge transform the Berry phase and time-evolution operator are found explicitly in the adiabatic approximation. The general solutions for arbitrary spins are applied to the spin-1/2 system as an example of explanation.

Aiping Zhang

A quantum system with time-dependent Hamiltonian which transports slowly will acquire an undynamic phase factor exp{ iγ n(t) } factor during evolution in addition to a dynamic phase factor. By means of time-dependent gauge transformation, we do a thorough study on undynamic phase which emerge in the quantum system. The results show that the system will gain an non-integrable phase when a periodic evolution doesn't accomplished; however, only when the system achieves a periodic evolution, an integrable phase will be acquire, namely Berry phase, and the phase is invariable under periodic time-dependent gauge transformation, thereby it is observable. Accordingly, we do a general interpretation on the topological property of Berry's phase as an example of NMR.

Charis Anastopoulos, Ntina Savvidou