2022/01/01 by Yan Gu, Gu, Yan, Bai, Xue-Min +4
Physics and Astronomy · #FOS: Physical sciences #Quantum Mechanics and Non-Hermitian Physics #Quantum Physics (quant-ph)
paper · pdf · doi:10.48550/arxiv.2201.00158
openalex publication_date 2022/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study in this paper the time evolution of PT-symmetric non-Hermitian Hamiltonian consisting of periodically driven SU(1,1) generators. A non-Hermitian invariant operator is adopted to solve the Schr"odinger equation, since the time-dependent Hamiltonian is no longer a conserved quantity. We propose a scheme to construct the non-Hermitian invariant with a PT-symmetric but non-unitary transformation operator. The eigenstates of invariant and its complex conjugate form a bi-orthogonal basis to formulate the exact solution. We obtain the non-adiabatic Berry phase, which reduces to the adiabatic one in the slow time-variation limit. A non-unitary time-evolution operator is found analytically. As an consequence of the non-unitarity the ket (|ψ (t)⟩ ) and bra (⟨ ψ (t)|) states are not normalized each other. While the inner product of two states can be evaluated with the help of a metric operator. It is shown explicitly that the model can be realized by a periodically driven oscillator.